A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

Directory of Open Access Journals (Sweden)

S.H. Chen

1996-01-01

Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

Science.gov (United States)

Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

2018-03-01

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities (vol 24, pg 2752, 2007)

DEFF Research Database (Denmark)

Bache, Morten; Moses, J.; Wise, F.W.

2010-01-01

Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)].......Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)]....

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

Science.gov (United States)

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.

Integrable systems with quadratic nonlinearity in Fourier space

International Nuclear Information System (INIS)

Marikhin, V.G.

2003-01-01

The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed

Design of Linear-Quadratic-Regulator for a CSTR process

Science.gov (United States)

Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

2017-11-01

This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

Directory of Open Access Journals (Sweden)

Minsong Zhang

2014-01-01

Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD

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H. Jafari

2010-07-01

Full Text Available In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM.Comparisons are made between the Adomian decomposition method (ADM, the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

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

International Nuclear Information System (INIS)

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

2013-01-01

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. (paper)

Multiple-octave spanning high-energy mid-IR supercontinuum generation in bulk quadratic nonlinear crystals

DEFF Research Database (Denmark)

Zhou, Binbin; Bache, Morten

2016-01-01

Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystals like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband...

Stationary walking solitons in bulk quadratic nonlinear media

OpenAIRE

Mihalache, Dumitru; Mazilu, D; Crasonavn, L C; Torner Sabata, Lluís

1997-01-01

We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional wa...

Stationary solutions and self-trapping in discrete quadratic nonlinear systems

DEFF Research Database (Denmark)

Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev

1998-01-01

We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...

BRST operator for superconformal algebras with quadratic nonlinearity

International Nuclear Information System (INIS)

Khviengia, Z.; Sezgin, E.

1993-07-01

We construct the quantum BRST operators for a large class of superconformal and quasi-superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the Z 2 x Z 2 -graded superconformal algebras with a Kac-Moody sector based on the superalgebra osp(N modul 2M) or sl (N + 2 modul N). (author). 22 refs, 3 tabs

A New Chaotic Attractor with Quadratic Exponential Nonlinear Term from Chen’s Attractor

Directory of Open Access Journals (Sweden)

Iftikhar Ahmed

2014-02-01

Full Text Available In this paper a new three-dimensional chaotic system is proposed, which relies on a nonlinear exponential term and a nonlinear quadratic cross term necessary for folding trajectories. Basic dynamical characteristics of the new system are analyzed. Compared with the Chen system, the equilibrium points of the new system does not contain the origin, and has a greater positive Lyapunov index, can produce more complex shaped chaotic attractor.

Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

International Nuclear Information System (INIS)

Kartashov, Yaroslav V; Egorov, Alexey A; Vysloukh, Victor A; Torner, Lluis

2004-01-01

We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns

Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

Three-wave interaction in two-component quadratic nonlinear lattices

DEFF Research Database (Denmark)

Konotop, V. V.; Cunha, M. D.; Christiansen, Peter Leth

1999-01-01

We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that. energy conversion and pulse propagation known...... from three-wave interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained in non-phase-matched lattices by tilting the interacting plane waves with respect to each other. [S1063-651X(99)15110-9]....

On solutions of stochastic oscillatory quadratic nonlinear equations using different techniques, a comparison study

International Nuclear Information System (INIS)

El-Tawil, M A; Al-Jihany, A S

2008-01-01

In this paper, nonlinear oscillators under quadratic nonlinearity with stochastic inputs are considered. Different methods are used to obtain first order approximations, namely, the WHEP technique, the perturbation method, the Pickard approximations, the Adomian decompositions and the homotopy perturbation method (HPM). Some statistical moments are computed for the different methods using mathematica 5. Comparisons are illustrated through figures for different case-studies

Asymptotic behavior for a quadratic nonlinear Schrodinger equation

Directory of Open Access Journals (Sweden)

Pavel I. Naumkin

2008-02-01

Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.

Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

Linear quadratic Gaussian controller design for plasma current, position and shape control system in ITER

International Nuclear Information System (INIS)

Belyakov, V.; Kavin, A.; Rumyantsev, E.; Kharitonov, V.; Misenov, B.; Ovsyannikov, A.; Ovsyannikov, D.; Veremei, E.; Zhabko, A.; Mitrishkin, Y.

1999-01-01

This paper is focused on the linear quadratic Gaussian (LQG) controller synthesis methodology for the ITER plasma current, position and shape control system as well as power derivative management system. It has been shown that some poloidal field (PF) coils have less influence on reference plasma-wall gaps control during plasma disturbances and hence they have been used to reduce total control power derivative by means of the additional non-linear feedback. The design has been done on the basis of linear models. Simulation was provided for non-linear model and results are presented and discussed. (orig.)

Fabrication of three-dimensional polymer quadratic nonlinear grating structures by layer-by-layer direct laser writing technique

Science.gov (United States)

Bich Do, Danh; Lin, Jian Hung; Diep Lai, Ngoc; Kan, Hung-Chih; Hsu, Chia Chen

2011-08-01

We demonstrate the fabrication of a three-dimensional (3D) polymer quadratic nonlinear (χ(2)) grating structure. By performing layer-by-layer direct laser writing (DLW) and spin-coating approaches, desired photobleached grating patterns were embedded in the guest--host dispersed-red-1/poly(methylmethacrylate) (DR1/PMMA) active layers of an active-passive alternative multilayer structure through photobleaching of DR1 molecules. Polyvinyl-alcohol and SU8 thin films were deposited between DR1/PMMA layers serving as a passive layer to separate DR1/PMMA active layers. After applying the corona electric field poling to the multilayer structure, nonbleached DR1 molecules in the active layers formed polar distribution, and a 3D χ(2) grating structure was obtained. The χ(2) grating structures at different DR1/PMMA nonlinear layers were mapped by laser scanning second harmonic (SH) microscopy, and no cross talk was observed between SH images obtained from neighboring nonlinear layers. The layer-by-layer DLW technique is favorable to fabricating hierarchical 3D polymer nonlinear structures for optoelectronic applications with flexible structural design.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

Science.gov (United States)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

Science.gov (United States)

Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

2018-04-01

We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

KAUST Repository

Domínguez, Luis F.

2012-06-25

An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).

Solutions to the equations describing materials with competing quadratic and cubic nonlinearities

International Nuclear Information System (INIS)

Li-Na, Zhao; Ji, Lin; Zi-Shuang, Tong

2009-01-01

The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation

On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

International Nuclear Information System (INIS)

Aristov, Anatoly I

2011-01-01

We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

New hybrid non-linear transformations of divergent perturbation series for quadratic Zeeman effects

International Nuclear Information System (INIS)

Belkic, D.

1989-01-01

The problem of hydrogen atoms in an external uniform magnetic field (quadratic Zeeman effect) is studied by means of perturbation theory. The power series for the ground-state energy in terms of magnetic-field strength B is divergent. Nevertheless, it is possible to induce convergence of this divergent series by applying various non-linear transformations. These transformations of originally divergent perturbation series yield new sequences, which then converge. The induced convergence is, however, quite slow. A new hybrid Shanks-Levin non-linear transform is devised here for accelerating these slowly converging series and sequences. Significant improvement in the convergence rate is obtained. Agreement with the exact results is excellent. (author)

Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities

Directory of Open Access Journals (Sweden)

Akira Abe

2010-01-01

and are the driving and natural frequencies, respectively. The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms. The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions. The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.

Linear parameter varying representations for nonlinear control design

Science.gov (United States)

Carter, Lance Huntington

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

A Trust-region-based Sequential Quadratic Programming Algorithm

DEFF Research Database (Denmark)

Henriksen, Lars Christian; Poulsen, Niels Kjølstad

This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system.

Science.gov (United States)

Wang, Chunhua; Liu, Xiaoming; Xia, Hu

2017-03-01

In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

International Nuclear Information System (INIS)

Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan

2007-01-01

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

Science.gov (United States)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Separable quadratic stochastic operators

International Nuclear Information System (INIS)

Rozikov, U.A.; Nazir, S.

2009-04-01

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

Constrained quadratic stabilization of discrete-time uncertain nonlinear multi-model systems using piecewise affine state-feedback

Directory of Open Access Journals (Sweden)

Olav Slupphaug

1999-07-01

Full Text Available In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space called clusters the plant is assumed to be an element in a polytope which vertices (local models are affine systems. In the clusters containing the origin in their closure, the local models are restricted to be linear systems. The clusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-and-bound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained nonlinear model predictive control is presented. Also, the control design method is applied to a simple example.

Noise-induced chaos in a quadratically nonlinear oscillator

International Nuclear Information System (INIS)

Gan Chunbiao

2006-01-01

The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system

Designing microstructured polymer optical fibers for cascaded quadratic soliton compression of femtosecond pulses

DEFF Research Database (Denmark)

Bache, Morten

2009-01-01

The dispersion of index-guiding microstructured polymer optical fibers is calculated for second-harmonic generation. The quadratic nonlinearity is assumed to come from poling of the polymer, which in this study is chosen to be the cyclic olefin copolymer Topas. We found a very large phase mismatc...

Orthogonality preserving infinite dimensional quadratic stochastic operators

International Nuclear Information System (INIS)

Akın, Hasan; Mukhamedov, Farrukh

2015-01-01

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

Cascaded Quadratic Soliton Compression in Waveguide Structures

DEFF Research Database (Denmark)

Guo, Hairun

between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...

Spatial solitons in nonlinear photonic crystals

DEFF Research Database (Denmark)

Corney, Joel Frederick; Bang, Ole

2000-01-01

We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....

Design with Nonlinear Constraints

KAUST Repository

Tang, Chengcheng

2015-12-10

Most modern industrial and architectural designs need to satisfy the requirements of their targeted performance and respect the limitations of available fabrication technologies. At the same time, they should reflect the artistic considerations and personal taste of the designers, which cannot be simply formulated as optimization goals with single best solutions. This thesis aims at a general, flexible yet e cient computational framework for interactive creation, exploration and discovery of serviceable, constructible, and stylish designs. By formulating nonlinear engineering considerations as linear or quadratic expressions by introducing auxiliary variables, the constrained space could be e ciently accessed by the proposed algorithm Guided Projection, with the guidance of aesthetic formulations. The approach is introduced through applications in different scenarios, its effectiveness is demonstrated by examples that were difficult or even impossible to be computationally designed before. The first application is the design of meshes under both geometric and static constraints, including self-supporting polyhedral meshes that are not height fields. Then, with a formulation bridging mesh based and spline based representations, the application is extended to developable surfaces including origami with curved creases. Finally, general approaches to extend hard constraints and soft energies are discussed, followed by a concluding remark outlooking possible future studies.

Quadratic Interpolation and Linear Lifting Design

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Joel Solé

2007-03-01

Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.

Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals

DEFF Research Database (Denmark)

Liu, Xing; Zhou, Binbin; Guo, Hairun

2015-01-01

in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between. lambda = 2.2-2.4 mu m as a resonant dispersive wave. This process relies...... on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation. (C) 2015 Optical Society of America...

Dynamical invariants for variable quadratic Hamiltonians

International Nuclear Information System (INIS)

Suslov, Sergei K

2010-01-01

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

Quadratic measurement and conditional state preparation in an optomechanical system

DEFF Research Database (Denmark)

A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.

2014-01-01

We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....

Combining support vector machines with linear quadratic regulator adaptation for the online design of an automotive active suspension system

International Nuclear Information System (INIS)

Chiou, J-S; Liu, M-T

2008-01-01

As a powerful machine-learning approach to pattern recognition problems, the support vector machine (SVM) is known to easily allow generalization. More importantly, it works very well in a high-dimensional feature space. This paper presents a nonlinear active suspension controller which achieves a high level performance by compensating for actuator dynamics. We use a linear quadratic regulator (LQR) to ensure optimal control of nonlinear systems. An LQR is used to solve the problem of state feedback and an SVM is used to address the question of the estimation and examination of the state. These two are then combined and designed in a way that outputs feedback control. The real-time simulation demonstrates that an active suspension using the combined SVM-LQR controller provides passengers with a much more comfortable ride and better road handling

Gain-scheduled Linear Quadratic Control of Wind Turbines Operating at High Wind Speed

DEFF Research Database (Denmark)

Østergaard, Kasper Zinck; Stoustrup, Jakob; Brath, Per

2007-01-01

This paper addresses state estimation and linear quadratic (LQ) control of variable speed variable pitch wind turbines. On the basis of a nonlinear model of a wind turbine, a set of operating conditions is identified and a LQ controller is designed for each operating point. The controller gains...... are then interpolated linearly to get a control law for the entire operating envelope. A nonlinear state estimator is designed as a combination of two unscented Kalman filters and a linear disturbance estimator. The gain-scheduling variable (wind speed) is then calculated from the output of these state estimators...

A Quasi-Dynamic Optimal Control Strategy for Non-Linear Multivariable Processes Based upon Non-Quadratic Objective Functions

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Jens G. Balchen

1984-10-01

Full Text Available The problem of systematic derivation of a quasi-dynamic optimal control strategy for a non-linear dynamic process based upon a non-quadratic objective function is investigated. The wellknown LQG-control algorithm does not lead to an optimal solution when the process disturbances have non-zero mean. The relationships between the proposed control algorithm and LQG-control are presented. The problem of how to constrain process variables by means of 'penalty' - terms in the objective function is dealt with separately.

Propagation of a femtosecond laser pulse with duration of several optical oscillation periods in a medium with a quadratic nonlinearity

International Nuclear Information System (INIS)

Akopyan, A A; Oganesyan, D L

1998-01-01

It is shown that the wave equation can be solved by the method of unidirectional waves for a pulse with a duration of several oscillation periods in a medium with a quadratic nonlinearity, such as a group-3m crystal. The wave equation reduces to a system of two equations for waves with different polarisations. (laser applications and other topics in quantum electronics)

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Quadratic Lagrangians and Legendre transformation

International Nuclear Information System (INIS)

Magnano, G.

1988-01-01

In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor

Soliton interaction in quadratic and cubic bulk media

DEFF Research Database (Denmark)

Johansen, Steffen Kjær; Bang, Ole

2000-01-01

Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...

Distributed nonlinear optical response

DEFF Research Database (Denmark)

Nikolov, Nikola Ivanov

2005-01-01

of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?

Science.gov (United States)

Stinchcombe, John R; Agrawal, Aneil F; Hohenlohe, Paul A; Arnold, Stevan J; Blows, Mark W

2008-09-01

The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.

orthogonal and scaling transformations of quadratic functions

African Journals Online (AJOL)

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functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.

Few-cycle nonlinear mid-IR pulse generated with cascaded quadratic nonlinearities

DEFF Research Database (Denmark)

Bache, Morten; Liu, Xing; Zhou, Binbin

Generating few-cycle energetic and broadband mid-IR pulses is an urgent current challenge in nonlinear optics. Cascaded second-harmonic generation (SHG) gives access to an ultrafast and octave-spanning self-defocusing nonlinearity: when ΔkL >> 2π the pump experiences a Kerr-like nonlinear index...

Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

DEFF Research Database (Denmark)

Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

2013-01-01

We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

Design of reinforced areas of concrete column using quadratic polynomials

Science.gov (United States)

Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.

2017-11-01

Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.

Accurate nonlocal theory for cascaded quadratic soliton compression

DEFF Research Database (Denmark)

Bache, Morten; Bang, Ole; Moses, Jeffrey

2007-01-01

We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

A Design of a Hybrid Non-Linear Control Algorithm

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Farinaz Behrooz

2017-11-01

Full Text Available One of the high energy consuming devices in the buildings is the air-conditioning system. Designing a proper controller to consider the thermal comfort and simultaneously control the energy usage of the device will impact on the system energy efficiency and its performance. The aim of this study was to design a Multiple-Input and Multiple-Output (MIMO, non-linear, and intelligent controller on direct expansion air-conditioning system The control algorithm uses the Fuzzy Cognitive Map method as a main controller and the Generalized Predictive Control method is used for assigning the initial weights of the main controller. The results of the proposed controller shows that the controller was successfully designed and works in set point tracking and under disturbance rejection tests. The obtained results of the Generalized Predictive Control-Fuzzy Cognitive Map controller are compared with the previous MIMO Linear Quadratic Gaussian control design on the same direct expansion air-conditioning system under the same conditions. The comparative results indicate energy savings would be achieved with the proposed controller with long-term usage. Energy efficiency and thermal comfort conditions are achieved by the proposed controller.

Analysis, Adaptive Control and Adaptive Synchronization of a Nine-Term Novel 3-D Chaotic System with Four Quadratic Nonlinearities and its Circuit Simulation

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S. Vaidyanathan

2014-11-01

Full Text Available This research work describes a nine-term novel 3-D chaotic system with four quadratic nonlinearities and details its qualitative properties. The phase portraits of the 3-D novel chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as L1 = 6.8548, L2 = 0 and L3 = −32.8779. Also, the Kaplan-Yorke dimension of the novel chaotic system is obtained as DKY = 2.2085. Next, an adaptive controller is design to achieve global stabilization of the 3-D novel chaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.

Quadratic spatial soliton interactions

Science.gov (United States)

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

Robust stabilization of nonlinear systems: The LMI approach

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Šiljak D. D.

2000-01-01

Full Text Available This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI. The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable. We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems. Again, the LMI methods will be used to maximize the class of uncertain interconnections which leave the overall system connectively stable. It is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms. More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satisfy the generalized matching conditions.

Large-scale sequential quadratic programming algorithms

Energy Technology Data Exchange (ETDEWEB)

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.

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

Science.gov (United States)

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.

Invited Article: Multiple-octave spanning high-energy mid-IR supercontinuum generation in bulk quadratic nonlinear crystals

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Binbin Zhou

2016-08-01

Full Text Available Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystals like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband supercontinuum generation in the visible, near-IR, and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal is pumped in the mid-IR. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source leads to highly phase-mismatched second-harmonic generation. This self-acting cascaded process leads to the formation of a self-defocusing soliton at the mid-IR pump wavelength and after the self-compression point multiple octave-spanning supercontinua are observed. The results were recorded in a commercially available crystal LiInS2 pumped in the 3-4 μm range with 85 fs 50 μJ pulse energy, with the broadest supercontinuum covering 1.6-7.0 μm. We measured up 30 μJ energy in the supercontinuum, and the energy promises to scale favorably with an increased pump energy. Other mid-IR crystals can readily be used as well to cover other pump wavelengths and target other supercontinuum wavelength ranges.

Beams configuration design in target area with successive quadratic programming method

International Nuclear Information System (INIS)

Shi Zhiquan; Tan Jichun; Wei Xiaofeng; Man Jongzai; Zhang Xiaomin; Yuan Jing; Yuan Xiaodong

1998-01-01

The author describes the application of successive quadratic programming method (SQP) to design laser beam configuration in target area. Based on the requirement of ICF experiment physics, a math model of indirect-driver beam geometry is given. A 3D wire-frame is plotted, in which support lines represent 60 laser entireties and 240 turning points of support lines' segments stand for the spatial positions of reflectors

Spatiotemporal solitons in quadratic nonlinear media

Indian Academy of Sciences (India)

Optical solitons are localized electromagnetic waves that propagate stably in .... conversion generates a nonlinear phase shift ∆ΦNL at the FH frequency. ... to incidence on the SHG crystal (lithium iodate or barium borate, cut for type-I interac-.

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

2015-01-01

be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

Two-photon Anderson localization in a disordered quadratic waveguide array

International Nuclear Information System (INIS)

Bai, Y F; Xu, P; Lu, L L; Zhong, M L; Zhu, S N

2016-01-01

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. (paper)

All-optical signal processing in quadratic nonlinear materials

DEFF Research Database (Denmark)

Johansen, Steffen Kjær

2002-01-01

of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH......). During this project the interaction between such spatial solitons has been investigated theoretically through perturbation theory and experimentally via numerical simulations. The outcome of this research isnew theoretical tools for quantitatively predicting the escape angle, i.e. the angle of incidence...... are dedicated to this part of the research. In chapter 4 the generality of the theoretical approach is emphasised with the derivation and verification of equivalent tools for media with a saturable nonlinearity. The strength of the X(2) nonlinearity strongly depends on the phase mismatch between the FW...

Initial post dynamic buckling of a quadratic-cubic column ...

African Journals Online (AJOL)

In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

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Y. N. Pavlov

2015-01-01

Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

Limits to compression with cascaded quadratic soliton compressors

DEFF Research Database (Denmark)

Bache, Morten; Bang, Ole; Krolikowski, Wieslaw

2008-01-01

We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong....... This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find......, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account....

Octave-Spanning Mid-IR Supercontinuum Generation with Ultrafast Cascaded Nonlinearities

DEFF Research Database (Denmark)

Zhou, Binbin; Guo, Hairun; Liu, Xing

2014-01-01

An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation.......An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation....

Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal

DEFF Research Database (Denmark)

Zhou, Binbin; Guo, Hairun; Bache, Morten

2015-01-01

Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and with...... by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR....... and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...

Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

Science.gov (United States)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

A nonlinear plate control without linearization

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Yildirim Kenan

2017-03-01

Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

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Bapurao C. Dhage

2015-01-01

Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

Study on TVD parameters sensitivity of a crankshaft using multiple scale and state space method considering quadratic and cubic non-linearities

Directory of Open Access Journals (Sweden)

R. Talebitooti

Full Text Available In this paper the effect of quadratic and cubic non-linearities of the system consisting of the crankshaft and torsional vibration damper (TVD is taken into account. TVD consists of non-linear elastomer material used for controlling the torsional vibration of crankshaft. The method of multiple scales is used to solve the governing equations of the system. Meanwhile, the frequency response of the system for both harmonic and sub-harmonic resonances is extracted. In addition, the effects of detuning parameters and other dimensionless parameters for a case of harmonic resonance are investigated. Moreover, the external forces including both inertia and gas forces are simultaneously applied into the model. Finally, in order to study the effectiveness of the parameters, the dimensionless governing equations of the system are solved, considering the state space method. Then, the effects of the torsional damper as well as all corresponding parameters of the system are discussed.

