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Sample records for nonlinear hamiltonian systems

  1. Hamiltonian formalism of weakly nonlinear hydrodynamic systems

    SciTech Connect

    Pavlov, M.V.

    1988-05-01

    A study is made of systems of quasilinear equations that are diagonalizable and Hamiltonian and have the condition /delta//sub i/v/sub i/ /triple bond/ 0, where u/sub t//sup i/ /equal/ v/sup i/(u)u/sub x//sup i/, i = 1, ..., N. The conservation laws of such systems are found, together with the metric and Poisson bracket. For definite examples it is shown how solutions are found. The conditions for the existence of solutions and continuity of commuting flows are found.

  2. Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Feng, Ju; Zhu, Weiqiu; Ying, Zuguang

    2010-01-01

    The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.

  3. On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems.

    PubMed

    Zhu, Wei-qiu; Ying, Zu-guang

    2004-11-01

    A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy. PMID:15495321

  4. A stochastic optimal control strategy for partially observable nonlinear quasi-Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Ying, Z. G.; Zhu, W. Q.

    2008-02-01

    A stochastic optimal control strategy for partially observable nonlinear quasi-Hamiltonian systems is proposed. The optimal control force consists of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi-Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimate errors of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.

  5. Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

    SciTech Connect

    Cruz, Hans; Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar

    2015-09-15

    The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

  6. Cloning in nonlinear Hamiltonian quantum and hybrid mechanics

    NASA Astrophysics Data System (ADS)

    Arsenović, D.; Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

    2014-10-01

    The possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at superluminal speed, but at the same time it is impossible to clone quantum pure states.

  7. Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil

    SciTech Connect

    Gadzhiev, I.T.; Gerdzhikov, V.S.; Ivanov, M.I.

    1986-09-10

    For a generalized Zakharov-Shabat system in which the matrix potential is a polynomial in the spectral parameter a generating operator is constructed which makes it possible to compactly write out the nonlinear evolution equations (NEE) connected with the system. The eigenfunctions of the generating operator - the squares of solutions of the original system - are found. The Hamiltonian property of the NEE and the existence of a hierarchy of Hamiltonian structures are established.

  8. Hamiltonian structures of nonlinear evolution equations associated with a polynomial bundle

    SciTech Connect

    Gadzhiev, I.T.; Gerdzhikov, V.S.; Ivanov, M.I.

    1987-05-20

    For the generalized Zakharov-Shabat system with the matrix potential a polynomial in the spectral parameter, they construct a generating operator which leads to a compact representation of the nonlinear evolution equations (NEE) associated with the system. The eigenfunctions of the generating operator are obtained as the squares of the solutions of the original system. The Hamiltonian nature of the NEE and the existence of a hierarchy of Hamiltonian structures is established.

  9. Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil

    SciTech Connect

    Gadzhiev, I.T.; Gerdzhikov, V.S.; Ivanov, M.I.

    1986-09-01

    For a generalized Zakharov-Shabat system in which the matrix potential is a polynomial in the spectral parameter a generating operator is constructed which makes it possible to compactly write out the nonlinear evolution equations (NEE) connected with the system. The eigenfunctions of the generating operator - the ''squares'' of solutions of the original system - are found. The Hamiltonian property of the NEE and the existence of a hierachy of Hamiltonian structures are established.

  10. Computing statistics for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Tupper, P. F.

    2007-08-01

    We present the results of a set of numerical experiments designed to investigate the appropriateness of various integration schemes for molecular dynamics simulations. In particular, we wish to identify which numerical methods, when applied to an ergodic Hamiltonian system, sample the state-space in an unbiased manner. We do this by describing two Hamiltonian system for which we can analytically compute some of the important statistical features of its trajectories, and then applying various numerical integration schemes to them. We can then compare the results from the numerical simulation against the exact results for the system and see how closely they agree. The statistic we study is the empirical distribution of particle velocity over long trajectories of the systems. We apply four methods: one symplectic method (Stormer-Verlet) and three energy-conserving step-and-project methods. The symplectic method performs better on both test problems, accurately computing empirical distributions for all step-lengths consistent with stability. Depending on the test system and the method, the step-and-project methods are either no longer ergodic for any step length (thus giving the wrong empirical distribution) or give the correct distribution only in the limit of step-size going to zero.

  11. Incomplete Dirac reduction of constrained Hamiltonian systems

    SciTech Connect

    Chandre, C.

    2015-10-15

    First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.

  12. Integrability of Hamiltonian systems with algebraic potentials

    NASA Astrophysics Data System (ADS)

    Maciejewski, Andrzej J.; Przybylska, Maria

    2016-01-01

    Problem of integrability for Hamiltonian systems with potentials that are algebraic thus multivalued functions of coordinates is discussed. Introducing potential as a new variable the original Hamiltonian system on 2n dimensional phase space is extended to 2 n + 1 dimensional system with rational right-hand sides. For extended system its non-canonical degenerated Poisson structure of constant rank 2n and rational Hamiltonian is identified. For algebraic homogeneous potentials of non-zero rational homogeneity degree necessary integrability conditions are formulated. These conditions are deduced from an analysis of the differential Galois group of variational equations around particular solutions of a straight line type. Obtained integrability obstructions are applied to the class of monomial homogeneous potentials. Some integrable potentials satisfying these conditions are found.