Binary classification posed as a quadratically constrained quadratic ...

Indian Academy of Sciences (India)

Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...

Physics constrained nonlinear regression models for time series

International Nuclear Information System (INIS)

Majda, Andrew J; Harlim, John

2013-01-01

A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)

Theory and design of nonlinear metamaterials

Science.gov (United States)

Rose, Alec Daniel

If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers

Non-chaotic behaviour for a class of quadratic jerk equations

International Nuclear Information System (INIS)

Malasoma, J.-M.

2009-01-01

It is shown that a class constituted by 27 different types of non-linear third-order differential equations of the form x - =j(x,x . ,x), where j is a quadratic polynomial with only one or two terms, and for which ∂j(x,y,z)/∂z is not a constant function of time, does not exhibit chaos. The three-dimensional dynamical systems associated to these equations are not necessarily dissipative everywhere nor conservative everywhere in the corresponding phase spaces. Our results include and improve some recent results obtained by Yang and Chen who only considered the case where j was a homogeneous quadratic polynomial with two terms.

Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study

International Nuclear Information System (INIS)

Mukhopadhyay, S.; Ramasesha, S.; Pandey, Ravindra; Das, Puspendu K.

2011-01-01

In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, β HRS and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.

Designing quadratic nonlinear photonic crystal fibers for soliton compression to few-cycle pulses

DEFF Research Database (Denmark)

Bache, Morten; Moses, Jeffrey; Lægsgaard, Jesper

2007-01-01

phase shifts accessible. This self-defocusing nonlinearity can be used to compress a pulse when combined with normal dispersion, and problems normally encountered due to self-focusing in cubic media are avoided. Thus, having no power limit, in bulk media a self-defocusing soliton compressor can create...... high-energy near single-cycle fs pulses (Liu et al., 2006). However, the group-velocity mismatch (GVM) between the FW and second harmonic (SH), given by the inverse group velocity difference d12=1/Vg,1 - 1/Vg,2, limits the pulse quality and compression ratio. Especially very short input pulses (...

One Layer Nonlinear Economic Closed-Loop Generalized Predictive Control for a Wastewater Treatment Plant

Directory of Open Access Journals (Sweden)

Hicham El bahja

2018-04-01

Full Text Available The main scope of this paper is the proposal of a new single layer Nonlinear Economic Closed-Loop Generalized Predictive Control (NECLGPC as an efficient advanced control technique for improving economics in the operation of nonlinear plants. Instead of the classic dual-mode MPC (model predictive controller schemes, where the terminal control law defined in the terminal region is obtained offline solving a linear quadratic regulator problem, here the terminal control law in the NECLGPC is determined online by an unconstrained Nonlinear Generalized Predictive Control (NGPC. In order to make the optimization problem more tractable two considerations have been made in the present work. Firstly, the prediction model consisting of a nonlinear phenomenological model of the plant is expressed with linear structure and state dependent matrices. Secondly, instead of including the nonlinear economic cost in the objective function, an approximation of the reduced gradient of the economic function is used. These assumptions allow us to design an economic unconstrained nonlinear GPC analytically and to state the NECLGPC allow for the design of an economic problem as a QP (Quadratic Programing problem each sampling time. Four controllers based on GPC that differ in designs and structures are compared with the proposed control technique in terms of process performance and energy costs. Particularly, the methodology is implemented in the N-Removal process of a Wastewater Treatment Plant (WWTP and the results prove the efficiency of the method and that it can be used profitably in practical cases.

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

Science.gov (United States)

Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent

2018-03-01

The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.

Further Developments on Optimum Structural Design Using MSC/Nastran and Sequential Quadratic Programming

DEFF Research Database (Denmark)

Holzleitner, Ludwig

1996-01-01

, here the shape of two dimensional parts with different thickness areas will be optimized. As in the previos paper, a methodology for structural optimization using the commercial finite element package MSC/NASTRAN for structural analysis is described. Three different methods for design sensitivity......This work is closely connected to the paper: K.G. MAHMOUD, H.W. ENGL and HOLZLEITNER: "OPTIMUM STRUCTURAL DESIGN USING MSC/NASTRAN AND SEQUENTIAL QUADRATIC PROGRAMMING", Computers & Structures, Vol. 52, No. 3, pp. 437-447, (1994). In contrast to that paper, where thickness optimization is described...

Design of a nonlinear torsional vibration absorber

Science.gov (United States)

Tahir, Ammaar Bin

Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is

Magnitude and nature of the quadratic electro-optic effect in potassium dihydrogen phosphate and ammonium dihydrogen phosphate crystals

International Nuclear Information System (INIS)

Gunning, Mark J.; Raab, Roger E.; Kucharczyk, Wlodimierz

2001-01-01

Measurements of the magnitude and the sign of certain quadratic electro-optic coefficients of potassium dihydrogen phosphate (KDP) and ammonium dihydrogen phosphate (ADP) were made with an actively stabilized Michelson interferometer. The results obtained for these coefficients are, in units of 10 -20 m 2 V -2 (as opposed to literature values of order 10 -18 m 2 V -2 ), as follows: (KDP)g xxxx =-3.4±0.5, g yyxx =-0.2±0.4, and g zzxx =-0.7±0.4; (ADP)g xxxx =-7.4±1.0, g yyxx =-1.7±0.9, and g zzxx =-1.4±0.9. The quadratic Faust--Henry coefficient describing the lattice and the electronic contributions to the quadratic electro-optic effect in KDP and ADP is estimated from our results. These show that the nonlinear susceptibility responsible for the quadratic electro-optic effect in these crystals is due mainly to nonlinear interactions of the low-frequency electric field with the crystal lattice. Copyright 2001 Optical Society of America

Nonlinear diffraction from a virtual beam

DEFF Research Database (Denmark)

Saltiel, Solomon M.; Neshev, Dragomir N.; Krolikowski, Wieslaw

2010-01-01

We observe experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic grating.We demonstrate that when the nonlinear grating is illuminated simultaneously by two noncollinear beams, a second-harmonic diffraction pattern is generated by a virtual...... beam propagating along the bisector of the two pump beams. The observed iffraction phenomena is a purely nonlinear effect that has no analogue in linear diffraction...

Classification of ξ(s)-Quadratic Stochastic Operators on 2D simplex

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Saburov, Mansoor; Qaralleh, Izzat

2013-01-01

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some QSO has been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for the quadratic stochastic operators. To study this problem it was investigated several classes of such QSO. In this paper we study ξ (s) -QSO class of operators. We study such kind of operators on 2D simplex. We first classify these ξ (s) -QSO into 20 classes. Further, we investigate the dynamics of one class of such operators.

Hidden conic quadratic representation of some nonconvex quadratic optimization problems

NARCIS (Netherlands)

Ben-Tal, A.; den Hertog, D.

The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated

Universal formats for nonlinear ordinary differential systems

International Nuclear Information System (INIS)

Kerner, E.H.

1981-01-01

It is shown that very general nonlinear ordinary differential systems (embracing all that arise in practice) may, first, be brought down to polynomial systems (where the nonlinearities occur only as polynomials in the dependent variables) by introducing suitable new variables into the original system; second, that polynomial systems are reducible to ''Riccati systems,'' where the nonlinearities are quadratic at most; third, that Riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity. The elemental systems have representations as novel types of matrix Riccati equations. Different starting systems and their associated Riccati systems differ from one another, at the final elemental level, in order and in initial data, but not in format

Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control

OpenAIRE

Härkegård, Ola

2004-01-01

When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...

Observation of an octave-spanning supercontinuum in the mid-infrared using ultrafast cascaded nonlinearities

DEFF Research Database (Denmark)

Bache, Morten; Liu, Xing; Zhou, Binbin

2014-01-01

An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation. ©OSA 2014.......An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation. ©OSA 2014....

Design of variable-weight quadratic congruence code for optical CDMA

Science.gov (United States)

Feng, Gang; Cheng, Wen-Qing; Chen, Fu-Jun

2015-09-01

A variable-weight code family referred to as variable-weight quadratic congruence code (VWQCC) is constructed by algebraic transformation for incoherent synchronous optical code division multiple access (OCDMA) systems. Compared with quadratic congruence code (QCC), VWQCC doubles the code cardinality and provides the multiple code-sets with variable code-weight. Moreover, the bit-error rate (BER) performance of VWQCC is superior to those of conventional variable-weight codes by removing or padding pulses under the same chip power assumption. The experiment results show that VWQCC can be well applied to the OCDMA with quality of service (QoS) requirements.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

Science.gov (United States)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Diagonalizing quadratic bosonic operators by non-autonomous flow equations

CERN Document Server

Bach, Volker

2016-01-01

The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

International Nuclear Information System (INIS)

Qu Gai-Zhu; Zhang Shun-Li; Li Yao-Long

2014-01-01

In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators. (general)

Separation of variables for the nonlinear wave equation in polar coordinates

International Nuclear Information System (INIS)

Shermenev, Alexander

2004-01-01

Some classical types of nonlinear wave motion in polar coordinates are studied within quadratic approximation. When the nonlinear quadratic terms in the wave equation are arbitrary, the usual perturbation techniques used in polar coordinates leads to overdetermined systems of linear algebraic equations for the unknown coefficients. However, we show that these overdetermined systems are compatible with the special case of the nonlinear shallow water equation and express explicitly the coefficients of the first two harmonics as polynomials of the Bessel functions of radius and of the trigonometric functions of angle. It gives a series of solutions to the nonlinear shallow water equation that are periodic in time and found with the same accuracy as the equation is derived

Self-Replicating Quadratics

Science.gov (United States)

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…

On bent and semi-bent quadratic Boolean functions

DEFF Research Database (Denmark)

Charpin, P.; Pasalic, Enes; Tavernier, C.

2005-01-01

correlation and high nonlinearity. We say that such a sequence is generated by a semi-bent function. Some new families of such function, represented by f(x) = Sigma(i=1)(n-1/2) c(i)Tr(x(2t+1)), n odd and c(i) is an element of F-2, have recently (2002) been introduced by Khoo et al. We first generalize......The maximum-length sequences, also called m-sequences, have received a lot of attention since the late 1960s. In terms of linear-feedback shift register (LFSR) synthesis they are usually generated by certain power polynomials over a finite field and in addition are characterized by a low cross...... their results to even n. We further investigate the conditions on the choice of ci for explicit definitions of new infinite families having three and four trace terms. Also, a class of nonpermutation polynomials whose composition with a quadratic function yields again a quadratic semi-bent function is specified...

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

Directory of Open Access Journals (Sweden)

Feng-Tao He

2013-01-01

Full Text Available We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton’s dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1 if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton’s width increases, while its amplitude and wave velocity reduce. (2 If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton’s width increases, while its amplitude and the wave velocity reduce.

Gain scheduled linear quadratic control for quadcopter

Science.gov (United States)

Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.

2017-12-01

This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.

Parametric localized modes in quadratic nonlinear photonic structures

DEFF Research Database (Denmark)

Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole

2001-01-01

interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...

Controller Design of Complex System Based on Nonlinear Strength

Directory of Open Access Journals (Sweden)

Rongjun Mu

2015-01-01

Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator

International Nuclear Information System (INIS)

Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping

2017-01-01

A direct photon–phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field. (paper)

STRUCTURE OPTIMIZATION OF RESERVATION BY PRECISE QUADRATIC REGULARIZATION

Directory of Open Access Journals (Sweden)

KOSOLAP A. I.

2015-11-01

Full Text Available The problem of optimization of the structure of systems redundancy elements. Such problems arise in the design of complex systems. To improve the reliability of operation of such systems of its elements are duplicated. This increases system cost and improves its reliability. When optimizing these systems is maximized probability of failure of the entire system while limiting its cost or the cost is minimized for a given probability of failure-free operation. A mathematical model of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of Lagrange multipliers, coordinate descent, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension. In the work for solving redundancy uses a new method for accurate quadratic regularization. This method allows you to convert the original discrete problem to the maximization of multi vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straightdual interior point methods. Currently, it is the best method for local optimization of nonlinear problems. Transformed the task includes a new auxiliary variable, which is determined by dichotomy. There have been numerous comparative numerical experiments in problems with the number of redundant subsystems to one hundred. These experiments confirm the effectiveness of the method of precise quadratic regularization for solving problems of redundancy.

Quadratic Damping

Science.gov (United States)

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…

Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions

Science.gov (United States)

Valchev, T. I.

2016-02-01

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m + n)/S(U(m) × U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schrödinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.

The Kerr nonlinearity of the beta-barium borate crystal

DEFF Research Database (Denmark)

Bache, Morten; Guo, Hairun; Zhou, Binbin

2013-01-01

A popular crystal for ultrafast cascading experiments is beta-barium-borate (β-BaB2O4, BBO). It has a decent quadratic nonlinear coefficient, and because the crystal is anisotropie it can be birefringence phase-matched for type I (oo → e) second-harmonic generation (SHG). For femtosecond experime......A popular crystal for ultrafast cascading experiments is beta-barium-borate (β-BaB2O4, BBO). It has a decent quadratic nonlinear coefficient, and because the crystal is anisotropie it can be birefringence phase-matched for type I (oo → e) second-harmonic generation (SHG). For femtosecond...

Quadratic reactivity fuel cycle model

International Nuclear Information System (INIS)

Lewins, J.D.

1985-01-01

For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper

A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

Science.gov (United States)

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…

Optimal Quadratic Programming Algorithms

CERN Document Server

Dostal, Zdenek

2009-01-01

Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers

Engineered nonlinear lattices

DEFF Research Database (Denmark)

Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.

1999-01-01

We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...... discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term...

Generation and dynamics of quadratic birefringent spatial gap solitons

International Nuclear Information System (INIS)

Anghel-Vasilescu, P.; Dorignac, J.; Geniet, F.; Leon, J.; Taki, A.

2011-01-01

A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe 2 (LGT) crystals. Once irradiated by a cw laser beam of 10 μm wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.

Generation and growth rates of nonlinear distortions in a traveling wave tube

International Nuclear Information System (INIS)

Woehlbier, John G.; Dobson, Ian; Booske, John H.

2002-01-01

The structure of a steady state multifrequency model of a traveling wave tube amplifier is exploited to describe the generation of intermodulation frequencies and calculate their growth rates. The model describes the evolution of Fourier coefficients of circuit and electron beam quantities and has the form of differential equations with quadratic nonlinearities. Intermodulation frequencies are sequentially generated by the quadratic nonlinearities in a series solution of the differential equations. A formula for maximum intermodulation growth rates is derived and compared to simulation results

New generalized conjugate gradient methods for the non-quadratic model in unconstrained optimization

International Nuclear Information System (INIS)

Al-Bayati, A.

2001-01-01

This paper present two new conjugate gradient algorithms which use the non-quadratic model in unconstrained optimization. The first is a new generalized self-scaling variable metric algorithm based on the sloboda generalized conjugate gradient method which is invariant to a nonlinear scaling of a stricity convex quadratic function; the second is an interleaving between the generalized sloboda method and the first algorithm; all these algorithm use exact line searches. Numerical comparisons over twenty test functions show that the interleaving algorithm is best overall and requires only about half the function evaluations of the Sloboda method: interleaving algorithms are likely to be preferred when the dimensionality of the problem is increased. (author). 29 refs., 1 tab

Linear-quadratic control and quadratic differential forms for multidimensional behaviors

NARCIS (Netherlands)

Napp, D.; Trentelman, H.L.

2011-01-01

This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look

Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings

DEFF Research Database (Denmark)

Corney, Joel F.; Bang, Ole

2004-01-01

We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phasematching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands....

Rescuing Quadratic Inflation

CERN Document Server

Ellis, John; Sueiro, Maria

2014-01-01

Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

Modified Emden-type equation with dissipative term quadratic in velocity

International Nuclear Information System (INIS)

Ghosh, Subrata; Talukdar, B; Das, Umapada; Saha, Aparna

2012-01-01

Based on some physical observation we introduce a generalized modified Emden-type equation (MEE) with a position-dependent dissipative term which is quadratic in velocity. Unlike the usual MEE, the first integral of the proposed generalized MEE is such that one can express the velocity of the system as a function of coordinate for all values of the parameters of the system. This permits us to study the dynamical properties of the system using straightforward analytical methods. The results presented in the phase diagram and plots of vector fields clearly delineate how does the presence of quadratic damping affect the motion of our nonlinear oscillator. From the differential equation provided by the first integral of the generalized MEE, we have found an approximate analytical solution of the equation which reproduces the time variation of the corresponding numerical solution to a fair degree of accuracy. (paper)

Molecular design for nonpolar chiral-axial quadratic nonlinear optics

Science.gov (United States)

Wiggers, Gregory A.

In this thesis the hyperpolarizability of various multi-dimensional molecules is studied theoretically/computationally, with particular focus on the second-rank Kleinman-disallowed (KD) component of the hyperpolarizability. This component, which transforms as a second-rank traceless symmetric tensor, could be utilized in certain chiral-axial molecular alignment schemes to produce a bulk response. Nonpolar chiral-axial systems have been proposed in contrast to polar media, which utilize the vector component of the molecular hyperpolarizability and require parallel alignment of the molecular dipoles. Such parallel alignment of dipoles must be "frozen in" in order to overcome the natural tendency for dipoles to align anti-parallel. This limits the density of chromophores that can be loaded into a polar material. Nonpolar materials do not have such limits in theory. The two geometric classes of molecules that can most easily be incorporated into nonpolar chiral-uniaxial materials are propeller-shaped (C3 or D3 symmetry) and Λ-shaped (C2v symmetry). This work describes efforts to design molecules within these classes that would be suitable for bulk NLO materials. The sum-over-states (SOS) expression is used to model the molecular hyperpolarizability, and quantum chemical calculations, along with linear absorption data (when available) provide the necessary parameters to evaluate truncated forms of the SOS expression. A host of chemical and geometric modifications will be considered in order to elucidate important structure/function relationships. Also, the SOS model will be tested in some cases when experimental measurements (via Kleinman-disallowed hyper-Rayleigh scattering) are available. While a majority of this work focuses on multi-dimensional molecules, a small section deals with the question of optimizing the hyperpolarizability of a one-dimensional system. It is suggested that the recently-proposed idea of "modulated conjugation" as a means for improving

Non-linearity aspects in the design of submarine pipelines

NARCIS (Netherlands)

Fernández, M.L.

1981-01-01

An arbitrary attempt has been made to classify and discuss some non-linearity aspects related to design, construction and operation of submarine pipelines. Non-linearities usually interrelate and take part of a comprehensive design, making difficult to quantify their individual influence or

Quadratic Plus Linear Operators which Preserve Pure States of Quantum Systems: Small Dimensions

International Nuclear Information System (INIS)

Saburov, Mansoor

2014-01-01

A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces. In the nonlinear case, this problem was open. In this paper, in the small dimensional spaces, we shall describe all quadratic plus linear operators which preserve pure states of the quantum system

Quadratic algebras

CERN Document Server

Polishchuk, Alexander

2005-01-01

Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

Solution strategies for linear and nonlinear instability phenomena for arbitrarily thin shell structures

International Nuclear Information System (INIS)

Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.

1983-01-01

In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)

Faithfully quadratic rings

CERN Document Server

Dickmann, M

2015-01-01

In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in

Management of linear quadratic regulator optimal control with full-vehicle control case study

Directory of Open Access Journals (Sweden)

Rodrigue Tchamna

2016-09-01

Full Text Available Linear quadratic regulator is a powerful technique for dealing with the control design of any linear and nonlinear system after linearization of the system around an operating point. For small systems, which have fewer state variables, the transformation of the performance index from scalar to matrix form can be straightforward. On the other hand, as the system becomes large with many state variables and controllers, appropriate design and notations should be defined to make it easy to automatically implement the technique for any large system without the need to redesign from scratch every time one requires a new system. The main aim of this article was to deal with this issue. This article shows how to automatically obtain the matrix form of the performance index matrices from the scalar version of the performance index. Control of a full-vehicle in cornering was taken as a case study in this article.

Computer-aided Nonlinear Control System Design Using Describing Function Models

CERN Document Server

Nassirharand, Amir

2012-01-01

A systematic computer-aided approach provides a versatile setting for the control engineer to overcome the complications of controller design for highly nonlinear systems. Computer-aided Nonlinear Control System Design provides such an approach based on the use of describing functions. The text deals with a large class of nonlinear systems without restrictions on the system order, the number of inputs and/or outputs or the number, type or arrangement of nonlinear terms. The strongly software-oriented methods detailed facilitate fulfillment of tight performance requirements and help the designer to think in purely nonlinear terms, avoiding the expedient of linearization which can impose substantial and unrealistic model limitations and drive up the cost of the final product. Design procedures are presented in a step-by-step algorithmic format each step being a functional unit with outputs that drive the other steps. This procedure may be easily implemented on a digital computer with example problems from mecha...

Gravitation and quadratic forms

International Nuclear Information System (INIS)

Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha

2017-01-01

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Gravitation and quadratic forms

Energy Technology Data Exchange (ETDEWEB)

Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)

2017-03-31

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Genetic design of interpolated non-linear controllers for linear plants

International Nuclear Information System (INIS)

Ajlouni, N.

2000-01-01

The techniques of genetic algorithms are proposed as a means of designing non-linear PID control systems. It is shown that the use of genetic algorithms for this purpose results in highly effective non-linear PID control systems. These results are illustrated by using genetic algorithms to design a non-linear PID control system and contrasting the results with an optimally tuned linear PID controller. (author)

Applications of Nonlinear Dynamics Model and Design of Complex Systems

CERN Document Server

In, Visarath; Palacios, Antonio

2009-01-01

This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design

Energy Technology Data Exchange (ETDEWEB)

Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC

2006-09-28

A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.

Nonlinear Dynamic Behavior of a Bi-Axial Torsional MEMS Mirror with Sidewall Electrodes

Directory of Open Access Journals (Sweden)

Mehmet Ozdogan

2016-03-01

Full Text Available Nonlinear dynamic responses of a Micro-Electro-Mechanical Systems (MEMS mirror with sidewall electrodes are presented that are in close agreement with previously-reported experimental data. An analysis of frequency responses reveals softening behavior, and secondary resonances originated from the dominant quadratic nonlinearity. The quadratic nonlinearity is an electromechanical coupling effect caused by the electrostatic force. This effect is reflected in our mathematical model used to simulate the dynamic response of the micro-mirror. The effects of increased forcing and decreased damping on the frequency response are investigated as the mirrors are mostly used in vacuum packages. The results can predict MEMS mirror behaviors in optical devices better than previously-reported models.

Vacuum solutions of Bianchi cosmologies in quadratic gravity

International Nuclear Information System (INIS)

Deus, Juliano Alves de; Muller, Daniel

2011-01-01

Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)

Group-velocity matched nonlinear photonic crystal fibers

DEFF Research Database (Denmark)

Bache, Morten; Lægsgaard, Jesper; Bang, Ole

2006-01-01

A quadratic nonlinear index-guiding silica PCF is optimized for efficient second-harmonic generation through dispersion calculations. Zero group-velocity mismatch is possible for any pump wavelength above 780 nm. Very high conversion efficiencies and bandwidths are found....

Bound-Electron Nonlinearity Beyond the Ionization Threshold

Science.gov (United States)

Wahlstrand, J. K.; Zahedpour, S.; Bahl, A.; Kolesik, M.; Milchberg, H. M.

2018-05-01

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

Photonic surfaces for designable nonlinear power shaping

Energy Technology Data Exchange (ETDEWEB)

Biswas, Roshni, E-mail: rbiswas@usc.edu; Povinelli, Michelle L. [Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089 (United States)

2015-02-09

We propose a method for designing nonlinear input-output power response based on absorptive resonances of nanostructured surfaces. We show that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the laser wavelength. We demonstrate our results in a silicon photonic crystal slab at a laser wavelength of 808 nm. We quantify the overall spectral red shift as a function of laser power. The shift results from absorptive heating and the thermo-optic effect. We then demonstrate devices with increasing, decreasing, and non-monotonic transmission as a function of laser power. The transmission changes are up to 7.5 times larger than in unpatterned silicon. The strong nonlinear transmission is due to a combination of resonantly enhanced absorption, reduced thermal conductivity, and the resonant transmission lineshape. Our results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest.

Photonic surfaces for designable nonlinear power shaping

International Nuclear Information System (INIS)

Biswas, Roshni; Povinelli, Michelle L.

2015-01-01

We propose a method for designing nonlinear input-output power response based on absorptive resonances of nanostructured surfaces. We show that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the laser wavelength. We demonstrate our results in a silicon photonic crystal slab at a laser wavelength of 808 nm. We quantify the overall spectral red shift as a function of laser power. The shift results from absorptive heating and the thermo-optic effect. We then demonstrate devices with increasing, decreasing, and non-monotonic transmission as a function of laser power. The transmission changes are up to 7.5 times larger than in unpatterned silicon. The strong nonlinear transmission is due to a combination of resonantly enhanced absorption, reduced thermal conductivity, and the resonant transmission lineshape. Our results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest

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

Science.gov (United States)

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.

Design of advanced materials for linear and nonlinear dynamics

DEFF Research Database (Denmark)

Frandsen, Niels Morten Marslev

to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple......The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... but general model of inhomogeneous structural materials with nonlinear material characteristics. The second material system is an “engineered” material in the sense that a classical structural element, a linear elastic and homogeneous rod, is “enhanced” by applying a mechanism on its surface, amplifying...

Theories of quantum dissipation and nonlinear coupling bath descriptors

Science.gov (United States)

Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing

2018-03-01

The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.

Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

Directory of Open Access Journals (Sweden)

E. George Walters III

2015-11-01

Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

A direct method for numerical solution of a class of nonlinear Volterra integro-differential equations and its application to the nonlinear fission and fusion reactor kinetics

International Nuclear Information System (INIS)

Nakahara, Yasuaki; Ise, Takeharu; Kobayashi, Kensuke; Itoh, Yasuyuki

1975-12-01

A new method has been developed for numerical solution of a class of nonlinear Volterra integro-differential equations with quadratic nonlinearity. After dividing the domain of the variable into subintervals, piecewise approximations are applied in the subintervals. The equation is first integrated over a subinterval to obtain the piecewise equation, to which six approximate treatments are applied, i.e. fully explicit, fully implicit, Crank-Nicolson, linear interpolation, quadratic and cubic spline. The numerical solution at each time step is obtained directly as a positive root of the resulting algebraic quadratic equation. The point reactor kinetics with a ramp reactivity insertion, linear temperature feedback and delayed neutrons can be described by one of this type of nonlinear Volterra integro-differential equations. The algorithm is applied to the Argonne benchmark problem and a model problem for a fast reactor without delayed neutrons. The fully implicit method has been found to be unconditionally stable in the sense that it always gives the positive real roots. The cubic spline method is divergent, and the other four methods are intermediate in between. From the estimation of the stability, convergency, accuracy and CPU time, it is concluded that the Crank-Nicolson method is best, then the linear interpolation method comes closely next to it. Discussions are also made on the possibility of applying the algorithm to the fusion reactor kinetics in the form of a nonlinear partial differential equation. (auth.)

Aspects of Quadratic Gravity

CERN Document Server

Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

2016-01-01

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

On Stabilization of Nonautonomous Nonlinear Systems

International Nuclear Information System (INIS)

Bogdanov, A. Yu.

2008-01-01

The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

Nonlinear vibrations of an inclined beam subjected to a moving load

International Nuclear Information System (INIS)

Mamandi, A; Kargarnovin, M H; Younesian, D

2009-01-01

In this paper, the nonlinear dynamic responses of an inclined pinned-pinned Euler-Bernoulli beam with a constant cross section and finite length subjected to a concentrated vertical force traveling with constant velocity is investigated by using the mode summation method. Frequency analysis of the PDE's governing equations of motion for steady-state response is studied by applying multiple scales method. The nonlinear dynamic deflections of the beam are obtained by solving two coupled nonlinear PDE's governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the numerical results are compared with those obtained from traditional linear solution. It is found that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also stability analysis of the steady-state response for the modes equations having quadratic nonlinearity is carried out and it is observed from the amplitude response curves that for the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon are predicted for the longitudinal excitation.

Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

Energy Technology Data Exchange (ETDEWEB)

Das, Sonjoy; Goswami, Kundan [University at Buffalo, NY (United States); Datta, Biswa N. [Northern Illinois University, IL (United States)

2014-12-10

Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.

Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

International Nuclear Information System (INIS)

Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.

2014-01-01

Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology

IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

CERN Document Server

Rega, Giuseppe

2013-01-01

Nonlinear dynamics has been enjoying a vast development for nearly four decades resulting in a range of well established theory, with the potential to significantly enhance performance, effectiveness, reliability and safety of physical systems as well as offering novel technologies and designs. By critically appraising the state-of-the-art, it is now time to develop design criteria and technology for new generation products/processes operating on principles of nonlinear interaction and in the nonlinear regime, leading to more effective, sensitive, accurate, and durable methods than what is currently available. This new approach is expected to radically influence the design, control and exploitation paradigms, in a magnitude of contexts. With a strong emphasis on experimentally calibrated and validated models, contributions by top-level international experts will foster future directions for the development of engineering technologies and design using robust nonlinear dynamics modelling and analysis.  

Vagal activity is quadratically related to prosocial traits, prosocial emotions, and observer perceptions of prosociality.

Science.gov (United States)

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.

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

Science.gov (United States)

Bick, Christian; Sebek, Michael; Kiss, István Z.

2017-10-01

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.

LQG/LTR [linear quadratic Gaussian with loop transfer recovery] robust control system design for a low-pressure feedwater heater train

International Nuclear Information System (INIS)

Murphy, G.V.; Bailey, J.M.

1990-01-01

This paper uses the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) control system design method to obtain a level control system for a low-pressure feedwater heater train. The control system performance and stability robustness are evaluated for a given set of system design specifications. The tools for analysis are the return ratio, return difference, and inverse return difference singular-valve plots for a loop break at the plant output. 3 refs., 7 figs., 2 tabs

TUNING PARAMETER LINEAR QUADRATIC TRACKING MENGGUNAKAN ALGORITMA GENETIKA UNTUK PENGENDALIAN GERAK LATERAL QUADCOPTER

Directory of Open Access Journals (Sweden)

Farid Choirul Akbar

2016-04-01

Full Text Available Gerakan lateral quadcopter dapat dilakukan apabila quadcopter dapat menjaga kestabilan pada saat hover, sehingga quadcopter dapat melakukan gerak rotasi. Perubahan sudut roll akan mengakibatkan gerak translasi pada sumbu Y, sedangkan perubahan sudut pitch akan mengakibatkan gerak translasi pada sumbu X. Disisi lain, quadcopter merupakan suatu sistem non-linear dan memiliki kestabilan yang rendah sehingga rentan terhadap gangguan. Pada penelitian Tugas Akhir ini dirancang pengendalian gerak rotasi quadcopter menggunakan Linear Quadratic Regulator (LQR dan Linear Quadratic Tracking (LQT untuk pengendalian gerak translasi. Untuk mendapatkan parameter dari LQT digunakan Algoritma Genetika (GA. Hasil tuning GA yang digunakan pada LQT memiliki nilai Qx 700,1884, nilai Qy 700,6315, nilai Rx 0,1568, dan  nilai Ry 0,1579. Respon LQT tersebut memiliki RMSE pada sumbu X dan sumbu Y sebesar 1,99 % serta memiliki time lagging 0,35 detik. Dengan hasil tersebut quadcopter mampu men-tracking trajectory berbentuk segitigaTekni

Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions

Indian Academy of Sciences (India)

2015-10-13

Oct 13, 2015 ... Isochronous system; Liénard-type system; singular and nonsingular Hamiltonian. ... Liénard-type nonlinear oscillators exhibiting isochronous properties, including linear, quadratic and ... Pramana – Journal of Physics | News.

On Characterization of Quadratic Splines

DEFF Research Database (Denmark)

Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

2005-01-01

that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....

Determination and evaluation of gas holdup time with the quadratic equation model and comparison with nonlinear equation models for isothermal gas chromatography

Science.gov (United States)

Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.

2013-01-01

Gas holdup time (tM) is a basic parameter in isothermal gas chromatography (GC). Determination and evaluation of tM and retention behaviors of n-alkanes under isothermal GC conditions have been extensively studied since the 1950s, but still remains unresolved. The difference equation (DE) model [J. Chromatogr. A 1260:215–223] reveals retention behaviors of n-alkanes excluding tM, while the quadratic equation (QE) model [J. Chromatogr. A 1260:224–231] including tM is suitable for applications. In the present study, tM values were calculated with the QE model, which is referred to as tMT, evaluated and compared with other three typical nonlinear models. The QE model gives an accurate estimation of tM in isothermal GC. The tMT values are highly accurate, stable, and easy to calculate and use. There is only one tMT value at each GC condition. The proper classification of tM values can clarify their disagreement and facilitate GC retention data standardization for which tMT values are promising reference tM values. PMID:23726077

On the reflection point where light reflects to a known destination on quadratic surfaces.

Science.gov (United States)

Gonçalves, Nuno

2010-01-15

We address the problem of determining the reflection point on a specular surface where a light ray that travels from a source to a target is reflected. The specular surfaces considered are those expressed by a quadratic equation. So far, there is no closed form explicit equation for the general solution of this determination of the reflection point, and the usual approach is to use the Snell law or the Fermat principle whose equations are derived in multidimensional nonlinear minimizations. We prove in this Letter that one can impose a set of three restrictions to the reflection point that can impose a set of three restrictions that culminates in a very elegant formalism of searching the reflection point in a unidimensional curve in space. This curve is the intersection of two quadratic equations. Some applications of this framework are also discussed.

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

Science.gov (United States)

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

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

Experimental Design for Hanford Low-Activity Waste Glasses with High Waste Loading

International Nuclear Information System (INIS)

Piepel, Gregory F.; Cooley, Scott K.; Vienna, John D.; Crum, Jarrod V.

2015-01-01

This report discusses the development of an experimental design for the initial phase of the Hanford low-activity waste (LAW) enhanced glass study. This report is based on a manuscript written for an applied statistics journal. Appendices A, B, and E include additional information relevant to the LAW enhanced glass experimental design that is not included in the journal manuscript. The glass composition experimental region is defined by single-component constraints (SCCs), linear multiple-component constraints (MCCs), and a nonlinear MCC involving 15 LAW glass components. Traditional methods and software for designing constrained mixture experiments with SCCs and linear MCCs are not directly applicable because of the nonlinear MCC. A modification of existing methodology to account for the nonlinear MCC was developed and is described in this report. One of the glass components, SO 3 , has a solubility limit in glass that depends on the composition of the balance of the glass. A goal was to design the experiment so that SO 3 would not exceed its predicted solubility limit for any of the experimental glasses. The SO 3 solubility limit had previously been modeled by a partial quadratic mixture model expressed in the relative proportions of the 14 other components. The partial quadratic mixture model was used to construct a nonlinear MCC in terms of all 15 components. In addition, there were SCCs and linear MCCs. This report describes how a layered design was generated to (i) account for the SCCs, linear MCCs, and nonlinear MCC and (ii) meet the goals of the study. A layered design consists of points on an outer layer, and inner layer, and a center point. There were 18 outer-layer glasses chosen using optimal experimental design software to augment 147 existing glass compositions that were within the LAW glass composition experimental region. Then 13 inner-layer glasses were chosen with the software to augment the existing and outer-layer glasses. The experimental

DESIGN AND IMPLEMENTATION OF POTENTIOMETER-BASED NONLINEAR TRANSDUCER EMULATOR

Directory of Open Access Journals (Sweden)

Sheroz Khan

2011-05-01

Full Text Available This work attempts to design and implement in hardware a transducer with a nonlinear response using potentiometer. Potentiometer is regarded as a linear transducer, while a the response of a nonlinear transducer can be treated as a concatenation of linear segments made out of the response curve of an actual nonlinear transducer at the points of inflections being exhibited by the nonlinear curve. Each straight line segment is characterized by its slope and a constant, called the y-intercept, which is ultimately realized by a corresponding electronic circuit. The complete circuit diagram is made of three stages: (i the input stage for range selection, (ii a digital logic to make appropriate selection, (iii a conditioning circuit for realizing a given straight-line segment identified by its relevant slope and reference voltage. The simulation of the circuit is carried using MULTISIM, and the designed circuit is afterward tested to verify that variations of the input voltage give us an output voltage very close to the response pattern envisaged in the analytical stage of the design. The utility of this work lies in its applications in emulating purpose built transducers that could be used to nicely emulate a transducer in a real world system that is to be controlled by a programmable digital system.

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields.

Science.gov (United States)

Rosnitskiy, Pavel B; Yuldashev, Petr V; Sapozhnikov, Oleg A; Maxwell, Adam D; Kreider, Wayne; Bailey, Michael R; Khokhlova, Vera A

2017-02-01

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

Quadratic third-order tensor optimization problem with quadratic constraints

Directory of Open Access Journals (Sweden)

Lixing Yang

2014-05-01

Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.

Nonlinear saturation controller for vibration supersession of a nonlinear composite beam

Energy Technology Data Exchange (ETDEWEB)

Hamed, Y. S. [Menofia University, Menouf (Egypt); Amer, Y. A. [Zagazig University, Zagazig (Egypt)

2014-08-15

In this paper, a study for nonlinear saturation controller (NSC) is presented that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities of the feedback gain and a two-to-one internal resonance. The analytical solution for the system and the nonlinear saturation controller are obtained using method of multiple time scales perturbation up to the second order approximation. All possible resonance cases were extracted at this approximation order and studied numerically. The stability of the system at the worst resonance case (Ω = 2ω{sub s} and ω{sub s} =2ω{sub C}) is investigated using both frequency response equations and phase-plane trajectories. The effects of different parameters on the system and the controller are studied numerically. The effect of some types of controller on the system is investigated numerically. The simulation results are achieved using Matlab and Maple programs.

Modeling of Nonlinear Beat Signals of TAE's

Science.gov (United States)

Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin

2012-03-01

Experiments on Alcator C-Mod reveal Toroidal Alfven Eigenmodes (TAE) together with signals at various beat frequencies, including those at twice the mode frequency. The beat frequencies are sidebands driven by quadratic nonlinear terms in the MHD equations. These nonlinear sidebands have not yet been quantified by any existing codes. We extend the AEGIS code to capture nonlinear effects by treating the nonlinear terms as a driving source in the linear MHD solver. Our goal is to compute the spatial structure of the sidebands for realistic geometry and q-profile, which can be directly compared with experiment in order to interpret the phase contrast imaging diagnostic measurements and to enable the quantitative determination of the Alfven wave amplitude in the plasma core

Quantum X waves with orbital angular momentum in nonlinear dispersive media

Science.gov (United States)

Ornigotti, Marco; Conti, Claudio; Szameit, Alexander

2018-06-01

We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.

A Conic Sector-Based Methodology for Nonlinear Control Design

OpenAIRE

Doyle, Francis J., III; Morari, Manfred

1990-01-01

A design method is presented for the analysis and synthesis of robust nonlinear controllers for chemical engineering systems. The method rigorously treats the effect of unmeasured disturbances and unmodeled dynamics on the stability and performance properties of a nonlinear system. The results utilise new extensions of structured singular value theory for analysis and recent synthesis results for approximate linearisation.

How universal is the period doubling phenomenon in equations with quadratic nonlinearity

International Nuclear Information System (INIS)

Malta, C.P.; Oliveira, C.R. de.

1983-09-01

Varying one parameter, the solution of nonlinear 1 sup(st) order differential equation with time delay tau is Fourier analysed. After the Hopf bifurcation, period-doubling phenomenon always occurs when tau is one of the fixed parameters (both for small and large tau). Varying tau, there are values of the fixed parameters for which no period-doubling occurs. 'Chaos' follows the period-doubling sequence and the rate at which 'chaos' is approached is very close to the universal delta = 4.6692016... characterising the period-doubling sequence to chaos in nonlinear difference equations. (Author) [pt

Nonlinear damping based semi-active building isolation system

Science.gov (United States)

Ho, Carmen; Zhu, Yunpeng; Lang, Zi-Qiang; Billings, Stephen A.; Kohiyama, Masayuki; Wakayama, Shizuka

2018-06-01

Many buildings in Japan currently have a base-isolation system with a low stiffness that is designed to shift the natural frequency of the building below the frequencies of the ground motion due to earthquakes. However, the ground motion observed during the 2011 Tohoku earthquake contained strong long-period waves that lasted for a record length of 3 min. To provide a novel and better solution against the long-period waves while maintaining the performance of the standard isolation range, the exploitation of the characteristics of nonlinear damping is proposed in this paper. This is motivated by previous studies of the authors, which have demonstrated that nonlinear damping can achieve desired performance over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Simulation results have shown strong vibration isolation performance on a building model with identified parameters and have indicated that nonlinear damping can achieve low acceleration transmissibilities round the structural natural frequency as well as the higher ground motion frequencies that have been frequently observed during most earthquakes in Japan. In addition, physical building model based laboratory experiments are also conducted, The results demonstrate the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. In comparison with the tuned-mass damper and other active control methods, the proposed solution offers a more pragmatic, low-cost, robust and effective alternative that can be readily installed into the base-isolation system of most buildings.

Factorization method of quadratic template

Science.gov (United States)

Kotyrba, Martin

2017-07-01

Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

Extending the Scope of Robust Quadratic Optimization

NARCIS (Netherlands)

Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in

Quadratic residues and non-residues selected topics

CERN Document Server

Wright, Steve

2016-01-01

This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

Quadratic obstructions to small-time local controllability for scalar-input systems

Science.gov (United States)

Beauchard, Karine; Marbach, Frédéric

2018-03-01

We consider nonlinear finite-dimensional scalar-input control systems in the vicinity of an equilibrium. When the linearized system is controllable, the nonlinear system is smoothly small-time locally controllable: whatever m > 0 and T > 0, the state can reach a whole neighborhood of the equilibrium at time T with controls arbitrary small in Cm-norm. When the linearized system is not controllable, we prove that: either the state is constrained to live within a smooth strict manifold, up to a cubic residual, or the quadratic order adds a signed drift with respect to it. This drift holds along a Lie bracket of length (2 k + 1), is quantified in terms of an H-k-norm of the control, holds for controls small in W 2 k , ∞-norm and these spaces are optimal. Our proof requires only C3 regularity of the vector field. This work underlines the importance of the norm used in the smallness assumption on the control, even in finite dimension.

Students' Understanding of Quadratic Equations

Science.gov (United States)

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…

Interactive Design of Developable Surfaces

KAUST Repository

Tang, Chengcheng

2016-01-15

We present a new approach to geometric modeling with developable surfaces and the design of curved-creased origami. We represent developables as splines and express the nonlinear conditions relating to developability and curved folds as quadratic equations. This allows us to utilize a constraint solver, which may be described as energy-guided projection onto the constraint manifold, and which is fast enough for interactive modeling. Further, a combined primal-dual surface representation enables us to robustly and quickly solve approximation problems.

Interactive Design of Developable Surfaces

KAUST Repository

Tang, Chengcheng; Bo, Pengbo; Wallner, Johannes; Pottmann, Helmut

2016-01-01

We present a new approach to geometric modeling with developable surfaces and the design of curved-creased origami. We represent developables as splines and express the nonlinear conditions relating to developability and curved folds as quadratic equations. This allows us to utilize a constraint solver, which may be described as energy-guided projection onto the constraint manifold, and which is fast enough for interactive modeling. Further, a combined primal-dual surface representation enables us to robustly and quickly solve approximation problems.

On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation

NARCIS (Netherlands)

Zarubinskaya, M.A.; Van Horssen, W.T.