  13. Energy Transfer in a Fast-Slow Hamiltonian System

    NASA Astrophysics Data System (ADS)

    Dolgopyat, Dmitry; Liverani, Carlangelo

    2011-11-01

    We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a nonlinear diffusion equation. This is a first step toward the derivation of macroscopic equations from a Hamiltonian microscopic dynamics in the case of weakly coupled systems.

  14. Convergence of Hamiltonian systems to billiards.

    PubMed

    Collas, Peter; Klein, David; Schwebler, Hans-Peter

    1998-06-01

    We examine in detail a physically natural and general scheme for gradually deforming a Hamiltonian to its corresponding billiard, as a certain parameter k varies from one to infinity. We apply this limiting process to a class of Hamiltonians with homogeneous potential-energy functions and further investigate the extent to which the limiting billiards inherit properties from the corresponding sequences of Hamiltonians. The results are mixed. Using theorems of Yoshida for the case of two degrees of freedom, we prove a general theorem establishing the "inheritability" of stability properties of certain orbits. This result follows naturally from the convergence of the traces of appropriate monodromy matrices to the billiard analog. However, in spite of the close analogy between the concepts of integrability for Hamiltonian systems and billiards, integrability properties of Hamiltonians in a sequence are not necessarily inherited by the limiting billiard, as we show by example. In addition to rigorous results, we include numerical examples of certain interesting cases, along with computer simulations. (c) 1998 American Institute of Physics. PMID:12779750

  15. Canonical transformations and Hamiltonian evolutionary systems

    SciTech Connect

    Al-Ashhab, Samer

    2012-06-15

    In many Lagrangian field theories, one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different cases. These three cases depend on the specific dimensions of the vector bundle of the theory and the associated Hamiltonian differential operator. We also show how a canonical transformation transforms a Hamiltonian evolutionary system and its conservation laws. Finally, we illustrate these ideas with three examples.

  16. Regular and Chaotic Motion in Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Varvoglis, Harry

    All laws that describe the time evolution of a continuous system are given in the form of differential equations, ordinary (if the law involves one independent variable) or partial (if the law involves two or more independent variables). Historically the first law of this type was Newton's second law of motion. Since then Dynamics, as it is customary to name the branch of Mechanics that studies the motion of a body as the result of a force acting on it, has become the “typical„ case that comes into one's mind when a system of ordinary differential equation is given, although this system might as well describe any other system, e.g. physical, chemical, biological, financial etc. In particular the study of “conservative„ dynamical systems, i.e. systems of ordinary differential equations that originate from a time-independent Hamiltonian function, has become a thoroughly developed area, because of the fact that mechanical energy is very often conserved, although many other physical phenomena, beyond motion, can be described by Hamiltonian systems as well. In what follows we will restrict ourselves exactly to the study of Hamiltonian systems, as typical dynamical systems that find applications in many scientific disciplines.

  17. Reinforcement learning for port-hamiltonian systems.

    PubMed

    Sprangers, Olivier; Babuška, Robert; Nageshrao, Subramanya P; Lopes, Gabriel A D

    2015-05-01

    Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning (RL) approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust. The parameters of the control law are found by using actor-critic (AC) RL, enabling the search for near-optimal control policies satisfying a desired closed-loop energy landscape. The advantage is that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the RL perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the AC framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments. PMID:25167564

  18. Polynomial approximation of Poincare maps for Hamiltonian system

    NASA Technical Reports Server (NTRS)

    Froeschle, Claude; Petit, Jean-Marc

    1992-01-01

    Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

  19. Hierarchical structure of noncanonical Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Yoshida, Z.; Morrison, P. J.

    2016-02-01

    Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of ‘equipartition’ may bear no specific structure. Fluid turbulence is a typical example—while turbulent mixing seems to increase entropy, a variety of sustained vortical structures can emerge. In Hamiltonian formalism, some topological constraints are represented by Casimir invariants (for example, helicities of a fluid or a plasma), and then, the effective phase space is reduced to the Casimir leaves. However, a general constraint is not necessarily integrable, which precludes the existence of an appropriate Casimir invariant; the circulation is an example of such an invariant. In this work, we formulate a systematic method to embed a Hamiltonian system in an extended phase space; we introduce phantom fields and extend the Poisson algebra. A phantom field defines a new Casimir invariant, a cross helicity, which represents a topological constraint that is not integrable in the original phase space. Changing the perspective, a singularity of the extended system may be viewed as a subsystem on which the phantom fields (though they are actual fields, when viewed from the extended system) vanish, i.e., the original system. This hierarchical relation of degenerate Poisson manifolds enables us to see the ‘interior’ of a singularity as a sub Poisson manifold. The theory can be applied to describe bifurcations and instabilities in a wide class of general Hamiltonian systems (Yoshida and Morrison 2014 Fluid Dyn. Res. 46 031412).