2003-01-01

In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is

Optimal control linear quadratic methods

CERN Document Server

Anderson, Brian D O

2007-01-01

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

Projection of curves on B-spline surfaces using quadratic reparameterization

KAUST Repository

Yang, Yijun; Zeng, Wei; Zhang, Hui; Yong, Junhai; Paul, Jean Claude

2010-01-01

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying

B-spline goal-oriented error estimators for geometrically nonlinear rods

Science.gov (United States)

2011-04-01

respectively, for the output functionals q2–q4 (linear and nonlinear with the trigonometric functions sine and cosine) in all the tests considered...of the errors resulting from the linear, quadratic and nonlinear (with trigonometric functions sine and cosine) outputs and for p = 1, 2. If the... Portugal . References [1] A.T. Adams. Sobolev Spaces. Academic Press, Boston, 1975. [2] M. Ainsworth and J.T. Oden. A posteriori error estimation in

Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

Science.gov (United States)

Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin

2017-10-01

We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.

Microscopic cascading of second-order molecular nonlinearity: New design principles for enhancing third-order nonlinearity.

Science.gov (United States)

Baev, Alexander; Autschbach, Jochen; Boyd, Robert W; Prasad, Paras N

2010-04-12

Herein, we develop a phenomenological model for microscopic cascading and substantiate it with ab initio calculations. It is shown that the concept of local microscopic cascading of a second-order nonlinearity can lead to a third-order nonlinearity, without introducing any new loss mechanisms that could limit the usefulness of our approach. This approach provides a new molecular design protocol, in which the current great successes achieved in producing molecules with extremely large second-order nonlinearity can be used in a supra molecular organization in a preferred orientation to generate very large third-order response magnitudes. The results of density functional calculations for a well-known second-order molecule, (para)nitroaniline, show that a head-to-tail dimer configuration exhibits enhanced third-order nonlinearity, in agreement with the phenomenological model which suggests that such an arrangement will produce cascading due to local field effects.

Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2006-01-01

This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

Quadratic theory and feedback controllers for linear time delay systems

International Nuclear Information System (INIS)

Lee, E.B.

1976-01-01

Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)

Quadratically convergent MCSCF scheme using Fock operators

International Nuclear Information System (INIS)

Das, G.

1981-01-01

A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations

Quadratic brackets from symplectic forms

International Nuclear Information System (INIS)

Alekseev, Anton Yu.; Todorov, Ivan T.

1994-01-01

We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))

Nonlinear observer designs for fuel cell power systems

Science.gov (United States)

Gorgun, Haluk

A fuel cell is an electrochemical device that combines hydrogen and oxygen, with the aid of electro-catalysts, to produce electricity. A fuel cell consists of a negatively charged anode, a positively charged cathode and an electrolyte, which transports protons or ions. A low temperature fuel cell has an electrical potential of about 0.7 Volt when generating a current density of 300--500 mA/cm2. Practical fuel cell power systems will require a combination of several cells in series (a stack) to satisfy the voltage requirements of specific applications. Fuel cells are suitable for a potentially wide variety of applications, from stationary power generation in the range of hundreds of megawatts to portable electronics in the range of a couple of watts. Efficient operation of a fuel cell system requires advanced feedback control designs. Reliable measurements from the system are necessary to implement such designs. However, most of the commercially available sensors do not operate properly in the reformate and humidified gas streams in fuel cell systems. Sensors working varying degrees of success are too big and costly, and sensors that are potentially low cost are not reliable or do not have the required life time [28]. Observer designs would eliminate sensor needs for measurements, and make feedback control implementable. Since the fuel cell system dynamics are highly nonlinear, observer design is not an easy task. In this study we aim to develop nonlinear observer design methods applicable to fuel cell systems. In part I of the thesis we design an observer to estimate the hydrogen partial pressure in the anode channel. We treat inlet partial pressure as an unknown slowly varying parameter and develop an adaptive observer that employs a nonlinear voltage injection term. However in this design Fuel Processing System (FPS) dynamics are not modelled, and their effect on the anode dynamics are treated as plant uncertainty. In part II of the thesis we study the FPS

Model Predictive Control of a Nonlinear System with Known Scheduling Variable

DEFF Research Database (Denmark)

Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik

2012-01-01

Model predictive control (MPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Consequently...... the control problem of the nonlinear system is simplied into a quadratic programming. Wind turbine is chosen as the case study and we choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon....

Nonlinear structural analysis methods and their application to elevated temperature design: A US perspective

International Nuclear Information System (INIS)

Dhalla, A.K.

1989-01-01

Technological advances over the last two decades have been assimilated into the routine design of Liquid Metal Reactor (LMR) structural components operating at elevated temperatures. The mature elevated temperature design technology is based upon: (a) an extensive material data base, (b) recent advances in nonlinear computational methods, and (c) conservative design criteria based upon past successful and reliable operating experiences with petrochemical and nonnuclear power plants. This survey paper provides a US perspective on the role of nonlinear analysis methods used in the design of LMR plants. The simplified and detailed nonlinear analysis methods and the level of computational effort required to qualify structural components for safe and reliable long-term operation are discussed. The paper also illustrates how a detailed nonlinear analysis can be used to resolve technical licensing issues, to understand complex nonlinear structural behavior, to identify predominant failure modes, and to guide future experimental programs

Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory

DEFF Research Database (Denmark)

Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav

model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable...

Experimental Design for Hanford Low-Activity Waste Glasses with High Waste Loading

Energy Technology Data Exchange (ETDEWEB)

Piepel, Gregory F. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Cooley, Scott K. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Vienna, John D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Crum, Jarrod V. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

2015-07-24

This report discusses the development of an experimental design for the initial phase of the Hanford low-activity waste (LAW) enhanced glass study. This report is based on a manuscript written for an applied statistics journal. Appendices A, B, and E include additional information relevant to the LAW enhanced glass experimental design that is not included in the journal manuscript. The glass composition experimental region is defined by single-component constraints (SCCs), linear multiple-component constraints (MCCs), and a nonlinear MCC involving 15 LAW glass components. Traditional methods and software for designing constrained mixture experiments with SCCs and linear MCCs are not directly applicable because of the nonlinear MCC. A modification of existing methodology to account for the nonlinear MCC was developed and is described in this report. One of the glass components, SO₃, has a solubility limit in glass that depends on the composition of the balance of the glass. A goal was to design the experiment so that SO₃ would not exceed its predicted solubility limit for any of the experimental glasses. The SO₃ solubility limit had previously been modeled by a partial quadratic mixture model expressed in the relative proportions of the 14 other components. The partial quadratic mixture model was used to construct a nonlinear MCC in terms of all 15 components. In addition, there were SCCs and linear MCCs. This report describes how a layered design was generated to (i) account for the SCCs, linear MCCs, and nonlinear MCC and (ii) meet the goals of the study. A layered design consists of points on an outer layer, and inner layer, and a center point. There were 18 outer-layer glasses chosen using optimal experimental design software to augment 147 existing glass compositions that were within the LAW glass composition experimental region. Then 13 inner-layer glasses were chosen with the software to augment the existing and outer

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard

2015-05-04

​In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport). ​

Modified wave operators for nonlinear Schrodinger equations in one and two dimensions

Directory of Open Access Journals (Sweden)

Nakao Hayashi

2004-04-01

Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13

An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

Science.gov (United States)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

The application of LQR synthesis techniques to the turboshaft engine control problem. [Linear Quadratic Regulator

Science.gov (United States)

Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

1985-01-01

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — Time simulation of a nonlinear aerodynamics model (NA) developed at Virginia Tech coupled with a nonlinear structure model (NS) is proposed as a design/analysis...

Numerical treatments for solving nonlinear mixed integral equation

Directory of Open Access Journals (Sweden)

M.A. Abdou

2016-12-01

Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.

Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics

Directory of Open Access Journals (Sweden)

J. Petrzela

2012-04-01

Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided

A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

KAUST Repository

Domí nguez, Luis F.; Pistikopoulos, Efstratios N.

2012-01-01

An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear

A revisit to quadratic programming with fuzzy parameters

International Nuclear Information System (INIS)

Liu, S.-T.

2009-01-01

Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.

Quadratic Boost A-Source Impedance Network

DEFF Research Database (Denmark)

Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

2016-01-01

A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...

Cost Cumulant-Based Control for a Class of Linear Quadratic Tracking Problems

National Research Council Canada - National Science Library

Pham, Khanh D

2007-01-01

.... For instance, the present paper extends the application of cost-cumulant controller design to control of a wide class of linear-quadratic tracking systems where output measurements of a tracker...

A comparative analysis of Painleve, Lax pair, and similarity transformation methods in obtaining the integrability conditions of nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Al Khawaja, U.

2010-01-01

We derive the integrability conditions of nonautonomous nonlinear Schroedinger equations using the Lax pair and similarity transformation methods. We present a comparative analysis of these integrability conditions with those of the Painleve method. We show that while the Painleve integrability conditions restrict the dispersion, nonlinearity, and dissipation/gain coefficients to be space independent and the external potential to be only a quadratic function of position, the Lax Pair and the similarity transformation methods allow for space-dependent coefficients and an external potential that is not restricted to the quadratic form. The integrability conditions of the Painleve method are retrieved as a special case of our general integrability conditions. We also derive the integrability conditions of nonautonomous nonlinear Schroedinger equations for two- and three-spacial dimensions.

Nonlinear Cointegration Approach for Condition Monitoring of Wind Turbines

Directory of Open Access Journals (Sweden)

Konrad Zolna

2015-01-01

Full Text Available Monitoring of trends and removal of undesired trends from operational/process parameters in wind turbines is important for their condition monitoring. This paper presents the homoscedastic nonlinear cointegration for the solution to this problem. The cointegration approach used leads to stable variances in cointegration residuals. The adapted Breusch-Pagan test procedure is developed to test for the presence of heteroscedasticity in cointegration residuals obtained from the nonlinear cointegration analysis. Examples using three different time series data sets—that is, one with a nonlinear quadratic deterministic trend, another with a nonlinear exponential deterministic trend, and experimental data from a wind turbine drivetrain—are used to illustrate the method and demonstrate possible practical applications. The results show that the proposed approach can be used for effective removal of nonlinear trends form various types of data, allowing for possible condition monitoring applications.

Improved effective potential by nonlinear canonical transformations

International Nuclear Information System (INIS)

Ritschel, U.

1990-01-01

We generalize the familiar gaussian-effective-potential formalism to a class of non-gaussian trial states. With the help of exact nonlinear canonical transformations, expectation values can be calculated analytically and in closed form. A detailed description of our method, particularly for quadratic and cubic transformations, and of the related renormalization procedure is given. Applications to φ 4 -models in various dimensionalities are treated. We find the expected critical behaviour in two space-time dimensions. In three and four dimensions we observe instabilities which go back the incompleteness of the gaussian-based renormalization. In the appendices it is shown that the quadratic transformation leads to a coherent state in a certain limiting case, and the generalization to systems at finite temperature is performed. (orig.)

A sequential quadratic programming algorithm using an incomplete solution of the subproblem

Energy Technology Data Exchange (ETDEWEB)

Murray, W. [Stanford Univ., CA (United States). Systems Optimization Lab.; Prieto, F.J. [Universidad `Carlos III` de Madrid (Spain). Dept. de Estadistica y Econometria

1993-05-01

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.

Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach

Directory of Open Access Journals (Sweden)

Olav Slupphaug

2001-01-01

Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.

Genetic algorithm–based varying parameter linear quadratic regulator control for four-wheel independent steering vehicle

Directory of Open Access Journals (Sweden)

Linlin Gao

2015-11-01

Full Text Available From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.

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

Science.gov (United States)

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

2016-10-01

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

Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic solid–shell elements combined with advanced anisotropic behavior models

Directory of Open Access Journals (Sweden)

Wang Peng

2016-01-01

Full Text Available A family of prismatic and hexahedral solid‒shell (SHB elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact. Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.

Differentiated Learning Environment--A Classroom for Quadratic Equation, Function and Graphs

Science.gov (United States)

Dinç, Emre

2017-01-01

This paper will cover the design of a learning environment as a classroom regarding the Quadratic Equations, Functions and Graphs. The goal of the learning environment offered in the paper is to design a classroom where students will enjoy the process, use their skills they already have during the learning process, control and plan their learning…

Nonlinearity measure and internal model control based linearization in anti-windup design

Energy Technology Data Exchange (ETDEWEB)

Perev, Kamen [Systems and Control Department, Technical University of Sofia, 8 Cl. Ohridski Blvd., 1756 Sofia (Bulgaria)

2013-12-18

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequency ranges.

Nonlinear analysis of doubly curved shells: An analytical approach

Indian Academy of Sciences (India)

Е10Ж. 0rЕs└1Ж. iY j. И Й0rs. iY j└1 З 0rs. iY jЗ1Кa2jX. Е11Ж. Nonlinearity in the governing equations of motion is due to the product of the dependent variables. The quadratic extrapolation technique is used for the linearization and a typical nonlinear function Gj can be expressed at any step j as,. Gj И Е0rЖJЕ0sЖJ. И. И.

On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model

International Nuclear Information System (INIS)

Unkel, Steffen; Belka, Claus; Lauber, Kirsten

2016-01-01

The most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited. Colony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis. Both the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed

Quadratic Diophantine equations

CERN Document Server

Andreescu, Titu

2015-01-01

This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

Nonlinear dynamics and cavity cooling of levitated nanoparticles

Science.gov (United States)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-09-01

We investigate a dynamic nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. Through the rich sideband structure displayed by the cavity output we can observe cooling of the linear and non-linear particle's motion. Here we present an experimental setup which allows full control over the cavity resonant frequencies, and shows cooling of the particle's motion as a function of the detuning. This work paves the way to strong-coupled quantum dynamics between a cavity and a mesoscopic object largely decoupled from its environment.

A genuine nonlinear approach for controller design of a boiler-turbine system.

Science.gov (United States)

Yang, Shizhong; Qian, Chunjiang; Du, Haibo

2012-05-01

This paper proposes a genuine nonlinear approach for controller design of a drum-type boiler-turbine system. Based on a second order nonlinear model, a finite-time convergent controller is first designed to drive the states to their setpoints in a finite time. In the case when the state variables are unmeasurable, the system will be regulated using a constant controller or an output feedback controller. An adaptive controller is also designed to stabilize the system since the model parameters may vary under different operating points. The novelty of the proposed controller design approach lies in fully utilizing the system nonlinearities instead of linearizing or canceling them. In addition, the newly developed techniques for finite-time convergent controller are used to guarantee fast convergence of the system. Simulations are conducted under different cases and the results are presented to illustrate the performance of the proposed controllers. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Non-linear variation of the beta function with momentum

International Nuclear Information System (INIS)

Parzen, G.

1983-07-01

A theory is presented for computing the non-linear dependence of the β-functions on momentum. Results are found for the quadratic term. The results of the theory are compared with computed results. A procedure is proposed for computing the strengths of the sextupole correctors to correct the dependence of the β-function on momentum

On a Highly Nonlinear Self-Obstacle Optimal Control Problem

Energy Technology Data Exchange (ETDEWEB)

Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)

2015-10-15

We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.

Non-linear analysis in Light Water Reactor design

International Nuclear Information System (INIS)

Rashid, Y.R.; Sharabi, M.N.; Nickell, R.E.; Esztergar, E.P.; Jones, J.W.

1980-03-01

The results obtained from a scoping study sponsored by the US Department of Energy (DOE) under the Light Water Reactor (LWR) Safety Technology Program at Sandia National Laboratories are presented. Basically, this project calls for the examination of the hypothesis that the use of nonlinear analysis methods in the design of LWR systems and components of interest include such items as: the reactor vessel, vessel internals, nozzles and penetrations, component support structures, and containment structures. Piping systems are excluded because they are being addressed by a separate study. Essentially, the findings were that nonlinear analysis methods are beneficial to LWR design from a technical point of view. However, the costs needed to implement these methods are the roadblock to readily adopting them. In this sense, a cost-benefit type of analysis must be made on the various topics identified by these studies and priorities must be established. This document is the complete report by ANATECH International Corporation

Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

Directory of Open Access Journals (Sweden)

Xue-Gang Zhou

2014-01-01

Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

Nonlinear control system analysis and design with Maple

NARCIS (Netherlands)

Jager, de A.G.; Houstis, E.N.; Rice, J.R.

1992-01-01

For the analysis and design of nonlinear control systems non-numerical methods are available. The required analytical computations are mostly too tedious to be done error free in a reasonable time by hand, so the use of symbolic computation programs can be of advantage. To show that the symbolic

Geometry and transport in a model of two coupled quadratic nonlinear waveguides

DEFF Research Database (Denmark)

Stirling, James R.; Bang, Ole; Christiansen, Peter Leth

2008-01-01

This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled X(2) waveguides is modeled and analyzed in terms of transport and geometry in the pha...

Nonlinear adaptive control system design with asymptotically stable parameter estimation error

Science.gov (United States)

Mishkov, Rumen; Darmonski, Stanislav

2018-01-01

The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.

Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

Directory of Open Access Journals (Sweden)

Mishra Vinod

2016-01-01

Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.

Designs for highly nonlinear ablative Rayleigh-Taylor experiments on the National Ignition Facility

International Nuclear Information System (INIS)

Casner, A.; Masse, L.; Liberatore, S.; Jacquet, L.; Loiseau, P.; Poujade, O.; Smalyuk, V. A.; Bradley, D. K.; Park, H. S.; Remington, B. A.; Igumenshchev, I.; Chicanne, C.

2012-01-01

We present two designs relevant to ablative Rayleigh-Taylor instability in transition from weakly nonlinear to highly nonlinear regimes at the National Ignition Facility [E. I. Moses, J. Phys.: Conf. Ser. 112, 012003 (2008)]. The sensitivity of nonlinear Rayleigh-Taylor instability physics to ablation velocity is addressed with targets driven by indirect drive, with stronger ablative stabilization, and by direct drive, with weaker ablative stabilization. The indirect drive design demonstrates the potential to reach a two-dimensional bubble-merger regime with a 20 ns duration drive at moderate radiation temperature. The direct drive design achieves a 3 to 5 times increased acceleration distance for the sample in comparison to previous experiments allowing at least 2 more bubble generations when starting from a three-dimensional broadband spectrum.

Designs for highly nonlinear ablative Rayleigh-Taylor experiments on the National Ignition Facility

Energy Technology Data Exchange (ETDEWEB)

Casner, A.; Masse, L.; Liberatore, S.; Jacquet, L.; Loiseau, P.; Poujade, O. [CEA, DAM, DIF, F-91297 Arpajon (France); Smalyuk, V. A.; Bradley, D. K.; Park, H. S.; Remington, B. A. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Igumenshchev, I. [Laboratory of Laser Energetics, University of Rochester, Rochester, New York 14623-1299 (United States); Chicanne, C. [CEA, DAM, VALDUC, F-21120 Is-sur-Tille (France)

2012-08-15

We present two designs relevant to ablative Rayleigh-Taylor instability in transition from weakly nonlinear to highly nonlinear regimes at the National Ignition Facility [E. I. Moses, J. Phys.: Conf. Ser. 112, 012003 (2008)]. The sensitivity of nonlinear Rayleigh-Taylor instability physics to ablation velocity is addressed with targets driven by indirect drive, with stronger ablative stabilization, and by direct drive, with weaker ablative stabilization. The indirect drive design demonstrates the potential to reach a two-dimensional bubble-merger regime with a 20 ns duration drive at moderate radiation temperature. The direct drive design achieves a 3 to 5 times increased acceleration distance for the sample in comparison to previous experiments allowing at least 2 more bubble generations when starting from a three-dimensional broadband spectrum.

Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

Energy Technology Data Exchange (ETDEWEB)

Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

2013-09-02

We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

1999-01-01

The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

The Changing Nonlinear Relationship between Income and Terrorism

Science.gov (United States)

Enders, Walter; Hoover, Gary A.

2014-01-01

This article reinvestigates the relationship between real per capita gross domestic product (GDP) and terrorism. We devise a terrorism Lorenz curve to show that domestic and transnational terrorist attacks are each more concentrated in middle-income countries, thereby suggesting a nonlinear income–terrorism relationship. Moreover, this point of concentration shifted to lower income countries after the rising influence of the religious fundamentalist and nationalist/separatist terrorists in the early 1990s. For transnational terrorist attacks, this shift characterized not only the attack venue but also the perpetrators’ nationality. The article then uses nonlinear smooth transition regressions to establish the relationship between real per capita GDP and terrorism for eight alternative terrorism samples, accounting for venue, perpetrators’ nationality, terrorism type, and the period. Our nonlinear estimates are shown to be favored over estimates using linear or quadratic income determinants of terrorism. These nonlinear estimates are robust to additional controls. PMID:28579636

An online re-linearization scheme suited for Model Predictive and Linear Quadratic Control

DEFF Research Database (Denmark)

Henriksen, Lars Christian; Poulsen, Niels Kjølstad

This technical note documents the equations for primal-dual interior-point quadratic programming problem solver used for MPC. The algorithm exploits the special structure of the MPC problem and is able to reduce the computational burden such that the computational burden scales with prediction...... horizon length in a linear way rather than cubic, which would be the case if the structure was not exploited. It is also shown how models used for design of model-based controllers, e.g. linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium points, making...

Quadratic programming with fuzzy parameters: A membership function approach

International Nuclear Information System (INIS)

Liu, S.-T.

2009-01-01

Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.

Structural Design Optimization On Thermally Induced Vibration

International Nuclear Information System (INIS)

Gu, Yuanxian; Chen, Biaosong; Zhang, Hongwu; Zhao, Guozhong

2002-01-01

The numerical method of design optimization for structural thermally induced vibration is originally studied in this paper and implemented in application software JIFEX. The direct and adjoint methods of sensitivity analysis for thermal induced vibration coupled with both linear and nonlinear transient heat conduction is firstly proposed. Based on the finite element method, the structural linear dynamics is treated simultaneously with coupled linear and nonlinear transient heat structural linear dynamics is treated simultaneously with coupled linear and nonlinear transient heat conduction. In the thermal analysis model, the nonlinear heat conduction considered is result from the radiation and temperature-dependent materials. The sensitivity analysis of transient linear and nonlinear heat conduction is performed with the precise time integration method. And then, the sensitivity analysis of structural transient dynamics is performed by the Newmark method. Both the direct method and the adjoint method are employed to derive the sensitivity equations of thermal vibration, and there are two adjoint vectors of structure and heat conduction respectively. The coupling effect of heat conduction on thermal vibration in the sensitivity analysis is particularly investigated. With coupling sensitivity analysis, the optimization model is constructed and solved by the sequential linear programming or sequential quadratic programming algorithm. The methods proposed have been implemented in the application software JIFEX of structural design optimization, and numerical examples are given to illustrate the methods and usage of structural design optimization on thermally induced vibration

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

Science.gov (United States)

Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F

2016-10-21

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Science.gov (United States)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-10-01

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Convergence Guaranteed Nonlinear Constraint Model Predictive Control via I/O Linearization

Directory of Open Access Journals (Sweden)

Xiaobing Kong

2013-01-01

Full Text Available Constituting reliable optimal solution is a key issue for the nonlinear constrained model predictive control. Input-output feedback linearization is a popular method in nonlinear control. By using an input-output feedback linearizing controller, the original linear input constraints will change to nonlinear constraints and sometimes the constraints are state dependent. This paper presents an iterative quadratic program (IQP routine on the continuous-time system. To guarantee its convergence, another iterative approach is incorporated. The proposed algorithm can reach a feasible solution over the entire prediction horizon. Simulation results on both a numerical example and the continuous stirred tank reactors (CSTR demonstrate the effectiveness of the proposed method.

Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions

International Nuclear Information System (INIS)

Hong-Bin, Zhang; Jian-Wei, Xia; Yong-Bin, Yu; Chuang-Yin, Dang

2010-01-01

This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions (pwLDIs) model of synchronisation error dynamics, then we design a switching (piecewise-linear) feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results

Thermoviscous Model Equations in Nonlinear Acoustics

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne

Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

A Novel Rational Design Method for Laminated Composite Structures Exhibiting Complex Geometrically Nonlinear Buckling Behaviour

DEFF Research Database (Denmark)

Lindgaard, Esben; Lund, Erik

2012-01-01

This paper presents a novel FEM-based approach for fiber angle optimal design of laminated composite structures exhibiting complicated nonlinear buckling behavior, thus enabling design of lighter and more cost-effective structures. The approach accounts for the geometrically nonlinear behavior of...

Stability in quadratic torsion theories

Energy Technology Data Exchange (ETDEWEB)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)

2017-11-15

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Stability in quadratic torsion theories

International Nuclear Information System (INIS)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado

2017-01-01

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Fitness analysis method for magnesium in drinking water with atomic absorption using quadratic curve calibration

Directory of Open Access Journals (Sweden)

Esteban Pérez-López

2014-11-01

Full Text Available Because of the importance of quantitative chemical analysis in research, quality control, sales of services and other areas of interest , and the limiting of some instrumental analysis methods for quantification with linear calibration curve, sometimes because the short linear dynamic ranges of the analyte, and sometimes by limiting the technique itself, is that there is a need to investigate a little more about the convenience of using quadratic curves for analytical quantification, which seeks demonstrate that it is a valid calculation model for chemical analysis instruments. To this was taken as an analysis method based on the technique and atomic absorption spectroscopy in particular a determination of magnesium in a sample of drinking water Tacares sector Northern Grecia, employing a nonlinear calibration curve and a curve specific quadratic behavior, which was compared with the test results obtained for the same analysis with a linear calibration curve. The results show that the methodology is valid for the determination referred to, with all confidence, since the concentrations are very similar, and as used hypothesis testing can be considered equal.

ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed

2014-01-01

In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

Science.gov (United States)

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

Science.gov (United States)

Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.

2017-12-01

Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.

An example in linear quadratic optimal control

NARCIS (Netherlands)

Weiss, George; Zwart, Heiko J.

1998-01-01

We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme

Radiotherapy treatment planning linear-quadratic radiobiology

CERN Document Server

Chapman, J Donald

2015-01-01

Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

Science.gov (United States)

El-Khoury, O.; Kim, C.; Shafieezadeh, A.; Hur, J. E.; Heo, G. H.

2015-06-01

This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion.

Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

International Nuclear Information System (INIS)

El-Khoury, O; Shafieezadeh, A; Hur, J E; Kim, C; Heo, G H

2015-01-01

This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion. (paper)

Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR

Directory of Open Access Journals (Sweden)

Dong Zhang

2017-03-01

Full Text Available This article presents a new fractional-order sliding mode control (FOSMC strategy based on a linear-quadratic regulator (LQR for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

Science.gov (United States)

Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

2018-03-01

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

Quadratic independence of coordinate functions of certain ...

Indian Academy of Sciences (India)

... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

Science.gov (United States)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Current interactions from the one-form sector of nonlinear higher-spin equations

Science.gov (United States)

Gelfond, O. A.; Vasiliev, M. A.

2018-06-01

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp ⁡ iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.

Synthesis of state observer and nonlinear output feedback controller design of AC machines

International Nuclear Information System (INIS)

Al-Tahir, Ali Abdul Razzaq

2016-01-01

The research work developed in this thesis has been mainly devoted to the observation and sensor-less control problems of electrical systems. Three major contributions have been carried out using the high - gain concept and output feedback adaptive nonlinear control for online UPS. In this thesis, we dealt with synthesis of sampled high - gain observers for nonlinear systems application to PMSMs and DFIGs. We particularly focus on two constraints: sampling effect and tracking unmeasured mechanical and magnetic state variables. The first contribution consists in a high gain observer design that performs a relatively accurate estimation of both mechanical and magnetic state variable using the available measurements on stator currents and voltages of PMSM. We propose a global exponential observer having state predictor for a class of nonlinear globally Lipschitz system. In second contribution, we proposed a novel non - standard HGO design for non-injective feedback relation application to variable speed DFIG based WPGS. Meanwhile, a reduced system model is analyzed, provided by observability test to check is it possible synthesis state observer for sensor-less control. In last contribution, an adaptive observer for states and parameters estimation are designed for a class of state - affine systems application to output feedback adaptive nonlinear control of three-phase AC/DC boost power converter for online UPS systems. Basically, the problem focused on cascade nonlinear adaptive controller that is developed making use Lyapunov theory. The parameters uncertainties are processed by the practical control laws under back-stepping design techniques with capacity of adaptation. (author)

On the nonlinear design of industrial arc spring dampers

DEFF Research Database (Denmark)

Lahriri, Said; Santos, Ilmar; Hartmann, Henning

2011-01-01

The objective of this paper is to present a numerical approach for analyzing parameter excited vibrations on a gas compressor, induced by the nonlinear characteristic of the arc spring feature of certain designs of squeeze film dampers, SFDs. The behavior of the journal is studied in preparation...

Designing a Robust Nonlinear Dynamic Inversion Controller for Spacecraft Formation Flying

Directory of Open Access Journals (Sweden)

Inseok Yang

2014-01-01

Full Text Available The robust nonlinear dynamic inversion (RNDI control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI. NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC. SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.

Robust fast controller design via nonlinear fractional differential equations.

Science.gov (United States)

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

On the Cauchy problem for nonlinear Schrödinger equations with rotation

KAUST Repository

Antonelli, Paolo; Marahrens, Daniel; Sparber, Christof

2011-01-01

We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable in fiuence in proving finite time blow-up in the focusing case.

On the Cauchy problem for nonlinear Schrödinger equations with rotation

KAUST Repository

Antonelli, Paolo

2011-10-01

We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable in fiuence in proving finite time blow-up in the focusing case.

Exact cancellation of quadratic divergences in top condensation models

International Nuclear Information System (INIS)

Blumhofer, A.

1995-01-01

We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))

Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

African Journals Online (AJOL)

Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

Realization and utilization of a harmonic light scattering experiment to select new molecules with great optical nonlinearity

International Nuclear Information System (INIS)

Dhenaut, Christophe

1995-01-01

Conception of new organic materials for nonlinear optics is generally driven by a molecular engineering approach. The usual technique for determining the quadratic hyper polarizability of designed molecules is the electric field induced second harmonic (EFISH) experiment. However this technique is limited to neutral molecules with a permanent dipole moment. We have realized an harmonic light scattering (HLS) experiment which allow the measurement of any kind of molecules, polar or non polar, neutral or ionic. Using this technique we have been able to demonstrate experimentally the validity of the octupole concept (molecules without dipole moment) which has been proposed recently. We have studied molecules corresponding to various octupolar geometries. Nonlinearities are found to be comparable to those of the best dipolar compounds. We have also investigated other molecular families with different symmetry such as polyenes, sub-phthalocyanines and phthalocyanines by EFISH and HLS techniques. We have confronted results obtained by the two experiments. It appears that these results are not easy to compare, the tensorial components accessible by each experiment being different. The two experiments seems complementary. HLS experiments allow the observation of a quadratic hyper polarizability for centrosymmetric molecules. This surprising observation could be explained by the contribution of a vibration al part to the hyper polarizability measured by HLS (but not present in EFISH). Interpretation of this dynamic process is still in progress. (author) [fr

On nonlinear control design for autonomous chaotic systems of integer and fractional orders

International Nuclear Information System (INIS)

Ahmad, Wajdi M.; Harb, Ahmad M.

2003-01-01

In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

Instantaneous nonlinear assessment of complex cardiovascular dynamics by Laguerre-Volterra point process models.

Science.gov (United States)

Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo

2013-01-01

We report an exemplary study of instantaneous assessment of cardiovascular dynamics performed using point-process nonlinear models based on Laguerre expansion of the linear and nonlinear Wiener-Volterra kernels. As quantifiers, instantaneous measures such as high order spectral features and Lyapunov exponents can be estimated from a quadratic and cubic autoregressive formulation of the model first order moment, respectively. Here, these measures are evaluated on heartbeat series coming from 16 healthy subjects and 14 patients with Congestive Hearth Failure (CHF). Data were gathered from the on-line repository PhysioBank, which has been taken as landmark for testing nonlinear indices. Results show that the proposed nonlinear Laguerre-Volterra point-process methods are able to track the nonlinear and complex cardiovascular dynamics, distinguishing significantly between CHF and healthy heartbeat series.

Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms

KAUST Repository

Carrillo, José A.

2016-09-22

In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large class of nonlinear continuity equations, whose dynamics are driven by internal energies, given external potentials and/or interaction energies. The solver is based on its variational formulation as a gradient flow with respect to the Wasserstein distance. Positivity of solutions as well as energy decrease of the semi-discrete scheme are guaranteed by its construction. We illustrate this property with various examples in spatial dimension one and two.

TS Fuzzy Model-Based Controller Design for a Class of Nonlinear Systems Including Nonsmooth Functions

DEFF Research Database (Denmark)

Vafamand, Navid; Asemani, Mohammad Hassan; Khayatiyan, Alireza

2018-01-01

This paper proposes a novel robust controller design for a class of nonlinear systems including hard nonlinearity functions. The proposed approach is based on Takagi-Sugeno (TS) fuzzy modeling, nonquadratic Lyapunov function, and nonparallel distributed compensation scheme. In this paper, a novel...... criterion, new robust controller design conditions in terms of linear matrix inequalities are derived. Three practical case studies, electric power steering system, a helicopter model and servo-mechanical system, are presented to demonstrate the importance of such class of nonlinear systems comprising...

Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearities.

Science.gov (United States)

Ulvila, Ville; Phillips, C R; Halonen, Lauri; Vainio, Markku

2013-11-01

We report optical frequency comb generation by a continuous-wave pumped optical parametric oscillator (OPO) without any active modulation. The OPO is configured as singly resonant with an additional nonlinear crystal (periodically poled MgO:LiNbO3) placed inside the OPO for phase mismatched second harmonic generation (SHG) of the resonating signal beam. The phase mismatched SHG causes cascading χ(2) nonlinearities, which can substantially increase the effective χ(3) nonlinearity in MgO:LiNbO3, leading to spectral broadening of the OPO signal beam via self-phase modulation. The OPO generates a stable 4 THz wide (-30 dB) frequency comb centered at 1.56 μm.

Quadratic tracer dynamical models tobacco growth

International Nuclear Information System (INIS)

Qiang Jiyi; Hua Cuncai; Wang Shaohua

2011-01-01

In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)

A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

International Nuclear Information System (INIS)

Ge, Gen; Li, ZePeng

2016-01-01

A modified stochastic averaging method on single-degree-of-freedom (SDOF) oscillators under white noise excitations with strongly nonlinearity was proposed. Considering the existing approach dealing with strongly nonlinear SDOFs derived by Zhu and Huang [14, 15] is quite time consuming in calculating the drift coefficient and diffusion coefficients and the expressions of them are considerable long, the so-called He's energy balance method was applied to overcome the minor defect of the Zhu and Huang's method. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much by giving an averaged frequency beforehand. Three examples, a cubic and quadratic nonlinearity coexisting oscillator, a quadratic nonlinear oscillator under external white noise excitations and an externally excited Duffing–Rayleigh oscillator, were given to illustrate the approach we proposed. The three examples were excited by the Gaussian white noise and the Gaussian colored noise separately. The stationary responses of probability density of amplitudes and energy, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems were also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

Science.gov (United States)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

Science.gov (United States)

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…

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

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

International Nuclear Information System (INIS)

Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

2014-01-01

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

Bound constrained quadratic programming via piecewise

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.

1999-01-01

of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...

Incorporation of amphiphilic ruthenium(II) ammine complexes into Langmuir-Blodgett thin films with switchable quadratic nonlinear optical behavior.

Science.gov (United States)

Boubekeur-Lecaque, Leïla; Coe, Benjamin J; Harris, James A; Helliwell, Madeleine; Asselberghs, Inge; Clays, Koen; Foerier, Stijn; Verbiest, Thierry

2011-12-19

Nine nonlinear optical (NLO) chromophores with pyridinium electron acceptors have been synthesized by complexing new proligands with {Ru(II)(NH(3))(5)}(2+) electron-donor centers. The presence of long alkyl/fluoroalkyl chain substituents imparts amphiphilic properties, and these cationic complexes have been characterized as their PF(6)(-) salts by using various techniques including electronic absorption spectroscopy and cyclic voltammetry. Each complex shows three reversible/quasireversible redox processes; a Ru(III/II) oxidation and two ligand-based reductions. The energies of the intense visible d → π* metal-to-ligand charge-transfer (MLCT) absorptions correlate to some extent with the ligand reduction potentials. (1)H NMR spectroscopy also provides insights into the relative electron-withdrawing strengths of the new ligands. Single crystal X-ray structures have been determined for two of the proligand salts and one complex salt, [Ru(II)(NH(3))(5)(4-C(16)H(33)PhQ(+))]Cl(3)·3.25H(2)O (PhQ(+) = N-phenyl-4,4'-bipyridinium), showing centrosymmetric packing structures in each case. The PF(6)(-) analogue of the latter complex has been used to deposit reproducibly high-quality, multilayered Langmuir-Blodgett (LB) thin films. These films show a strong second harmonic generation (SHG) response from a 1064 nm laser; their MLCT absorbance increases linearly with the number of layers (N) and I(2ω)/I(ω)(2) (I(2ω) = intensity at 532 nm; I(ω) = intensity at 1064 nm) scales quadratically with N, consistent with homogeneous deposition. LB films on indium tin oxide (ITO)-coated glass show electrochemically induced switching of the SHG response, with a decrease in activity of about 50% on Ru(II) → Ru(III) oxidation. This effect is reversible, but reproducible over only a few cycles before the signal from the Ru(II) species diminishes. This work extrapolates our original solution studies (Coe, B. J. et al. Angew. Chem., Int. Ed.1999, 38, 366) to the first demonstration of

Low cost metamodel for robust design of periodic nonlinear coupled micro-systems

Directory of Open Access Journals (Sweden)

Chikhaoui K.

2016-01-01

Full Text Available To achieve robust design, in presence of uncertainty, nonlinearity and structural periodicity, a metamodel combining the Latin Hypercube Sampling (LHS method for uncertainty propagation and an enriched Craig-Bampton Component Mode Synthesis approach (CB-CMS for model reduction is proposed. Its application to predict the time responses of a stochastic periodic nonlinear micro-system proves its efficiency in terms of accuracy and reduction of computational cost.

AUTOJOM, Quadratic Equation Coefficient for Conic Volume, Parallelepipeds, Wedges, Pyramids. JOMREAD, Check of 3-D Geometry Structure from Quadratic Surfaces

International Nuclear Information System (INIS)

2005-01-01

Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces

The stability of quadratic-reciprocal functional equation

Science.gov (United States)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

Nonlinearly driven harmonics of Alfvén modes

Science.gov (United States)

Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.

2014-01-01

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Nonlinearly driven harmonics of Alfvén modes

Energy Technology Data Exchange (ETDEWEB)

Zhang, B., E-mail: bozhang@austin.utexas.edu; Breizman, B. N.; Zheng, L. J.; Berk, H. L. [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)

2014-01-15

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Optimization strategies based on sequential quadratic programming applied for a fermentation process for butanol production.

Science.gov (United States)

Pinto Mariano, Adriano; Bastos Borba Costa, Caliane; de Franceschi de Angelis, Dejanira; Maugeri Filho, Francisco; Pires Atala, Daniel Ibraim; Wolf Maciel, Maria Regina; Maciel Filho, Rubens

2009-11-01

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.

PWR control system design using advanced linear and non-linear methodologies

International Nuclear Information System (INIS)

Rabindran, N.; Whitmarsh-Everiss, M.J.

2004-01-01

Consideration is here given to the methodology deployed for non-linear heuristic analysis in the time domain supported by multi-variable linear control system design methods for the purposes of operational dynamics and control system analysis. This methodology is illustrated by the application of structural singular value μ analysis to Pressurised Water Reactor control system design. (author)

Complex fluid network optimization and control integrative design based on nonlinear dynamic model

International Nuclear Information System (INIS)

Sui, Jinxue; Yang, Li; Hu, Yunan

2016-01-01

In view of distribution according to complex fluid network’s needs, this paper proposed one optimization computation method of the nonlinear programming mathematical model based on genetic algorithm. The simulation result shows that the overall energy consumption of the optimized fluid network has a decrease obviously. The control model of the fluid network is established based on nonlinear dynamics. We design the control law based on feedback linearization, take the optimal value by genetic algorithm as the simulation data, can also solve the branch resistance under the optimal value. These resistances can provide technical support and reference for fluid network design and construction, so can realize complex fluid network optimization and control integration design.

Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

International Nuclear Information System (INIS)

Khaki-Sedigh, A.; Yazdanpanah-Goharrizi, A.

2006-01-01

A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology

Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Khaki-Sedigh, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: sedigh@kntu.ac.ir; Yazdanpanah-Goharrizi, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: yazdanpanah@ee.kntu.ac.ir

2006-09-15

A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology.

Estimation of Synaptic Conductances in Presence of Nonlinear Effects Caused by Subthreshold Ionic Currents

DEFF Research Database (Denmark)

Vich, Catalina; Berg, Rune W.; Guillamon, Antoni

2017-01-01

Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo...... recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical...... models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures...

Robust optimal control design using a differential game approach for open-loop linear quadratic descriptor systems

NARCIS (Netherlands)

Musthofa, M.W.; Salmah, S.; Engwerda, Jacob; Suparwanto, A.

This paper studies the robust optimal control problem for descriptor systems. We applied differential game theory to solve the disturbance attenuation problem. The robust control problem was converted into a reduced ordinary zero-sum game. Within a linear quadratic setting, we solved the problem for

Wind turbine power tracking using an improved multimodel quadratic approach.

Science.gov (United States)

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. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Orthogonal and Scaling Transformations of Quadratic Functions with ...

African Journals Online (AJOL)

In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

Science.gov (United States)

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

Discrete oscillator design linear, nonlinear, transient, and noise domains

CERN Document Server

Rhea, Randall W

2014-01-01

Oscillators are an essential part of all spread spectrum, RF, and wireless systems, and today's engineers in the field need to have a firm grasp on how they are designed. Presenting an easy-to-understand, unified view of the subject, this authoritative resource covers the practical design of high-frequency oscillators with lumped, distributed, dielectric and piezoelectric resonators. Including numerous examples, the book details important linear, nonlinear harmonic balance, transient and noise analysis techniques. Moreover, the book shows you how to apply these techniques to a wide range of os

Nonlinear associations between plasma cholesterol levels and neuropsychological function.

Science.gov (United States)

Wendell, Carrington R; Zonderman, Alan B; Katzel, Leslie I; Rosenberger, William F; Plamadeala, Victoria V; Hosey, Megan M; Waldstein, Shari R

2016-11-01

Although both high and low levels of total and low-density lipoprotein (LDL) cholesterol have been associated with poor neuropsychological function, little research has examined nonlinear effects. We examined quadratic relations of cholesterol to performance on a comprehensive neuropsychological battery. Participants were 190 older adults (53% men, ages 54-83) free of major medical, neurologic, and psychiatric disease. Measures of fasting plasma total and high-density lipoprotein (HDL) cholesterol were assayed, and LDL cholesterol was calculated. Participants completed neuropsychological measures of attention, executive function, memory, visuospatial judgment, and manual speed and dexterity. Multiple regression analyses examined cholesterol levels as quadratic predictors of each measure of cognitive performance, with age (dichotomized as Reproduction II ( b = -.0020, p = .026) and log of the Trail Making Test, Part B (b = .0001, p = .044). Quadratic associations between HDL cholesterol and cognitive performance were nonsignificant. Results indicate differential associations between cholesterol and neuropsychological function across different ages and domains of function. High and low total and LDL cholesterol may confer both risk and benefit for suboptimal cognitive function at different ages. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

A Quadratic Spring Equation

Science.gov (United States)

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]…

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

Science.gov (United States)

van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

2017-12-01

A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

Hidden acoustic information revealed by intentional nonlinearity

Science.gov (United States)

Dowling, David R.