  20. Engineering Floquet Hamiltonians in Cold Atom Systems

    NASA Astrophysics Data System (ADS)

    Polkovnikov, Anatoli

    2016-05-01

    In this talk I will first give a brief overview of the Floquet theory, describing periodically driven systems. Then I will introduce the concept of the high-frequency expansion and will show how it generalizes the celebrated Schrieffer-Wolff transformation to driven systems. Using these tools I will illustrate how one can engineer non-trivial interacting Hamiltonians mostly in the context of cold atom systems and discuss some experimental examples. In the end I will talk about issues of heating and adiabaticity and show that there are very strong parallels between Floquet systems and disordered systems. In particular, I will argue that the heating transition is closely analogous to the many-body localization transition. AFOSR, ARO, NSF.

  1. A Hamiltonian-Free Description of Single Particle Dynamics for Hopelessly Complex Periodic Systems

    SciTech Connect

    Forest, E.

    1990-01-01

    We develop a picture of periodic systems which does not rely on the Hamiltonian of the system but on maps between a finite number of time locations. Moser or Deprit-like normalizations are done directly on the maps thereby avoiding the complex time-dependent theory. We redefine linear and nonlinear Floquet variables entirely in terms of maps. This approach relies heavily on the Lie representation of maps introduced by Dragt and Finn. One might say that although we do not use the Hamiltonian in the normalization transformation, we are using Lie operators which are themselves, in some sense, pseudo-Hamiltonians for the maps they represent. Our techniques find application in accelerator dynamics or in any field where the Hamiltonian is periodic but hopelessly complex, such as magnetic field design in stellarators.

  2. Sqeezing generated by a nonlinear master equation and by amplifying-dissipative Hamiltonians

    NASA Technical Reports Server (NTRS)

    Dodonov, V. V.; Marchiolli, M. A.; Mizrahi, Solomon S.; Moussa, M. H. Y.

    1994-01-01

    In the first part of this contribution we show that the master equation derived from the generalized version of the nonlinear Doebner-Goldin equation leads to the squeezing of one of the quadratures. In the second part we consider two familiar Hamiltonians, the Bateman- Caldirola-Kanai and the optical parametric oscillator; going back to their classical Lagrangian form we introduce a stochastic force and a dissipative factor. From this new Lagrangian we obtain a modified Hamiltonian that treats adequately the simultaneous amplification and dissipation phenomena, presenting squeezing, too.

  3. The Tremblay-Turbiner-Winternitz system as extended Hamiltonian

    NASA Astrophysics Data System (ADS)

    Chanu, Claudia Maria; Degiovanni, Luca; Rastelli, Giovanni

    2014-12-01

    We generalize the idea of "extension of Hamiltonian systems"—developed in a series of previous articles—which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of arbitrarily high degree, as well as the determination of new superintegrable systems from old ones. The present generalization, that we call "modified extension of Hamiltonian systems," produces the third independent first integral for the (complete) Tremblay-Turbiner-Winternitz system, as well as for the caged anisotropic oscillator in dimension two.

  4. Uncertainty relation for non-Hamiltonian quantum systems

    SciTech Connect

    Tarasov, Vasily E.

    2013-01-15

    General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.

  5. Two time physics and Hamiltonian Noether theorem for gauge systems

    SciTech Connect

    Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.

    2006-09-25

    Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints.

  6. Linear transformation and oscillation criteria for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Zheng, Zhaowen

    2007-08-01

    Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.

  7. Applications of Noether conservation theorem to Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Mouchet, Amaury

    2016-09-01

    The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.

  8. Limit of small exits in open Hamiltonian systems.

    PubMed

    Aguirre, Jacobo; Sanjuán, Miguel A F

    2003-05-01

    The nature of open Hamiltonian systems is analyzed, when the size of the exits decreases and tends to zero. Fractal basins appear typically in open Hamiltonian systems, but we claim that in the limit of small exits, the invariant sets tend to fill up the whole phase space with the strong consequence that a new kind of basin appears, where the unpredictability grows indefinitely. This means that for finite, arbitrarily small accuracy, we can find uncertain basins, where any information about the future of the system is lost. This total indeterminism had only been reported in dissipative systems, in particular in the so-called intermingled riddled basins, as well as in the riddledlike basins. We show that this peculiar, behavior is a general feature of open Hamiltonian systems. PMID:12786244

  9. Versal unfolding of planar Hamiltonian systems at fully degenerate equilibrium

    NASA Astrophysics Data System (ADS)

    Tang, Yilei; Zhang, Weinian

    2016-07-01

    In this paper we study bifurcations of a planar Hamiltonian system at a fully degenerate equilibrium, which has a zero linearization. Since the Poincaré normal form theory is not applicable to such a degenerate system, we investigate its restrictive normal forms in the class of Hamiltonian fields and prove that such a degenerate system is of codimension 3 degeneracy in the class, so that we introduce three parameters to versally unfold the degenerate system in the class. In order to discuss further the qualitative properties of the versal unfolding, we use the Poincaré index to determine the number and distribution of hyperbolic sectors near the degenerate equilibrium. We display its all bifurcations such as pitchfork bifurcation, saddle-center bifurcation and the Bogdanov-Takens bifurcation within Hamiltonian systems.