2017-11-01

Acoustic waves are omnipresent in modern life and are well described by the linearized equations of fluid dynamics. Once generated, acoustic waves carry and collect information about their source and the environment through which they propagate, respectively, and this information may be retrieved by analyzing recordings of these waves. Because of this, acoustics is the primary means for observation, surveillance, reconnaissance, and remote sensing in otherwise opaque environments, such as the Earth's oceans and crust, and the interior of the human body. For such information-retrieval tasks, acoustic fields are nearly always interrogated within their recorded frequency range or bandwidth. However, this frequency-range restriction is not general; acoustic fields may also carry (hidden) information at frequencies outside their bandwidth. Although such a claim may seem counter intuitive, hidden acoustic-field information can be revealed by re-introducing a marquee trait of fluid dynamics: nonlinearity. In particular, an intentional quadratic nonlinearity - a form of intra-signal heterodyning - can be used to obtain acoustic field information at frequencies outside a recorded acoustic field's bandwidth. This quadratic nonlinearity enables a variety of acoustic remote sensing applications that were long thought to be impossible. In particular, it allows the detrimental effects of sparse recordings and random scattering to be suppressed when the original acoustic field has sufficient bandwidth. In this presentation, the topic is developed heuristically, with a just brief exposition of the relevant mathematics. Hidden acoustic field information is then revealed from simulated and measured acoustic fields in simple and complicated acoustic environments involving frequencies from a few Hertz to more than 100 kHz, and propagation distances from tens of centimeters to hundreds of kilometers. Sponsored by ONR, NAVSEA, and NSF.

A nonlinear analytic function expansion nodal method for transient calculations

Energy Technology Data Exchange (ETDEWEB)

Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1999-12-31

The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)

A nonlinear analytic function expansion nodal method for transient calculations

Energy Technology Data Exchange (ETDEWEB)

Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1998-12-31

The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)

An Extension to a Filter Implementation of Local Quadratic Surface for Image Noise Estimation

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

1999-01-01

Based on regression analysis this paper gives a description for simple image filter design. Specifically 3x3 filter implementations of a quadratic surface, residuals from this surface, gradients and the Laplacian are given. For the residual a 5x5 filter is given also. It is shown that the 3x3......) it is concluded that if striping is to be considered as a part of the noise, the residual from a 3x3 median filter seems best. If we are interested in a salt-and-pepper noise estimator the proposed extension to the 3x3 filter for the residual from a quadratic surface seems best. Simple statistics...

Designing Non-linear Frequency Modulated Signals For Medical Ultrasound Imaging

DEFF Research Database (Denmark)

Gran, Fredrik; Jensen, Jørgen Arendt

2006-01-01

In this paper a new method for designing non-linear frequency modulated (NLFM) waveforms for ultrasound imaging is proposed. The objective is to control the amplitude spectrum of the designed waveform and still keep a constant transmit amplitude, so that the transmitted energy is maximized....... The signal-to-noise-ratio can in this way be optimized. The waveform design is based on least squares optimization. A desired amplitude spectrum is chosen, hereafter the phase spectrum is chosen, so that the instantaneous frequency takes on the form of a third order polynomial. The finite energy waveform...

Indirect quantum tomography of quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

2011-01-15

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

On orthogonality preserving quadratic stochastic operators

Energy Technology Data Exchange (ETDEWEB)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

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.

On orthogonality preserving quadratic stochastic operators

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-01-01

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

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite

Quadratic Twists of Rigid Calabi–Yau Threefolds Over

DEFF Research Database (Denmark)

Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko

2013-01-01

of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...

Application of H∞ control theory to power control of a nonlinear reactor model

International Nuclear Information System (INIS)

Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni

1993-01-01

The H∞ control theory is applied to the compensator design of a nonlinear nuclear reactor model, and the results are compared with standard linear quadratic Gaussian (LQG) control. The reactor model is assumed to be provided with a control rod drive system having the compensation of rod position feedback. The nonlinearity of the reactor model exerts a great influence on the stability of the control system, and hence, it is desirable for a power control system of a nuclear reactor to achieve robust stability and to improve the sensitivity of the feedback control system. A computer simulation based on a power control system synthesized by LQG control was performed revealing that the control system has some stationary offset and less stability. Therefore, here, attention is given to the development of a methodology for robust control that can withstand exogenous disturbances and nonlinearity in view of system parameter changes. The developed methodology adopts H∞ control theory in the feedback system and shows interesting features of robustness. The results of the computer simulation indicate that the feedback control system constructed by the developed H∞ compensator possesses sufficient robustness of control on the stability and disturbance attenuation, which are essential for the safe operation of a nuclear reactor

Heart Motion Prediction in Robotic-Assisted Beating Heart Surgery: A Nonlinear Fast Adaptive Approach

Directory of Open Access Journals (Sweden)

Fan Liang

2013-01-01

Full Text Available Off-pump Coronary Artery Bypass Graft (CABG surgery outperforms traditional on-pump surgery because the assisted robotic tools can alleviate the relative motion between the beating heart and robotic tools. Therefore, it is possible for the surgeon to operate on the beating heart and thus lessens post surgery complications for the patients. Due to the highly irregular and non-stationary nature of heart motion, it is critical that the beating heart motion is predicted in the model-based track control procedures. It is technically preferable to model heart motion in a nonlinear way because the characteristic analysis of 3D heart motion data through Bi-spectral analysis and Fourier methods demonstrates the involved nonlinearity of heart motion. We propose an adaptive nonlinear heart motion model based on the Volterra Series in this paper. We also design a fast lattice structure to achieve computational-efficiency for real-time online predictions. We argue that the quadratic term of the Volterra Series can improve the prediction accuracy by covering sharp change points and including the motion with sufficient detail. The experiment results indicate that the adaptive nonlinear heart motion prediction algorithm outperforms the autoregressive (AR and the time-varying Fourier-series models in terms of the root mean square of the prediction error and the prediction error in extreme cases.

Design and volume optimization of space structures

KAUST Repository

Jiang, Caigui; Tang, Chengcheng; Seidel, Hans-Peter; Wonka, Peter

2017-01-01

We study the design and optimization of statically sound and materially efficient space structures constructed by connected beams. We propose a systematic computational framework for the design of space structures that incorporates static soundness, approximation of reference surfaces, boundary alignment, and geometric regularity. To tackle this challenging problem, we first jointly optimize node positions and connectivity through a nonlinear continuous optimization algorithm. Next, with fixed nodes and connectivity, we formulate the assignment of beam cross sections as a mixed-integer programming problem with a bilinear objective function and quadratic constraints. We solve this problem with a novel and practical alternating direction method based on linear programming relaxation. The capability and efficiency of the algorithms and the computational framework are validated by a variety of examples and comparisons.

Design and volume optimization of space structures

KAUST Repository

Jiang, Caigui

2017-07-21

We study the design and optimization of statically sound and materially efficient space structures constructed by connected beams. We propose a systematic computational framework for the design of space structures that incorporates static soundness, approximation of reference surfaces, boundary alignment, and geometric regularity. To tackle this challenging problem, we first jointly optimize node positions and connectivity through a nonlinear continuous optimization algorithm. Next, with fixed nodes and connectivity, we formulate the assignment of beam cross sections as a mixed-integer programming problem with a bilinear objective function and quadratic constraints. We solve this problem with a novel and practical alternating direction method based on linear programming relaxation. The capability and efficiency of the algorithms and the computational framework are validated by a variety of examples and comparisons.

On Convex Quadratic Approximation

NARCIS (Netherlands)

den Hertog, D.; de Klerk, E.; Roos, J.

2000-01-01

In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

Nonlinear robust hierarchical control for nonlinear uncertain systems

Directory of Open Access Journals (Sweden)

Leonessa Alexander

1999-01-01

Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.

The Model and Quadratic Stability Problem of Buck Converter in DCM

Directory of Open Access Journals (Sweden)

Li Xiaojing

2016-01-01

Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.

Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates

International Nuclear Information System (INIS)

Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young

2010-01-01

Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters

Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channel's Nonlinear Controllers Design

Directory of Open Access Journals (Sweden)

Juing-Shian Chiou

2013-01-01

Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.

Superposition of elliptic functions as solutions for a large number of nonlinear equations

International Nuclear Information System (INIS)

Khare, Avinash; Saxena, Avadh

2014-01-01

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ 4 , the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn 2 (x, m), it also admits solutions in terms of dn 2 (x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations

Flaw characterization through nonlinear ultrasonics and wavelet cross-correlation algorithms

Science.gov (United States)

Bunget, Gheorghe; Yee, Andrew; Stewart, Dylan; Rogers, James; Henley, Stanley; Bugg, Chris; Cline, John; Webster, Matthew; Farinholt, Kevin; Friedersdorf, Fritz

2018-04-01

Ultrasonic measurements have become increasingly important non-destructive techniques to characterize flaws found within various in-service industrial components. The prediction of remaining useful life based on fracture analysis depends on the accurate estimation of flaw size and orientation. However, amplitude-based ultrasonic measurements are not able to estimate the plastic zones that exist ahead of crack tips. Estimating the size of the plastic zone is an advantage since some flaws may propagate faster than others. This paper presents a wavelet cross-correlation (WCC) algorithm that was applied to nonlinear analysis of ultrasonically guided waves (GW). By using this algorithm, harmonics present in the waveforms were extracted and nonlinearity parameters were used to indicate both the tip of the cracks and size of the plastic zone. B-scans performed with the quadratic nonlinearities were sensitive to micro-damage specific to plastic zones.

Linear Quadratic Controller with Fault Detection in Compact Disk Players

DEFF Research Database (Denmark)

Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.

2001-01-01

The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....

Nonlinear effects in dynamic analysis and design of nuclear power plant components: research status and needs

Energy Technology Data Exchange (ETDEWEB)

Stoykovich, M [Burns and Roe, Inc., New York (USA)

1978-10-01

This paper encompasses nonlinear effects in dynamic analysis and design of nuclear power plant facilities. The history of plasticity as a science is briefly discussed, and nonlinear cases of special interest are described. Approaches to some of the nonlinear problems are presented. These include the nonlinearity due to foundation-structure interaction associated with the base slab uplift during seismic disturbances, the nonlinear base-isolation system for the reduction of earthquake-generated forces and deformations of superstructures, nonlinear systems having restoring-force functions in case of gaps and liift-off conditions, and nonlinearity of viscoelastic systems due to inelastic deformations. Available computer programs information for the solution of various types of nonlinear problems are provided. Advantages and disadvantages of some of the nonlinear and linear analyses are discussed. Comparison of some nonlinear and linear results of analyses are presented. Conclusions are reached with regard to research status and recommendations for further studies and for performing non-linear analyses associated with the problems of nonlinearity are presented.

Nonlinear effects in dynamic analysis and design of nuclear power plant components: research status and needs

International Nuclear Information System (INIS)

Stoykovich, M.

1978-01-01

This paper encompasses nonlinear effects in dynamic analysis and design of nuclear power plant facilities. The history of plasticity as a science is briefly discussed, and nonlinear cases of special interest are described. Approaches to some of the nonlinear problems are presented. These include the nonlinearity due to foundation-structure interaction associated with the base slab uplift during seismic disturbances, the nonlinear base-isolation system for the reduction of earthquake-generated forces and deformations of superstructures, nonlinear systems having restoring-force functions in case of gaps and liift-off conditions, and nonlinearity of viscoelastic systems due to inelastic deformations. Available computer programs information for the solution of various types of nonlinear problems are provided. Advantages and disadvantages of some of the nonlinear and linear analyses are discussed. Comparison of some nonlinear and linear results of analyses are presented. Conclusions are reached with regard to research status and recommendations for further studies and for performing non-linear analyses associated with the problems of nonlinearity are presented. (Auth.)

Two-dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions. I. Gaussian-white case

NARCIS (Netherlands)

Steffen, T; Tanimura, Y

The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2002-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2003-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2004-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Linear quadratic optimization for positive LTI system

Science.gov (United States)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

Directory of Open Access Journals (Sweden)

Madjid Eshaghi Gordji

2012-01-01

Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.

Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1981-01-01

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

Comparison between linear quadratic and early time dose models

International Nuclear Information System (INIS)

Chougule, A.A.; Supe, S.J.

1993-01-01

During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs

Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

Science.gov (United States)

Lesmana, E.; Chaerani, D.; Khansa, H. N.

2018-03-01

Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

A comparative analysis of alternative approaches for quantifying nonlinear dynamics in cardiovascular system.

Science.gov (United States)

Chen, Yun; Yang, Hui

2013-01-01

Heart rate variability (HRV) analysis has emerged as an important research topic to evaluate autonomic cardiac function. However, traditional time and frequency-domain analysis characterizes and quantify only linear and stationary phenomena. In the present investigation, we made a comparative analysis of three alternative approaches (i.e., wavelet multifractal analysis, Lyapunov exponents and multiscale entropy analysis) for quantifying nonlinear dynamics in heart rate time series. Note that these extracted nonlinear features provide information about nonlinear scaling behaviors and the complexity of cardiac systems. To evaluate the performance, we used 24-hour HRV recordings from 54 healthy subjects and 29 heart failure patients, available in PhysioNet. Three nonlinear methods are evaluated not only individually but also in combination using three classification algorithms, i.e., linear discriminate analysis, quadratic discriminate analysis and k-nearest neighbors. Experimental results show that three nonlinear methods capture nonlinear dynamics from different perspectives and the combined feature set achieves the best performance, i.e., sensitivity 97.7% and specificity 91.5%. Collectively, nonlinear HRV features are shown to have the promise to identify the disorders in autonomic cardiovascular function.

Guises and disguises of quadratic divergences

Energy Technology Data Exchange (ETDEWEB)

Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

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.

PSQP: Puzzle Solving by Quadratic Programming.

Science.gov (United States)

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

Estimation of Synaptic Conductances in Presence of Nonlinear Effects Caused by Subthreshold Ionic Currents

Directory of Open Access Journals (Sweden)

Catalina Vich

2017-07-01

Full Text Available Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures for the models tested here.

Visualising the Roots of Quadratic Equations with Complex Coefficients

Science.gov (United States)

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…

EURDYN: computer programs for the nonlinear transient analysis of structures submitted to dynamic loading. EURDYN (Release 3): users' manual

International Nuclear Information System (INIS)

Halleux, J.P.

1983-01-01

The EURDYN computer codes are mainly designed for the simulation of nonlinear dynamic response of fast-reactor compoments submitted to impulse loading due to abnormal working conditions. Two releases of the structural computer codes EURDYN 01 (2-D beams and triangles and axisymmetric conical shells and triangular tores), 02 (axisymmetric and 2-D quadratic isoparametric elements) and 03 (triangular plate elements) have already been produced. They include material (elasto-plasticity using the classical flow theory approach) and geometrical (large displacements and rotations treated by a corotational technique) nonlinearities. The new features of Release 3 roughly consist in: full large strain capability for 9-node isoparametric elements, generalized array dimensions, introduction of the radial return algorithm for elasto-plastic material modelling, extension of the energy check facility to the case of prescribed displacements, and, possible interface to a post-processing package including time plot facilities

Frequency domain analysis and design of nonlinear systems based on Volterra series expansion a parametric characteristic approach

CERN Document Server

Jing, Xingjian

2015-01-01

This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain.  The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis a...

Scale-Invariant Rotating Black Holes in Quadratic Gravity

Directory of Open Access Journals (Sweden)

Guido Cognola

2015-07-01

Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.

Technical program to study the benefits of nonlinear analysis methods in LWR component designs. Technical report TR-3723-1

International Nuclear Information System (INIS)

Raju, P.P.

1980-05-01

This report summarizes the results of the study program to assess the benefits of nonlinear analysis methods in Light Water Reactor (LWR) component designs. The current study reveals that despite its increased cost and other complexities, nonlinear analysis is a practical and valuable tool for the design of LWR components, especially under ASME Level D service conditions (faulted conditions) and it will greatly assist in the evaluation of ductile fracture potential of pressure boundary components. Since the nonlinear behavior is generally a local phenomenon, the design of complex components can be accomplished through substructuring isolated localized regions and evaluating them in detail using nonlinear analysis methods

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

Science.gov (United States)

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

International Nuclear Information System (INIS)

Marquette, Ian

2011-01-01

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Geometric Approaches to Quadratic Equations from Other Times and Places.

Science.gov (United States)

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

Directory of Open Access Journals (Sweden)

Park Choonkil

2011-01-01

Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.

Fitness of the analysis method of magnesium in drinking water using atomic absorption with quadratic calibration curve

International Nuclear Information System (INIS)

Perez-Lopez, Esteban

2014-01-01

The quantitative chemical analysis has been importance in research. Also, aspects like: quality control, sales of services and other areas of interest. Some instrumental analysis methods for quantification with linear calibration curve have presented limitations, because the short liner dynamic ranges of the analyte, or sometimes, by limiting the technique itself. The need has been to investigate a little more about the convenience of using quadratic calibration curves for analytical quantification, with which it has seeked demonstrate that has been a valid calculation model for chemical analysis instruments. An analysis base method is used on the technique of atomic absorption spectroscopy and in particular a determination of magnesium in a drinking water sample of the Tacares sector North of Grecia. A nonlinear calibration curve was used and specifically a curve with quadratic behavior. The same was compared with the test results obtained for the equal analysis with a linear calibration curve. The results have showed that the methodology has been valid for the determination referred with all confidence, since the concentrations have been very similar and, according to the used hypothesis testing, can be considered equal. (author) [es

Quadratic function between arterial partial oxygen pressure and mortality risk in sepsis patients: an interaction with simplified acute physiology score.

Science.gov (United States)

Zhang, Zhongheng; Ji, Xuqing

2016-10-13

Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO 2 ) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO 2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO 2 and its interaction with other covariates were explored. A total of 199,125 PaO 2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO 2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO 2 on mortality risk was in quadratic form. There was significant interaction between PaO 2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO 2 on SOFA score was nonlinear. The study shows that the effect of PaO 2 on mortality risk is in quadratic function form, and there is significant interaction between PaO 2 and severity of illness.

Nonlinearly coupled dynamics of irregularities in the equatorial electrojet

Energy Technology Data Exchange (ETDEWEB)

Atul, J.K., E-mail: jkatulphysics@gmail.com [Department of Physics, College of Commerce under Magadh University, Patna 800020 (India); Sarkar, S. [FCIPT, Institute for Plasma Research, Gandhinagar 382428 (India); Singh, S.K. [Department of Physics, College of Commerce under Magadh University, Patna 800020 (India)

2016-04-01

Kinetic wave description is used to study the nonlinear influence of background Farley Buneman (FB) modes on the Gradient Drift (GD) modes in the equatorial electrojet ionosphere. The dominant nonlinearity is mediated through the electron flux term in the governing fluid equation which further invokes a turbulent current into the system. Electron dynamics reveals the modification in electron collision frequency and inhomogeneity scale length. It is seen that the propagation and growth rate of GD modes get modified by the background FB modes. Also, a new quasimode gets excited through the quadratic dispersion relation. Physical significance of coupled dynamics between the participating modes is also discussed. - Highlights: • Nonlinear influence of Farley Buneman mode on the Gradient drift mode, is investigated. • Electron collision frequency and density gradient scale length get modified. • A new quasimode gets excited due to the competition between these modes. • It seems to be important for modelling of Equatorial Electrojet current system.

Nonlinearly coupled dynamics of irregularities in the equatorial electrojet

International Nuclear Information System (INIS)

Atul, J.K.; Sarkar, S.; Singh, S.K.

2016-01-01

Kinetic wave description is used to study the nonlinear influence of background Farley Buneman (FB) modes on the Gradient Drift (GD) modes in the equatorial electrojet ionosphere. The dominant nonlinearity is mediated through the electron flux term in the governing fluid equation which further invokes a turbulent current into the system. Electron dynamics reveals the modification in electron collision frequency and inhomogeneity scale length. It is seen that the propagation and growth rate of GD modes get modified by the background FB modes. Also, a new quasimode gets excited through the quadratic dispersion relation. Physical significance of coupled dynamics between the participating modes is also discussed. - Highlights: • Nonlinear influence of Farley Buneman mode on the Gradient drift mode, is investigated. • Electron collision frequency and density gradient scale length get modified. • A new quasimode gets excited due to the competition between these modes. • It seems to be important for modelling of Equatorial Electrojet current system.

Nonlinear flow model for well production in an underground formation

Directory of Open Access Journals (Sweden)

J. C. Guo

2013-05-01

Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

Analysis of Students' Error in Learning of Quadratic Equations

Science.gov (United States)

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…

Quadratic hamiltonians and relativistic quantum mechanics

International Nuclear Information System (INIS)

Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

1981-01-01

For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

Science.gov (United States)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

Robust nonlinear control design with application to a marine cooling system

DEFF Research Database (Denmark)

Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon

2012-01-01

. In this context, we apply a bilinear transformation to obtain a well-posed H-inf problem. The design procedure is applied to a marine cooling system with flow dependent delays and performance of the resulting control design is evaluated through a simulation example where a comparison is made to a linear control......In this paper we consider design of control laws for a class of nonlinear systems with time-varying state delays by use of principles from feedback linearization. To deal with model uncertainties and delay mismatches, a robust linear H-inf controller is designed for the feedback linearized system...

Topological approximation of the nonlinear Anderson model

Science.gov (United States)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the

Lambda-lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, O.; Schultz, U.P.

2004-01-01

-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

Science.gov (United States)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Sketching the General Quadratic Equation Using Dynamic Geometry Software

Science.gov (United States)

Stols, G. H.

2005-01-01

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

Tangent Lines without Derivatives for Quadratic and Cubic Equations

Science.gov (United States)

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.)

A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures

Science.gov (United States)

Bednarcyk, Brett A.; Arnold, Steven M.

2012-01-01

A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.

Robust Control Design for Uncertain Nonlinear Dynamic Systems

Science.gov (United States)

Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.