  10. On chaotic dynamics in "pseudobilliard" Hamiltonian systems with two degrees of freedom

    NASA Astrophysics Data System (ADS)

    Eleonsky, V. M.; Korolev, V. G.; Kulagin, N. E.

    1997-12-01

    A new class of Hamiltonian dynamical systems with two degrees of freedom is studied, for which the Hamiltonian function is a linear form with respect to moduli of both momenta. For different potentials such systems can be either completely integrable or behave just as normal nonintegrable Hamiltonian systems with two degrees of freedom: one observes many of the phenomena characteristic of the latter ones, such as a breakdown of invariant tori as soon as the integrability is violated; a formation of stochastic layers around destroyed separatrices; bifurcations of periodic orbits, etc. At the same time, the equations of motion are simply integrated on subsequent adjacent time intervals, as in billiard systems; i.e., all the trajectories can be calculated explicitly: Given an initial data, the state of the system is uniquely determined for any moment. This feature of systems in interest makes them very attractive models for a study of nonlinear phenomena in finite-dimensional Hamiltonian systems. A simple representative model of this class (a model with quadratic potential), whose dynamics is typical, is studied in detail.

  11. Extensions of Hamiltonian systems dependent on a rational parameter

    NASA Astrophysics Data System (ADS)

    Chanu, Claudia Maria; Degiovanni, Luca; Rastelli, Giovanni

    2014-12-01

    The technique of "extension" allows to build (d + 2)-dimensional Hamiltonian systems with a non-trivial polynomial in the momenta first integral of any given degree starting from a suitable d-dimensional Hamiltonian. Until now, the application of the technique was restricted to integer values of a certain fundamental parameter determining the degree of the additional first integral. In this article, we show how the technique of extension can be generalized to any rational value of the same parameter. Several examples are given, among them the two uncoupled oscillators and a special case of the Tremblay-Turbiner-Winternitz system.

  12. Integrable Hamiltonian systems on low-dimensional Lie algebras

    SciTech Connect

    Korotkevich, Aleksandr A

    2009-12-31

    For any real Lie algebra of dimension 3, 4 or 5 and any nilpotent algebra of dimension 6 an integrable Hamiltonian system with polynomial coefficients is found on its coalgebra. These systems are constructed using Sadetov's method for constructing complete commutative families of polynomials on a Lie coalgebra. Bibliography: 17 titles.

  13. Symplectic ray-tracing: a new approach for nonlinear ray tracings by Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Satoh, Tetsu R.

    2003-05-01

    This paper describes a method of symplectic ray tracing for calculating the flows of non-linear dynamical systems. Symplectic ray tracing method traces the path of photons moving along the orbit calculated by using Hamilton's canonical equation. Using this method, we can simulate non-linear dynamical systems with various dimensions, accurate calculation, and quick implementation of scientif visualization system. This paper also demonstrates some visualization results of non-linear dynamical systems computed by using symplectic ray tracing method.

  14. Near strongly resonant periodic orbits in a Hamiltonian system

    PubMed Central

    Gelfreich, Vassili

    2002-01-01

    We study an analytic Hamiltonian system near a strongly resonant periodic orbit. We introduce a modulus of local analytic classification. We provide asymptotic formulae for the exponentially small splitting of separatrices for bifurcating hyperbolic periodic orbits. These formulae confirm a conjecture formulated by V. I. Arnold in the early 1970s. PMID:12391324

  15. Exponential energy growth in adiabatically changing Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Pereira, Tiago; Turaev, Dmitry

    2015-01-01

    We show that the mixed phase space dynamics of a typical smooth Hamiltonian system universally leads to a sustained exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of geometric Brownian motion with a positive drift, and relate it to the steady entropy increase after each period of the parameters variation.

  16. Hamiltonian-Based Model to Describe the Nonlinear Physics of Cascading Failures in Power-Grid Networks

    NASA Astrophysics Data System (ADS)

    Yang, Yang; Motter, Adilson

    A local disturbance to the state of a power-grid system can trigger a protective response that disables some grid components, which leads to further responses, and may finally result in large-scale failures. In this talk, I will introduce a Hamiltonian-like model of cascading failures in power grids. This model includes the state variables of generators, which are determined by the nonlinear swing equations and power-flow equations, as well as the on/off status of the network components. This framework allows us to view a cascading failure in the power grid as a phase-space transition from a fixed point with high energy to a fixed point with lower energy. Using real power-grid networks, I will demonstrate that possible cascade outcomes can be predicted by analyzing the stability of the system's equilibria. This work adds an important new dimension to the current understanding of cascading failures.

  17. Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

    PubMed

    Deng, Mao-Lin; Zhu, Wei-Qiu

    2016-08-01

    In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems. PMID:27586630

  18. Solving SAT and Hamiltonian Cycle Problem Using Asynchronous P Systems

    NASA Astrophysics Data System (ADS)

    Tagawa, Hirofumi; Fujiwara, Akihiro

    In the present paper, we consider fully asynchronous parallelism in membrane computing, and propose two asynchronous P systems for the satisfiability (SAT) and Hamiltonian cycle problem. We first propose an asynchronous P system that solves SAT with n variables and m clauses, and show that the proposed P system computes SAT in O(mn2n) sequential steps or O(mn) parallel steps using O(mn) kinds of objects. We next propose an asynchronous P system that solves the Hamiltonian cycle problem with n nodes, and show that the proposed P system computes the problem in O(n!) sequential steps or O(n2) parallel steps using O(n2) kinds of objects.

  19. Stability, bifurcation, and control of Hamiltonian systems

    SciTech Connect

    Marsden, J.E. . Dept. of Mathematics); Ratiu, T.S. . Dept. of Mathematics)

    1993-01-01

    Work is being done on dissipation-induced instabilities, gyroscopic stabilization and its destruction by a small damping for both finite dimensional and certain infinite dimensional systems (such as rotating rods, strings), nonabelian and abelian cases, Euler-Lagrange-Poincare equations, the Routhian having a form of a Lagrangian with a gyroscopic term, Euler-Lagrange equations, etc.

  20. Stability, bifurcation, and control of Hamiltonian systems

    SciTech Connect

    Marsden, J.E.; Ratiu, T.S.

    1993-04-01

    Work is being done on dissipation-induced instabilities, gyroscopic stabilization and its destruction by a small damping for both finite dimensional and certain infinite dimensional systems (such as rotating rods, strings), nonabelian and abelian cases, Euler-Lagrange-Poincare equations, the Routhian having a form of a Lagrangian with a gyroscopic term, Euler-Lagrange equations, etc.

  1. Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

    SciTech Connect

    Abedi-Fardad, J.; Rezaei-Aghdam, A.; Haghighatdoost, Gh.

    2014-05-15

    We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R{sup 4} and R{sup 6}. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

  2. Production and Transfer of Energy and Information in Hamiltonian Systems

    PubMed Central

    Antonopoulos, Chris G.; Bianco-Martinez, Ezequiel; Baptista, Murilo S.

    2014-01-01

    We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an “experimental” implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented. PMID:24586891

  3. Renormalization Group Reduction of Non Integrable Hamiltonian Systems

    SciTech Connect

    Stephan I. Tzenov

    2002-05-09

    Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail.

  4. Nonconventional fluctuation dissipation process in non-Hamiltonian dynamical systems

    NASA Astrophysics Data System (ADS)

    Bianucci, Marco

    2016-08-01

    Here, we introduce a statistical approach derived from dynamics, for the study of the geophysical fluid dynamics phenomena characterized by a weak interaction among the variables of interest and the rest of the system. The approach is reminiscent of the one developed some years ago [M. Bianucci, R. Mannella, P. Grigolini and B. J. West, Phys. Rev. E 51, 3002 (1995)] to derive statistical mechanics of macroscopic variables on interest starting from Hamiltonian microscopic dynamics. However, in the present work, we are interested to generalize this approach beyond the context of the foundation of thermodynamics, in fact, we take into account the cases where the system of interest could be non-Hamiltonian (dissipative) and also the interaction with the irrelevant part can be of a more general type than Hamiltonian. As such example, we will refer to a typical case from geophysical fluid dynamics: the complex ocean-atmosphere interaction that gives rise to the El Niño Southern Oscillation (ENSO). Here, changing all the scales, the role of the “microscopic” system is played by the atmosphere, while the ocean (or some ocean variables) plays the role of the intrinsically dissipative macroscopic system of interest. Thus, the chaotic and divergent features of the fast atmosphere dynamics remains in the decaying properties of the correlation functions and of the response function of the atmosphere variables, while the exponential separation of the perturbed (or close) single trajectories does not play a direct role. In the present paper, we face this problem in the frame of a not formal Langevin approach, limiting our discussion to physically based rather than mathematics arguments. Elsewhere, we obtain these results via a much more formal procedure, using the Zwanzing projection method and some elements from the Lie Algebra field.

  5. Algebraic aspects of Tremblay-Turbiner-Winternitz Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Calzada, J. A.; Celeghini, E.; del Olmo, M. A.; Velasco, M. A.

    2012-02-01

    Using the factorization method we find a hierarchy of Tremblay-Turbiner-Winternitz Hamiltonians labeled by discrete indices. The shift operators (those connecting eigenfunctions of different Hamiltonians of the hierarchy) as well the ladder operators (they connect eigenstates of a determined Hamiltonian) obtained in this way close different algebraic structures that are presented here.

  6. An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Chandre, C.; Jauslin, H. R.; Benfatto, G.

    1999-01-01

    We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.

  7. The symmetry groups of bifurcations of integrable Hamiltonian systems

    SciTech Connect

    Orlova, E I

    2014-11-30

    Two-dimensional atoms are investigated; these are used to code bifurcations of the Liouville foliations of nondegenerate integrable Hamiltonian systems. To be precise, the symmetry groups of atoms with complexity at most 3 are under study. Atoms with symmetry group Z{sub p}⊕Z{sub q} are considered. It is proved that Z{sub p}⊕Z{sub q} is the symmetry group of a toric atom. The symmetry groups of all nonorientable atoms with complexity at most 3 are calculated. The concept of a geodesic atom is introduced. Bibliography: 9 titles.