2012-01-01

Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.

Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

Directory of Open Access Journals (Sweden)

S. Vaidyanathan

2013-09-01

Full Text Available This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B. In this work, a detailed qualitative analysis of the novel chaotic systems (A and (B has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE for the novel chaotic systems (A and (B has a large value, viz. for the system (A and for the system (B. Thus, both the novel chaotic systems (A and (B display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A, identical chaotic systems (B and nonidentical chaotic systems (A and (B with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A and (B have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A and (B, and also the adaptive synchronization results derived for the novel chaotic systems (A and (B.

Designs for thermal harvesting with nonlinear coordinate transformation

Science.gov (United States)

Ji, Qingxiang; Fang, Guodong; Liang, Jun

2018-04-01

In this paper a thermal concentrating design method was proposed based on the concept of generating function without knowing the needed coordinate transformation beforehand. The thermal harvesting performance was quantitatively characterized by heat concentrating efficiency and external temperature perturbation. Nonlinear transformations of different forms were employed to design high order thermal concentrators, and corresponding harvesting performances were investigated by numerical simulations. The numerical results shows that the form of coordinate transformation directly influences the distributions of heat flows inside the concentrator, consequently, influences the thermal harvesting behaviors significantly. The concentrating performance can be actively controlled and optimized by changing the form of coordinate transformations. The analysis in this paper offers a beneficial method to flexibly tune the harvesting performance of the thermal concentrator according to the requirements of practical applications.

Stiffness design of geometrically nonlinear structures using topology optimization

DEFF Research Database (Denmark)

Buhl, Thomas; Pedersen, Claus B. Wittendorf; Sigmund, Ole

2000-01-01

of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. A filtering scheme is used to obtain checkerboard-free and mesh-independent designs and a continuation approach improves convergence to efficient designs. Different objective......The paper deals with topology optimization of structures undergoing large deformations. The geometrically nonlinear behaviour of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. The sensitivities...... functions are tested. Minimizing compliance for a fixed load results in degenerated topologies which are very inefficient for smaller or larger loads. The problem of obtaining degenerated "optimal" topologies which only can support the design load is even more pronounced than for structures with linear...

Control Law Design for Twin Rotor MIMO System with Nonlinear Control Strategy

Directory of Open Access Journals (Sweden)

M. Ilyas

2016-01-01

Full Text Available Modeling of complex air vehicles is a challenging task due to high nonlinear behavior and significant coupling effect between rotors. Twin rotor multi-input multioutput system (TRMS is a laboratory setup designed for control experiments, which resembles a helicopter with unstable, nonlinear, and coupled dynamics. This paper focuses on the design and analysis of sliding mode control (SMC and backstepping controller for pitch and yaw angle control of main and tail rotor of the TRMS under parametric uncertainty. The proposed control strategy with SMC and backstepping achieves all mentioned limitations of TRMS. Result analysis of SMC and backstepping control schemes elucidates that backstepping provides efficient behavior with the parametric uncertainty for twin rotor system. Chattering and oscillating behaviors of SMC are removed with the backstepping control scheme considering the pitch and yaw angle for TRMS.

Design and development of a parametrically excited nonlinear energy harvester

International Nuclear Information System (INIS)

Yildirim, Tanju; Ghayesh, Mergen H.; Li, Weihua; Alici, Gursel

2016-01-01

Highlights: • A parametrically broadband energy harvester was fabricated. • Strong softening-type nonlinear behaviour was observed. • Experiments were conducted showing the large bandwidth of the device. - Abstract: An energy harvester has been designed, fabricated and tested based on the nonlinear dynamical response of a parametrically excited clamped-clamped beam with a central point-mass; magnets have been used as the central point-mass which pass through a coil when parametrically excited. Experiments have been conducted for the energy harvester when the system is excited (i) harmonically near the primary resonance; (ii) harmonically near the principal parametric resonance; (iii) by means of a non-smooth periodic excitation. An electrodynamic shaker was used to parametrically excite the system and the corresponding displacement of the magnet and output voltages of the coil were measured. It has been shown that the system displays linear behaviour at the primary resonance; however, at the principal parametric resonance, the motion characteristic of the magnet substantially changed displaying a strong softening-type nonlinearity. Theoretical simulations have also been conducted in order to verify the experimental results; the comparison between theory and experiment were within very good agreement of each other. The energy harvester developed in this paper is capable of harvesting energy close to the primary resonance as well as the principal parametric resonance; the frequency-band has been broadened significantly mainly due to the nonlinear effects as well as the parametric excitation.

Nonlinear Optical Imaging for Sensitive Detection of Crystals in Bulk Amorphous Powders

OpenAIRE

KESTUR, UMESH S.; WANAPUN, DUANGPORN; TOTH, SCOTT J.; WEGIEL, LINDSAY A.; SIMPSON, GARTH J.; TAYLOR, LYNNE S.

2012-01-01

The primary aim of this study was to evaluate the utility of second-order nonlinear imaging of chiral crystals (SONICC) to quantify crystallinity in drug–polymer blends, including solid dispersions. Second harmonic generation (SHG) can potentially exhibit scaling with crystallinity between linear and quadratic depending on the nature of the source, and thus, it is important to determine the response of pharmaceutical powders. Physical mixtures containing different proportions of crystalline n...

The quadratic reciprocity law a collection of classical proofs

CERN Document Server

Baumgart, Oswald

2015-01-01

This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

Supersymmetric construction of exactly solvable potentials and nonlinear algebras

International Nuclear Information System (INIS)

Junker, G.; Roy, P.

1998-01-01

Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and lowering operators of these harmonic oscillators and the SUSY operators we construct ladder operators for these new conditionally solvable systems. It is found that these ladder operators together with the Hamilton operator form a nonlinear algebra which is of quadratic and cubic type for the SUSY partners of the linear and radial harmonic oscillator

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

Science.gov (United States)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

Energy Technology Data Exchange (ETDEWEB)

Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science

1996-12-31

This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.

Three-dimensional nonlinear H-infinity guidance design and H-infinity-based pursuit-evasion game

Science.gov (United States)

Chen, Hsin-Yuan; Yang, Chi-Ching

2001-08-01

There are five features in this approach: (1) The complete nonlinear dynamics of the pursuit-evasion motion is considered in 3D spherical coordinate system. Neither linearization nor small signal assumptions are made. (2) The nonlinear H-infinity guidance design is derived analytically and expressed in a very simple form. (3) Unlike adaptive control concept, implementation of the proposed H(infinity ) guidance design does not need the information on target acceleration while ensuring acceptable intercept performance for arbitrary targets with the finite acceleration. (4) The derived guidance design exhibits strong robustness against variations in target acceleration. (5) Finally the issues related to the validation of the control law using Hardware In The Loop simulation are presented. The effects of the Flight Motion Simulator static and dynamic accuracies (time delay etc...) are discussed.

Practical design of a nonlinear tuned vibration absorber

DEFF Research Database (Denmark)

Grappasonni, C.; Habib, G.; Detroux, T.

2014-01-01

The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent oscillations. A nonlinear generalization of Den Hartog's equal-peak method is proposed to ensure equa...

ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima

2014-12-01

In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown parameters are also adapted to their values. Sufficient conditions for the stability of the adaptive observer error dynamics are derived in terms of linear matrix inequalities. Simulation results for chaotic Lorenz systems with unknown parameters in the presence of external perturbations are given to illustrate the effectiveness of our proposed approach. © 2014 IEEE.

On quadratic variation of martingales

Indian Academy of Sciences (India)

On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...

Quadratic prediction of factor scores

NARCIS (Netherlands)

Wansbeek, T

1999-01-01

Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

The regular indefinite linear-quadratic problem with linear endpoint constraints

NARCIS (Netherlands)

Soethoudt, J.M.; Trentelman, H.L.

1989-01-01

This paper deals with the infinite horizon linear-quadratic problem with indefinite cost. Given a linear system, a quadratic cost functional and a subspace of the state space, we consider the problem of minimizing the cost functional over all inputs for which the state trajectory converges to that

Joint nonlinearity effects in the design of a flexible truss structure control system

Science.gov (United States)

Mercadal, Mathieu

1986-01-01

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

Science.gov (United States)

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…

Eigenfunctions of quadratic hamiltonians in Wigner representation

International Nuclear Information System (INIS)

Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

1984-01-01

Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

Science.gov (United States)

Adams, Richard J.

1993-01-01

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

Estimation of bone Calcium-to-Phosphorous mass ratio using dual-energy nonlinear polynomial functions

International Nuclear Information System (INIS)

Sotiropoulou, P; Koukou, V; Martini, N; Nikiforidis, G; Michail, C; Kandarakis, I; Fountos, G; Kounadi, E

2015-01-01

In this study an analytical approximation of dual-energy inverse functions is presented for the estimation of the calcium-to-phosphorous (Ca/P) mass ratio, which is a crucial parameter in bone health. Bone quality could be examined by the X-ray dual-energy method (XDEM), in terms of bone tissue material properties. Low- and high-energy, log- intensity measurements were combined by using a nonlinear function, to cancel out the soft tissue structures and generate the dual energy bone Ca/P mass ratio. The dual-energy simulated data were obtained using variable Ca and PO 4 thicknesses on a fixed total tissue thickness. The XDEM simulations were based on a bone phantom. Inverse fitting functions with least-squares estimation were used to obtain the fitting coefficients and to calculate the thickness of each material. The examined inverse mapping functions were linear, quadratic, and cubic. For every thickness, the nonlinear quadratic function provided the optimal fitting accuracy while requiring relative few terms. The dual-energy method, simulated in this work could be used to quantify bone Ca/P mass ratio with photon-counting detectors. (paper)

The bounds of feasible space on constrained nonconvex quadratic programming

Science.gov (United States)

Zhu, Jinghao

2008-03-01

This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.

Nonlinear stability of source defects in the complex Ginzburg–Landau equation

International Nuclear Information System (INIS)

Beck, Margaret; Nguyen, Toan T; Sandstede, Björn; Zumbrun, Kevin

2014-01-01

In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction–diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the defect. In this paper, we rigorously establish nonlinear stability of spectrally stable source defects in the complex Ginzburg–Landau equation. Due to the outward transport at the far field, localized perturbations may lead to a highly non-localized response even on the linear level. To overcome this, we first investigate in detail the dynamics of the solution to the linearized equation. This allows us to determine an approximate solution that satisfies the full equation up to and including quadratic terms in the nonlinearity. This approximation utilizes the fact that the non-localized phase response, resulting from the embedded zero eigenvalues, can be captured, to leading order, by the nonlinear Burgers equation. The analysis is completed by obtaining detailed estimates for the resolvent kernel and pointwise estimates for Green's function, which allow one to close a nonlinear iteration scheme. (paper)

Remarks on second-order quadratic systems in algebras

Directory of Open Access Journals (Sweden)

Art Sagle

2017-10-01

Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.

A Linear Programming Reformulation of the Standard Quadratic Optimization Problem

NARCIS (Netherlands)

de Klerk, E.; Pasechnik, D.V.

2005-01-01

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially

Estimating sample size for a small-quadrat method of botanical ...

African Journals Online (AJOL)

Reports the results of a study conducted to determine an appropriate sample size for a small-quadrat method of botanical survey for application in the Mixed Bushveld of South Africa. Species density and grass density were measured using a small-quadrat method in eight plant communities in the Nylsvley Nature Reserve.

Quadratic divergences and dimensional regularisation

International Nuclear Information System (INIS)

Jack, I.; Jones, D.R.T.

1990-01-01

We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)

Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2004-01-01

A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...

Lotka-Volterra representation of general nonlinear systems.

Science.gov (United States)

Hernández-Bermejo, B; Fairén, V

1997-02-01

In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modeling forms of biological interest, such as S-systems or mass-action systems, are naturally embedded into the GLV form, which thus provides a formal framework for their comparison and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so and point at possible sources of ambiguity that could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.

Isotropy of quadratic forms

Indian Academy of Sciences (India)

V. Suresh University Of Hyderabad Hyderabad

2008-10-31

Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...

Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems

International Nuclear Information System (INIS)

Haber, E; Horesh, L; Tenorio, L

2010-01-01

Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data

Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras

Science.gov (United States)

Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal

2017-03-01

Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

Effect of nonlinear void reactivity on bifurcation characteristics of a lumped-parameter model of a BWR: A study relevant to RBMK

Energy Technology Data Exchange (ETDEWEB)

Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)

2017-04-15

Highlights: • A simplified model with nonlinear void reactivity feedback is studied. • Method of multiple scales for nonlinear analysis and oscillation characteristics. • Second order void reactivity dominates in determining system dynamics. • Opposing signs of linear and quadratic void reactivity enhances global safety. - Abstract: In the present work, the effect of nonlinear void reactivity on the dynamics of a simplified lumped-parameter model for a boiling water reactor (BWR) is investigated. A mathematical model of five differential equations comprising of neutronics and thermal-hydraulics encompassing the nonlinearities associated with both the reactivity feedbacks and the heat transfer process has been used. To this end, we have considered parameters relevant to RBMK for which the void reactivity is known to be nonlinear. A nonlinear analysis of the model exploiting the method of multiple time scales (MMTS) predicts the occurrence of the two types of Hopf bifurcation, namely subcritical and supercritical, leading to the evolution of limit cycles for a range of parameters. Numerical simulations have been performed to verify the analytical results obtained by MMTS. The study shows that the nonlinear reactivity has a significant influence on the system dynamics. A parametric study with varying nominal reactor power and operating conditions in coolant channel has also been performed which shows the effect of change in concerned parameter on the boundary between regions of sub- and super-critical Hopf bifurcations in the space constituted by the two coefficients of reactivities viz. the void and the Doppler coefficient of reactivities. In particular, we find that introduction of a negative quadratic term in the void reactivity feedback significantly increases the supercritical region and dominates in determining the system dynamics.

Synthesis of robust nonlinear autopilots using differential game theory

Science.gov (United States)

Menon, P. K. A.

1991-01-01

A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.

Adaptive Neural Networks Decentralized FTC Design for Nonstrict-Feedback Nonlinear Interconnected Large-Scale Systems Against Actuator Faults.

Science.gov (United States)

Li, Yongming; Tong, Shaocheng

The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small

New robust chaotic system with exponential quadratic term

International Nuclear Information System (INIS)

Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping

2008-01-01

This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)

Sex-specific nonlinear associations between serum lipids and different domains of cognitive function in middle to older age individuals.

Science.gov (United States)

Lu, Yanhui; An, Yu; Yu, Huanling; Che, Fengyuan; Zhang, Xiaona; Rong, Hongguo; Xi, Yuandi; Xiao, Rong

2017-08-01

To examine how serum lipids relates to specific cognitive ability domains between the men and women in Chinese middle to older age individuals. A complete lipid panel was obtained from 1444 individuals, ages 50-65, who also underwent a selection of cognitive tests. Participants were 584 men and 860 women from Linyi city, Shandong province. Multiple linear regression analyses examined serum lipids level as quadratic predictors of sex-specific measure of performance in different cognitive domains, which were adjusted for sociodemographic and lifestyle characteristics. In men, a significant quadratic effect of total cholesterol (TC) was identified for Digit Symbol (B = -0.081, P = 0.044) and also quadratic effect of low density lipoprotein-cholesterol (LDL-C) was identified for Trail Making Test B (B = -0.082, P = 0.045). Differently in women, there were significant quadratic associations between high density lipoprotein-cholesterol (HDL-C) and multiple neuropsychological tests. The nonlinear lipid-cognition associations differed between men and women and were specific to certain cognitive domains and might be of potential relevance for prevention and therapy of cognitive decline.

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

Science.gov (United States)

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…

Causal properties of nonlinear gravitational waves in modified gravity

Science.gov (United States)

Suvorov, Arthur George; Melatos, Andrew

2017-09-01

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial f (R ) gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial f (R ) gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient a2 of the Taylor expansion of f (R ) is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of a2. Anisotropic solutions are found, whose wave fronts trace out time- or spacelike hypersurfaces with complicated geometric properties. We show that the solutions exist in f (R ) theories that are consistent with Solar System and pulsar timing experiments.

Three dimensional nonlinear magnetic AdS solutions through topological defects

International Nuclear Information System (INIS)

Hendi, S.H.; Panah, B.E.; Momennia, M.; Panahiyan, S.

2015-01-01

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known Born-Infeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appears too. (orig.)

Quadratic Functionals with General Boundary Conditions

International Nuclear Information System (INIS)

Dosla, Z.; Dosly, O.

1997-01-01

The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions

Spatial statistics of pitting corrosion patterning: Quadrat counts and the non-homogeneous Poisson process

International Nuclear Information System (INIS)

Lopez de la Cruz, J.; Gutierrez, M.A.

2008-01-01

This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed

Quadratic stabilisability of multi-agent systems under switching topologies

Science.gov (United States)

Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long

2014-12-01

This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.

Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

Directory of Open Access Journals (Sweden)

Wei Xie

2007-01-01

Full Text Available A linear time-invariant (LTI output feedback controller is designed for a linear parameter-varying (LPV control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.

Temporal quadratic expansion nodal Green's function method

International Nuclear Information System (INIS)

Liu Cong; Jing Xingqing; Xu Xiaolin

2000-01-01

A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method

On wave-packet dynamics in a decaying quadratic potential

DEFF Research Database (Denmark)

Møller, Klaus Braagaard; Henriksen, Niels Engholm

1997-01-01

We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....

Burgers' turbulence problem with linear or quadratic external potential

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.

2005-01-01

We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....

Simulation-based optimal Bayesian experimental design for nonlinear systems

KAUST Repository

Huan, Xun

2013-01-01

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters.Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics. © 2012 Elsevier Inc.

Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

Science.gov (United States)

Pathak, H. K.; Grewal, A. S.

2002-01-01

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

Initial-value problem for the Gardner equation applied to nonlinear internal waves

Science.gov (United States)

Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

2017-04-01

The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of

Geometrical and Graphical Solutions of Quadratic Equations.

Science.gov (United States)

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)

Commuting quantum traces for quadratic algebras

International Nuclear Information System (INIS)

Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve

2005-01-01

Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians

A multiple kernel classification approach based on a Quadratic Successive Geometric Segmentation methodology with a fault diagnosis case.

Science.gov (United States)

Honório, Leonardo M; Barbosa, Daniele A; Oliveira, Edimar J; Garcia, Paulo A Nepomuceno; Santos, Murillo F

2018-03-01

This work presents a new approach for solving classification and learning problems. The Successive Geometric Segmentation technique is applied to encapsulate large datasets by using a series of Oriented Bounding Hyper Box (OBHBs). Each OBHB is obtained through linear separation analysis and each one represents a specific region in a pattern's solution space. Also, each OBHB can be seen as a data abstraction layer and be considered as an individual Kernel. Thus, it is possible by applying a quadratic discriminant function, to assemble a set of nonlinear surfaces separating each desirable pattern. This approach allows working with large datasets using high speed linear analysis tools and yet providing a very accurate non-linear classifier as final result. The methodology was tested using the UCI Machine Learning repository and a Power Transformer Fault Diagnosis real scenario problem. The results were compared with different approaches provided by literature and, finally, the potential and further applications of the methodology were also discussed. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

QUADrATiC: scalable gene expression connectivity mapping for repurposing FDA-approved therapeutics.

Science.gov (United States)

O'Reilly, Paul G; Wen, Qing; Bankhead, Peter; Dunne, Philip D; McArt, Darragh G; McPherson, Suzanne; Hamilton, Peter W; Mills, Ken I; Zhang, Shu-Dong

2016-05-04

Gene expression connectivity mapping has proven to be a powerful and flexible tool for research. Its application has been shown in a broad range of research topics, most commonly as a means of identifying potential small molecule compounds, which may be further investigated as candidates for repurposing to treat diseases. The public release of voluminous data from the Library of Integrated Cellular Signatures (LINCS) programme further enhanced the utilities and potentials of gene expression connectivity mapping in biomedicine. We describe QUADrATiC ( http://go.qub.ac.uk/QUADrATiC ), a user-friendly tool for the exploration of gene expression connectivity on the subset of the LINCS data set corresponding to FDA-approved small molecule compounds. It enables the identification of compounds for repurposing therapeutic potentials. The software is designed to cope with the increased volume of data over existing tools, by taking advantage of multicore computing architectures to provide a scalable solution, which may be installed and operated on a range of computers, from laptops to servers. This scalability is provided by the use of the modern concurrent programming paradigm provided by the Akka framework. The QUADrATiC Graphical User Interface (GUI) has been developed using advanced Javascript frameworks, providing novel visualization capabilities for further analysis of connections. There is also a web services interface, allowing integration with other programs or scripts. QUADrATiC has been shown to provide an improvement over existing connectivity map software, in terms of scope (based on the LINCS data set), applicability (using FDA-approved compounds), usability and speed. It offers potential to biological researchers to analyze transcriptional data and generate potential therapeutics for focussed study in the lab. QUADrATiC represents a step change in the process of investigating gene expression connectivity and provides more biologically-relevant results than

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

Directory of Open Access Journals (Sweden)

Weiss Mathieu

2015-01-01

Full Text Available This work deals with the design and experiment of a cubic nonlinear energy sink (NES for horizontal vibration mitigation of a bridge cable. Modal analysis of horizontal linear modes of the cable is experimentally performed using accelerometers and displacement sensors. A theoretical simplified 2-dof model of the coupled cable-NES system is used to analytically design the NES by mean of multi-time scale systems behaviours and detection its invariant manifold, equilibrium and singular points which stand for periodic and strongly modulated regimes, respectively. Numerical integration is used to confirm the efficiency of the designed NES for the system under step release excitation. Then, the prototype system is built using geometrical cubic nonlinearity as the potential of the NES. Efficiency of the prototype system for mitigation of horizontal vibrations of the cable under for step release and forced excitations is experimentally demonstrated.

Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces

International Nuclear Information System (INIS)

Oyewumi, K.A.; Bangudu, E.A.