  8. Dynamics symmetries of Hamiltonian system on time scales

    SciTech Connect

    Peng, Keke Luo, Yiping

    2014-04-15

    In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.

  9. Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems

    SciTech Connect

    Doroshin, Anton V.

    2010-03-01

    This paper sets out to develop a spider-type multiple-rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor-equipped rays, so it was called a 'Spider-type System', also it can be called 'Rotary Hedgehog'. These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer-Deprit canonical variables. These variables allow obtaining exact solution for hetero- and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.

  10. Nonlinear systems in medicine.

    PubMed Central

    Higgins, John P.

    2002-01-01

    Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107

  11. The t expansion: A nonperturbative analytic tool for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Horn, D.; Weinstein, M.

    1984-09-01

    A systematic nonperturbative scheme is developed to calculate the ground-state expectation values of arbitrary operators for any Hamiltonian system. Quantities computed in this way converge rapidly to their true expectation values. The method is based upon the use of the operator e-tH to contract any trial state onto the true ground state of the Hamiltonian H. We express all expectation values in the contracted state as a power series in t, and reconstruct t-->∞ behavior by means of Padé approximants. The problem associated with factors of spatial volume is taken care of by developing a connected graph expansion for matrix elements of arbitrary operators taken between arbitrary states. We investigate Padé methods for the t series and discuss the merits of various procedures. As examples of the power of this technique we present results obtained for the Heisenberg and Ising models in 1+1 dimensions starting from simple mean-field wave functions. The improvement upon mean-field results is remarkable for the amount of effort required. The connection between our method and conventional perturbation theory is established, and a generalization of the technique which allows us to exploit off-diagonal matrix elements is introduced. The bistate procedure is used to develop a t expansion for the ground-state energy of the Ising model which is, term by term, self-dual.

  12. Nekhoroshev stability in quasi-integrable degenerate Hamiltonian systems.

    NASA Astrophysics Data System (ADS)

    Guzzo, M.

    A perturbation of a degenerate integrable Hamiltonian system has the form H(I,φ ,p,q)=h(I)+ɛ f(I,φ ,p,q) with (I,φ )in Rn x Tn, (p,q) in B subseteq R2m and the two-form is dI wedge dφ + dp wedge dq. In the case h is convex, Nekhoroshev theorem provides the usual bound to the motion of the actions I, but only for a time which is the smaller between the usual exponentially-long time and the escape time of (p,q) from B. Furthermore, the theorem does not provide any estimate for the `degenerate' variables (p,q) better than the a priori one dot p,dot q ~ ɛ, and actually in the literature there are examples of degenerate systems with degenerate variables that perform large chaotic motions in short times. Therefore, there is the problem of individuating which assumptions on the perturbation and on the initial data allows one to produce stability bounds for the degenerate variables over long times, thus preventing chaotic motions and escape. The problem is relevant to understand the long time stability of several systems, like the three body problem, the asteroid belt dynamical system and the fast rotations of the rigid body. In this work we show that if the `secular' hamiltonian of H, i.e the average of H with respect to the fast angles φ, is integrable (or quasi-integrable) and if it satisfies a suitable convexity condition, then a Nekhoroshev-like bound also holds for the degenerate variables (p,q) (actually for the actions of the secular integrable system) for all initial data except those with initial action I(0) in a small neighborhood of the resonant manifolds of order lower than ln 1 ɛ. It is worthwhile to note that even if the secular hamiltonian of H is integrable, strong chaotic motions can take place in short times near such low order resonant manifolds, as it can be shown on examples. This result was proved for the first time in connection with the problem of the long-time stability in the asteroid belt.

  13. A solvable Hamiltonian system: Integrability and action-angle variables

    SciTech Connect

    Karimipour, V.

    1997-03-01

    We prove that the dynamical system characterized by the Hamiltonian H={lambda}N{summation}{sub j}{sup N}p{sub j}+{mu}{summation} {sub j,k}{sup N}(p{sub j}p{sub k}){sup 1/2}{l_brace}cos[{nu}(q{sub j}{minus}q{sub k})]{r_brace} proposed and studied by Calogero [J. Math. Phys. {bold 36}, 9 (1994)] and Calogero and van Diejen [Phys. Lett. A {bold 205}, 143 (1995)] is equivalent to a system of {ital noninteracting} harmonic oscillators both classically and quantum mechanically. We find the explicit form of the conserved currents that are in involution. We also find the action-angle variables and solve the initial value problem in a very simple form.{copyright} {ital 1997 American Institute of Physics.}

  14. Necessary conditions for the existence of additional first integrals for Hamiltonian systems with homogeneous potential

    NASA Astrophysics Data System (ADS)

    Maciejewski, Andrzej J.; Przybylska, Maria; Yoshida, Haruo

    2012-02-01

    We consider a natural Hamiltonian system of n degrees of freedom with a homogeneous potential. We assume that the system admits 1 <= m < n independent and commuting first integrals F1, ... Fm. We give easily computable and effective necessary conditions for the existence of one additional first integral Fm+1 such that all integrals F1, ...Fm+1 are independent, pairwise commute and are meromorphic in a connected neighbourhood of a certain phase curve. These conditions are obtained from an analysis of the differential Galois group of variational equations along a particular solution of the system. We apply our result analysing the problem of the existence of one additional first integral for a homogeneous nonlinear lattice on a line.

  15. Solvable model for many-quark systems in QCD Hamiltonians

    SciTech Connect

    Yepez-Martinez, Tochtli; Hess, P. O.; Civitarese, O.

    2010-04-15

    Motivated by a canonical QCD Hamiltonian, we propose an effective Hamiltonian to represent an arbitrary number of quarks in hadronic bags. The structure of the effective Hamiltonian is discussed and the BCS-type solutions that may represent constituent quarks are presented. The single-particle orbitals are chosen as three-dimensional harmonic oscillators, and we discuss a class of exact solutions that can be obtained when a subset of single-particle basis states is restricted to include a certain number of orbital excitations. The general problem, which includes all possible orbital states, can also be solved by combining analytical and numerical methods.

  16. Noisy Nonlinear Systems

    SciTech Connect

    Dr. Katja Lindenberg

    2005-11-20

    During the one-year period 2004-2005 our work continued to focus on nonlinear noisy systems, with special attention to spatially extended systems. There is a history of many decades of research in the sciences and engineering on the behavior of noninear noisy systems, but only in the past ten years or so has a theoretical understanding of spatially extended systems begun to emerge. This has been the outcome of a symbiosis of numerical simulations not possible until recently, laboratory experiments, and new analytic methods.

  17. Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

    NASA Astrophysics Data System (ADS)

    Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

    2011-09-01

    The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

  18. Accelerator-Feasible N-Body Nonlinear Integrable System

    SciTech Connect

    Danilov, V.; Nagaitsev, S.

    2014-12-23

    Nonlinear N-body integrable Hamiltonian systems, where N is an arbitrary number, attract the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.

  19. Maxwell consideration of polaritonic quasi-particle Hamiltonians in multi-level systems

    SciTech Connect

    Richter, Steffen; Michalsky, Tom; Fricke, Lennart; Sturm, Chris; Franke, Helena; Grundmann, Marius; Schmidt-Grund, Rüdiger

    2015-12-07

    We address the problem of the correct description of light-matter coupling for excitons and cavity photons in the case of systems with multiple photon modes or excitons, respectively. In the literature, two different approaches for the phenomenological coupling Hamiltonian can be found: Either one single Hamiltonian with a basis whose dimension equals the sum of photonic modes and excitonic resonances is used. Or a set of independent Hamiltonians, one for each photon mode, is chosen. Both are usually used equivalently for the same kind of multi-photonic systems which cannot be correct. However, identifying the suitable Hamiltonian is difficult when modeling experimental data. By means of numerical transfer matrix calculations, we demonstrate the scope of application of each approach: The first one holds only for the coupling of a single photon state to several excitons, while in the case of multiple photon modes, separate Hamiltonians must be used for each photon mode.

  20. Energetic pulses in exciton-phonon molecular chains and conservative numerical methods for quasilinear Hamiltonian systems.

    PubMed

    Lemesurier, Brenton

    2013-09-01

    The phenomenon of coherent energetic pulse propagation in exciton-phonon molecular chains such as α-helix protein is studied using an ODE system model of Davydov-Scott type, both with numerical studies using a new unconditionally stable fourth-order accurate energy-momentum conserving time discretization and with analytical explanation of the main numerical observations. Impulsive initial data associated with initial excitation of a single amide-I vibration by the energy released by ATP hydrolysis are used as well as the best current estimates of physical parameter values. In contrast to previous studies based on a proposed long-wave approximation by the nonlinear Schrödinger (NLS) equation and focusing on initial data resembling the soliton solutions of that equation, the results here instead lead to approximation by the third derivative nonlinear Schrödinger equation, giving a far better fit to observed behavior. A good part of the behavior is indeed explained well by the linear part of that equation, the Airy PDE, while other significant features do not fit any PDE approximation but are instead explained well by a linearized analysis of the ODE system. A convenient method is described for construction of the highly stable, accurate conservative time discretizations used, with proof of its desirable properties for a large class of Hamiltonian systems, including a variety of molecular models. PMID:24125294

  1. Linear Hamiltonian systems - The Riccati group and its invariants

    NASA Technical Reports Server (NTRS)

    Garzia, M. R.; Martin, C. F.; Loparo, K. A.

    1982-01-01

    The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of Hamiltonian matrices. Within this framework canonical forms are developed for the matrix coefficients of the Riccati differential equation.

  2. Maxwell-Vlasov equations as a continuous Hamiltonian system

    SciTech Connect

    Morrison, P.J.

    1980-11-01

    The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B, and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.

  3. Maxwell-Vlasov equations as a continuous Hamiltonian system

    SciTech Connect

    Morrison, P.J.