2003-01-01

Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential were discussed. The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution. Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained. These are dimensionally dependent. The dependence of radial solution on the dimensions or potential strength and the degeneracy of the energy levels are discussed. (author)

Assessing robustness of designs for random effects parameters for nonlinear mixed-effects models.

Science.gov (United States)

Duffull, Stephen B; Hooker, Andrew C

2017-12-01

Optimal designs for nonlinear models are dependent on the choice of parameter values. Various methods have been proposed to provide designs that are robust to uncertainty in the prior choice of parameter values. These methods are generally based on estimating the expectation of the determinant (or a transformation of the determinant) of the information matrix over the prior distribution of the parameter values. For high dimensional models this can be computationally challenging. For nonlinear mixed-effects models the question arises as to the importance of accounting for uncertainty in the prior value of the variances of the random effects parameters. In this work we explore the influence of the variance of the random effects parameters on the optimal design. We find that the method for approximating the expectation and variance of the likelihood is of potential importance for considering the influence of random effects. The most common approximation to the likelihood, based on a first-order Taylor series approximation, yields designs that are relatively insensitive to the prior value of the variance of the random effects parameters and under these conditions it appears to be sufficient to consider uncertainty on the fixed-effects parameters only.

Low-power implementation of polyphase filters in Quadratic Residue Number System

DEFF Research Database (Denmark)

Cardarilli, Gian Carlo; Re, Andrea Del; Nannarelli, Alberto

2004-01-01

The aim of this work is the reduction of the power dissipated in digital filters, while maintaining the timing unchanged. A polyphase filter bank in the Quadratic Residue Number System (QRNS) has been implemented and then compared, in terms of performance, area, and power dissipation...... to the implementation of a polyphase filter bank in the traditional two's complement system (TCS). The resulting implementations, designed to have the same clock rates, show that the QRNS filter is smaller and consumes less power than the TCS one....

Design and Optimisation Strategies of Nonlinear Dynamics for Diffraction Limited Synchrotron Light Source

CERN Document Server

Bartolini, R.

2016-01-01

This paper introduces the most recent achievements in the control of nonlinear dynamics in electron synchrotron light sources, with special attention to diffraction limited storage rings. Guidelines for the design and optimization of the magnetic lattice are reviewed and discussed.

The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system

International Nuclear Information System (INIS)

Li, Chengzhi; Llibre, Jaume

2009-01-01

We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles

Nonlinear machine learning and design of reconfigurable digital colloids.

Science.gov (United States)

Long, Andrew W; Phillips, Carolyn L; Jankowksi, Eric; Ferguson, Andrew L

2016-09-14

Digital colloids, a cluster of freely rotating "halo" particles tethered to the surface of a central particle, were recently proposed as ultra-high density memory elements for information storage. Rational design of these digital colloids for memory storage applications requires a quantitative understanding of the thermodynamic and kinetic stability of the configurational states within which information is stored. We apply nonlinear machine learning to Brownian dynamics simulations of these digital colloids to extract the low-dimensional intrinsic manifold governing digital colloid morphology, thermodynamics, and kinetics. By modulating the relative size ratio between halo particles and central particles, we investigate the size-dependent configurational stability and transition kinetics for the 2-state tetrahedral (N = 4) and 30-state octahedral (N = 6) digital colloids. We demonstrate the use of this framework to guide the rational design of a memory storage element to hold a block of text that trades off the competing design criteria of memory addressability and volatility.

Quadratic contributions of softly broken supersymmetry in the light of loop regularization

Energy Technology Data Exchange (ETDEWEB)

Bai, Dong [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China); Wu, Yue-Liang [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China)

2017-09-15

Loop regularization (LORE) is a novel regularization scheme in modern quantum field theories. It makes no change to the spacetime structure and respects both gauge symmetries and supersymmetry. As a result, LORE should be useful in calculating loop corrections in supersymmetry phenomenology. To further demonstrate its power, in this article we revisit in the light of LORE the old issue of the absence of quadratic contributions (quadratic divergences) in softly broken supersymmetric field theories. It is shown explicitly by Feynman diagrammatic calculations that up to two loops the Wess-Zumino model with soft supersymmetry breaking terms (WZ' model), one of the simplest models with the explicit supersymmetry breaking, is free of quadratic contributions. All the quadratic contributions cancel with each other perfectly, which is consistent with results dictated by the supergraph techniques. (orig.)

On quadratic residue codes and hyperelliptic curves

Directory of Open Access Journals (Sweden)

David Joyner

2008-01-01

Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''

Modeling and Designing of A Nonlineartemperature-Humidity Controller Using Inmushroom-Drying Machine

Science.gov (United States)

Wu, Xiuhua; Luo, Haiyan; Shi, Minhui

Drying-process of many kinds of farm produce in a close room, such as mushroom-drying machine, is generally a complicated nonlinear and timedelay cause, in which the temperature and the humidity are the main controlled elements. The accurate controlling of the temperature and humidity is always an interesting problem. It's difficult and very important to make a more accurate mathematical model about the varying of the two. A math model was put forward after considering many aspects and analyzing the actual working circumstance in this paper. Form the model it can be seen that the changes of temperature and humidity in drying machine are not simple linear but an affine nonlinear process. Controlling the process exactly is the key that influences the quality of the dried mushroom. In this paper, the differential geometry theories and methods are used to analyze and solve the model of these smallenvironment elements. And at last a kind of nonlinear controller which satisfied the optimal quadratic performance index is designed. It can be proved more feasible and practical than the conventional controlling.

On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

KAUST Repository

Lima, Ricardo

2016-06-16

This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York

On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

KAUST Repository

Lima, Ricardo; Grossmann, Ignacio E.

2016-01-01

This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York

Projection of curves on B-spline surfaces using quadratic reparameterization

KAUST Repository

Yang, Yijun

2010-09-01

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is T-G 1 continuous, where T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm. © 2010 Elsevier Inc. All rights reserved.

Solving symmetric-definite quadratic lambda-matrix problems without factorization

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1982-01-01

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda 2 C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented

Nonlinear Disturbance Attenuation Controller for Turbo-Generators in Power Systems via Recursive Design

NARCIS (Netherlands)

Cao, M.; Shen, T.L.; Song, Y.H.; Mei, S.W.

2002-01-01

The paper proposes a nonlinear robust controller for steam governor control in power systems. Based on dissipation theory, an innovative recursive design method is presented to construct the storage function of single machine infinite bus (SMIB) and multi-machine power systems. Furthermore, the

Nonlinear Finite Element Analysis of Reinforced Concrete Shells

Directory of Open Access Journals (Sweden)

Mustafa K. Ahmed

2013-05-01

Full Text Available This investigation is to develop a numerical model suitable for nonlinear analysis of reinforced concrete shells. A nine-node Lagrangian element Figure (1 with enhanced shear interpolation will be used in this study. Table (1 describes shape functions and their derivatives of this element.An assumed transverse shear strain is used in the formulation of this element to overcome shear locking. Degenerated quadratic thick plate elements employing a layered discrelization through the thickness will be adopted. Different numbers of layers for different thickness can be used per element. A number of layers between (6 and 10 have proved to be appropriate to represent the nonlinear material behavior in structures. In this research 8 layers will be adequate. Material nonlinearities due to cracking of concrete, plastic flow or crushing of concrete in compression and yield condition of reinforcing steel are considered. The maximum tensile strength is used as a criterion for crack initiation. Attention is given to the tension stiffening phenomenon and the degrading effect of cracking on the compressive and shear strength of concrete. Perfect bond between concrete and steel is assumed. Attention is given also to geometric nonlinearities. An example have been chosen in order to demonstrate the suitability of the models by comparing the predicted behaviour with the experimental results for shell exhibiting various modes of failure.

Schur Stability Regions for Complex Quadratic Polynomials

Science.gov (United States)

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.)

Concrete damage diagnosed using the non-classical nonlinear acoustic method

International Nuclear Information System (INIS)

Dao, Zhou; Xiao-Zhou, Liu; Xiu-Fen, Gong; E, Nazarov V; Li, Ma

2009-01-01

It is known that the strength of concrete is seriously affected by damage and cracking. In this paper, six concrete samples under different damage levels are studied. The experimental results show a linear dependence of the resonance frequency shift on strain amplitude at the fundamental frequency, and approximate quadratic dependence of the amplitudes of the second and third harmonics on strain amplitude at the fundamental frequency as well. In addition, the amplitude of the third harmonics is shown to increase with the increase of damage level, which is even higher than that of the second harmonics in samples with higher damage levels. These are three properties of non-classical nonlinear acoustics. The nonlinear parameters increase from 10 6 to 10 8 with damage level, and are more sensitive to the damage level of the concrete than the linear parameters obtained by using traditional acoustics methods. So, this method based on non-classical nonlinear acoustics may provide a better means of non-destructive testing (NDT) of concrete and other porous materials

A Novel Single Switch Transformerless Quadratic DC/DC Buck-Boost Converter

DEFF Research Database (Denmark)

Mostaan, Ali; A. Gorji, Saman; N. Soltani, Mohsen

2017-01-01

A novel quadratic buck-boost DC/DC converter is presented in this study. The proposed converter utilizes only one active switch and can step-up/down the input voltage, while the existing single switch quadratic buck/boost converters can only work in step-up or step-down mode. First, the proposed ...

Multi-linear model set design based on the nonlinearity measure and H-gap metric.

Science.gov (United States)

Shaghaghi, Davood; Fatehi, Alireza; Khaki-Sedigh, Ali

2017-05-01

This paper proposes a model bank selection method for a large class of nonlinear systems with wide operating ranges. In particular, nonlinearity measure and H-gap metric are used to provide an effective algorithm to design a model bank for the system. Then, the proposed model bank is accompanied with model predictive controllers to design a high performance advanced process controller. The advantage of this method is the reduction of excessive switch between models and also decrement of the computational complexity in the controller bank that can lead to performance improvement of the control system. The effectiveness of the method is verified by simulations as well as experimental studies on a pH neutralization laboratory apparatus which confirms the efficiency of the proposed algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

On nonlinear dynamics and control of a robotic arm with chaos

Directory of Open Access Journals (Sweden)

Felix J. L. P.

2014-01-01

Full Text Available In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC and the optimal linear feedback control (OLFC. The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.

Measurement of quadratic electrogyration effect in castor oil

Science.gov (United States)

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.

On a quadratic inverse eigenvalue problem

International Nuclear Information System (INIS)

Cai, Yunfeng; Xu, Shufang

2009-01-01

This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas

International Nuclear Information System (INIS)

Perelomova, A.

2010-01-01

Two dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place, are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into thermal mode and internal vibrational degrees of freedom of a relaxing gas. The final dynamic equations are instantaneous; they include a quadratic nonlinear acoustic source, reflecting the nonlinear character of interaction of low-frequency acoustic and non-acoustic motions of the fluid. All types of sound, periodic or aperiodic, may serve as an acoustic source of both phenomena. The low-frequency sound is considered in this study. Some conclusions about temporal behavior of non-acoustic modes caused by periodic and aperiodic sound are made. Under certain conditions, acoustic cooling takes place instead of heating. (author)

Large N saddle formulation of quadratic building block theories

International Nuclear Information System (INIS)

Halpern, M.B.

1980-01-01

I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)

A penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography.

Science.gov (United States)

Shang, Shang; Bai, Jing; Song, Xiaolei; Wang, Hongkai; Lau, Jaclyn

2007-01-01

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

The Quadratic Selective Travelling Salesman Problem

DEFF Research Database (Denmark)

Thomadsen, Tommy; Stidsen, Thomas K.

2003-01-01

A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

On Quadratic Variation of Martingales

Indian Academy of Sciences (India)

where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

LQG Controller Design for Pitch Regulated Variable Speed Wind Turbine

DEFF Research Database (Denmark)

Imran, Raja Muhammed; Hussain, Dil Muhammad Akbar; Chen, Zhe

2014-01-01

Variable speed wind turbine is a complex and nonlinear system, a sophisticated control is required to meet the challenges posed by these systems. This paper is presenting a pitch regulation strategy based on LQG (Linear Quadratic Gaussian) to regulate turbine at its rated power and to reject...

Optimum Design of a Nonlinear Vibration Absorber Coupled to a Resonant Oscillator: A Case Study

Directory of Open Access Journals (Sweden)

H. F. Abundis-Fong

2018-01-01

Full Text Available This paper presents the optimal design of a passive autoparametric cantilever beam vibration absorber for a linear mass-spring-damper system subject to harmonic external force. The design of the autoparametric vibration absorber is obtained by using an approximation of the nonlinear frequency response function, computed via the multiple scales method. Based on the solution given by the perturbation method mentioned above, a static optimization problem is formulated in order to determine the optimum parameters (mass and length of the nonlinear absorber which minimizes the steady state amplitude of the primary mass under resonant conditions; then, a PZT actuator is cemented to the base of the beam, so the nonlinear absorber is made active, thus enabling the possibility of controlling the effective stiffness associated with the passive absorber and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty. Finally, some simulations and experimental results are included to validate and illustrate the dynamic performance of the overall system.

On Mixed Data and Event Driven Design for Adaptive-Critic-Based Nonlinear $H_{\\infty}$ Control.

Science.gov (United States)

Wang, Ding; Mu, Chaoxu; Liu, Derong; Ma, Hongwen

2018-04-01

In this paper, based on the adaptive critic learning technique, the control for a class of unknown nonlinear dynamic systems is investigated by adopting a mixed data and event driven design approach. The nonlinear control problem is formulated as a two-player zero-sum differential game and the adaptive critic method is employed to cope with the data-based optimization. The novelty lies in that the data driven learning identifier is combined with the event driven design formulation, in order to develop the adaptive critic controller, thereby accomplishing the nonlinear control. The event driven optimal control law and the time driven worst case disturbance law are approximated by constructing and tuning a critic neural network. Applying the event driven feedback control, the closed-loop system is built with stability analysis. Simulation studies are conducted to verify the theoretical results and illustrate the control performance. It is significant to observe that the present research provides a new avenue of integrating data-based control and event-triggering mechanism into establishing advanced adaptive critic systems.

Nonlinear magnetoelectric effect and magnetostriction in piezoelectric CsCuCl{sub 3} in paramagnetic and antiferromagnetic states

Energy Technology Data Exchange (ETDEWEB)

Kharkovskiy, A. I., E-mail: akharkovskiy@inbox.ru [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland); L.F. Vereshchagin Institute for High Pressure Physics RAS, 142190 Troitsk, Moscow (Russian Federation); Shaldin, Yu. V. [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland); Institute for Crystallography RAS, Lenin' s Avenue 59, 119333 Moscow (Russian Federation); Nizhankovskii, V. I. [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland)

2016-01-07

The direct nonlinear magnetoelectric (ME) effect and the magnetostriction of piezoelectric CsCuCl{sub 3} single crystals were comprehensively studied over a wide temperature range in stationary magnetic fields of up to 14 T. The direct nonlinear ME effect measurements were also performed in pulsed magnetic fields up to 31 T, at liquid helium temperature in the antiferromagnetic (AF) state for the crystallographic direction in which effect has the maximum value. The nonlinear ME effect was quadratic in the paramagnetic state for the whole range of magnetic fields. In the AF state the phase transition between different configurations of spins manifested itself as plateau-like peculiarity on the nonlinear ME effect. The nonlinear ME effect was saturated by the phase transition to the spin-saturated paramagnetic state. Two contributions to the nonlinear ME effects in CsCuCl{sub 3} were extracted from the experimental data: the intrinsic ME effect originated from the magnetoelectric interactions, and the extrinsic one, which resulted from a magnetostriction-induced piezoelectric effect.

Quantum tomography and classical propagator for quadratic quantum systems

International Nuclear Information System (INIS)

Man'ko, O.V.

1999-03-01

The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)

Nonlinear reflection of shock shear waves in soft elastic media.

Science.gov (United States)

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

Photon attenuation correction technique in SPECT based on nonlinear optimization

International Nuclear Information System (INIS)

Suzuki, Shigehito; Wakabayashi, Misato; Okuyama, Keiichi; Kuwamura, Susumu

1998-01-01

Photon attenuation correction in SPECT was made using a nonlinear optimization theory, in which an optimum image is searched so that the sum of square errors between observed and reprojected projection data is minimized. This correction technique consists of optimization and step-width algorithms, which determine at each iteration a pixel-by-pixel directional value of search and its step-width, respectively. We used the conjugate gradient and quasi-Newton methods as the optimization algorithm, and Curry rule and the quadratic function method as the step-width algorithm. Statistical fluctuations in the corrected image due to statistical noise in the emission projection data grew as the iteration increased, depending on the combination of optimization and step-width algorithms. To suppress them, smoothing for directional values was introduced. Computer experiments and clinical applications showed a pronounced reduction in statistical fluctuations of the corrected image for all combinations. Combinations using the conjugate gradient method were superior in noise characteristic and computation time. The use of that method with the quadratic function method was optimum if noise property was regarded as important. (author)

Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique

Directory of Open Access Journals (Sweden)

Zulqurnain Sabir

2014-06-01

Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

Science.gov (United States)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

Science.gov (United States)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem

NARCIS (Netherlands)

de Klerk, E.; Sotirov, R.

2007-01-01

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,

Methods of using the quadratic assignment problem solution

Directory of Open Access Journals (Sweden)

Izabela Kudelska

2012-09-01

Full Text Available Background: Quadratic assignment problem (QAP is one of the most interesting of combinatorial optimization. Was presented by Koopman and Beckamanna in 1957, as a mathematical model of the location of indivisible tasks. This problem belongs to the class NP-hard issues. This forces the application to the solution already approximate methods for tasks with a small size (over 30. Even though it is much harder than other combinatorial optimization problems, it enjoys wide interest because it models the important class of decision problems. Material and methods: The discussion was an artificial intelligence tool that allowed to solve the problem QAP, among others are: genetic algorithms, Tabu Search, Branch and Bound. Results and conclusions: QAP did not arise directly as a model for certain actions, but he found its application in many areas. Examples of applications of the problem is: arrangement of buildings on the campus of the university, layout design of electronic components in systems with large scale integration (VLSI, design a hospital, arrangement of keys on the keyboard.

Dynamics of a new family of iterative processes for quadratic polynomials

Science.gov (United States)

Gutiérrez, J. M.; Hernández, M. A.; Romero, N.

2010-03-01

In this work we show the presence of the well-known Catalan numbers in the study of the convergence and the dynamical behavior of a family of iterative methods for solving nonlinear equations. In fact, we introduce a family of methods, depending on a parameter . These methods reach the order of convergence m+2 when they are applied to quadratic polynomials with different roots. Newton's and Chebyshev's methods appear as particular choices of the family appear for m=0 and m=1, respectively. We make both analytical and graphical studies of these methods, which give rise to rational functions defined in the extended complex plane. Firstly, we prove that the coefficients of the aforementioned family of iterative processes can be written in terms of the Catalan numbers. Secondly, we make an incursion into its dynamical behavior. In fact, we show that the rational maps related to these methods can be written in terms of the entries of the Catalan triangle. Next we analyze its general convergence, by including some computer plots showing the intricate structure of the Universal Julia sets associated with the methods.

Quadratic time dependent Hamiltonians and separation of variables

International Nuclear Information System (INIS)

Anzaldo-Meneses, A.

2017-01-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.

Design automation for integrated nonlinear logic circuits (Conference Presentation)

Science.gov (United States)

Van Vaerenbergh, Thomas; Pelc, Jason; Santori, Charles; Bose, Ranojoy; Kielpinski, Dave; Beausoleil, Raymond G.

2016-05-01

A key enabler of the IT revolution of the late 20th century was the development of electronic design automation (EDA) tools allowing engineers to manage the complexity of electronic circuits with transistor counts now reaching into the billions. Recently, we have been developing large-scale nonlinear photonic integrated logic circuits for next generation all-optical information processing. At this time a sufficiently powerful EDA-style software tool chain to design this type of complex circuits does not yet exist. Here we describe a hierarchical approach to automating the design and validation of photonic integrated circuits, which can scale to several orders of magnitude higher complexity than the state of the art. Most photonic integrated circuits developed today consist of a small number of components, and only limited hierarchy. For example, a simple photonic transceiver may contain on the order of 10 building-block components, consisting of grating couplers for photonic I/O, modulators, and signal splitters/combiners. Because this is relatively easy to lay out by hand (or simple script) existing photonic design tools have relatively little automation in comparison to electronics tools. But demonstrating all-optical logic will require significantly more complex photonic circuits containing up to 1,000 components, hence becoming infeasible to design manually. Our design framework is based off Python-based software from Luceda Photonics which provides an environment to describe components, simulate their behavior, and export design files (GDS) to foundries for fabrication. At a fundamental level, a photonic component is described as a parametric cell (PCell) similarly to electronics design. PCells are described by geometric characteristics of their layout. A critical part of the design framework is the implementation of PCells as Python objects. PCell objects can then use inheritance to simplify design, and hierarchical designs can be made by creating composite

Staff turnover in hotels : exploring the quadratic and linear relationships.

OpenAIRE

Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.

2015-01-01

The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....

The mechanical properties of high speed GTAW weld and factors of nonlinear multiple regression model under external transverse magnetic field

Science.gov (United States)

Lu, Lin; Chang, Yunlong; Li, Yingmin; He, Youyou

2013-05-01

A transverse magnetic field was introduced to the arc plasma in the process of welding stainless steel tubes by high-speed Tungsten Inert Gas Arc Welding (TIG for short) without filler wire. The influence of external magnetic field on welding quality was investigated. 9 sets of parameters were designed by the means of orthogonal experiment. The welding joint tensile strength and form factor of weld were regarded as the main standards of welding quality. A binary quadratic nonlinear regression equation was established with the conditions of magnetic induction and flow rate of Ar gas. The residual standard deviation was calculated to adjust the accuracy of regression model. The results showed that, the regression model was correct and effective in calculating the tensile strength and aspect ratio of weld. Two 3D regression models were designed respectively, and then the impact law of magnetic induction on welding quality was researched.