    1980-09-01

    The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  5. Superradiance, disorder, and the non-Hermitian Hamiltonian in open quantum systems

    SciTech Connect

    Celardo, G. L.; Biella, A.; Giusteri, G. G.; Mattiotti, F.; Zhang, Y.; Kaplan, L.

    2014-10-15

    We first briefly review the non-Hermitian effective Hamiltonian approach to open quantum systems and the associated phenomenon of superradiance. We next discuss the superradiance crossover in the presence of disorder and the relationship between superradiance and the localization transition. Finally, we investigate the regime of validity of the energy-independent effective Hamiltonian approximation and show that the results obtained by these methods are applicable to realistic physical systems.

  6. Solution of Nonlinear Systems

    NASA Technical Reports Server (NTRS)

    Turner, L. R.

    1960-01-01

    The problem of solving systems of nonlinear equations has been relatively neglected in the mathematical literature, especially in the textbooks, in comparison to the corresponding linear problem. Moreover, treatments that have an appearance of generality fail to discuss the nature of the solutions and the possible pitfalls of the methods suggested. Probably it is unrealistic to expect that a unified and comprehensive treatment of the subject will evolve, owing to the great variety of situations possible, especially in the applied field where some requirement of human or mechanical efficiency is always present. Therefore we attempt here simply to pose the problem and to describe and partially appraise the methods of solution currently in favor.

  7. The tri-Hamiltonian dual system of supersymmetric two boson system

    NASA Astrophysics Data System (ADS)

    Zhang, Mengxia; Tian, Kai; Zhang, Lei

    2016-09-01

    The dual system of the supersymmetric two boson system is constructed through the approach of tri-Hamiltonian duality, and inferred from this duality, its zero-curvature representation is also figured out. Furthermore, the dual system is shown to be equivalent to a N = 2 supersymmetric Camassa-Holm equation, and this relation results in a new linear spectral problem for the N = 2 supersymmetric Camassa-Holm equation.

  8. The potential energy surface and chaos in 2D Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Li, Jiangdan; Zhang, Suying

    2011-02-01

    We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.

  9. Duality relation among the Hamiltonian structures of a parametric coupled Korteweg-de Vries system

    NASA Astrophysics Data System (ADS)

    Restuccia, Alvaro; Sotomayor, Adrián

    2016-03-01

    We obtain the full Hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated Hamiltonian functionals and the corresponding Poisson structures follow from the geometry of a constrained phase space by using the Dirac approach for constrained systems. The overall algebraic structure for the system is given in terms of two pencils of Poisson structures with associated Hamiltonians depending on the parameter of the Poisson pencils. The algebraic construction we present admits the most general space of observables related to the coupled system. We then construct two master lagrangians for the coupled system whose field equations are the ɛ-parametric Gardner equations obtained from the coupled KdV system through a Gardner transformation. In the weak limit ɛ → 0 the lagrangians reduce to the ones of the coupled KdV system while, after a suitable redefinition of the fields, in the strong limit ɛ → ∞ we obtain the lagrangians of the coupled modified KdV system. The Hamiltonian structures of the coupled KdV system follow from the Hamiltonian structures of the master system by taking the two limits ɛ → 0 and ɛ → ∞.

  10. Hamiltonian purification

    SciTech Connect

    Orsucci, Davide; Burgarth, Daniel; Facchi, Paolo; Pascazio, Saverio; Nakazato, Hiromichi; Yuasa, Kazuya; Giovannetti, Vittorio

    2015-12-15

    The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.

  11. From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity

    NASA Astrophysics Data System (ADS)

    Okuyama, Manaka; Takahashi, Kazutaka

    2016-08-01

    Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.

  12. Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation

    NASA Astrophysics Data System (ADS)

    Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

    2016-04-01

    Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

  13. Guidance of Nonlinear Systems

    NASA Technical Reports Server (NTRS)

    Meyer, George

    1997-01-01

    The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

  14. Generic fractal structure of finite parts of trajectories of piecewise smooth Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Hildebrand, R.; Lokutsievskiy, L. V.; Zelikin, M. I.

    2013-03-01

    Piecewise smooth Hamiltonian systems with tangent discontinuity are studied. A new phenomenon is discovered, namely, the generic chaotic behavior of finite parts of trajectories. The approach is to consider the evolution of Poisson brackets for smooth parts of the initial Hamiltonian system. It turns out that, near second-order singular points lying on a discontinuity stratum of codimension two, the system of Poisson brackets is reduced to the Hamiltonian system of the Pontryagin Maximum Principle. The corresponding optimization problem is studied and the topological structure of its optimal trajectories is constructed (optimal synthesis). The synthesis contains countably many periodic solutions on the quotient space by the scale group and a Cantor-like set of nonwandering points (NW) having fractal Hausdorff dimension. The dynamics of the system is described by a topological Markov chain. The entropy is evaluated, together with bounds for the Hausdorff and box dimension of (NW).

  15. Canonical Hamiltonians for waves in inhomogeneous media

    NASA Astrophysics Data System (ADS)

    Gershgorin, Boris; Lvov, Yuri V.; Nazarenko, Sergey

    2009-01-01

    We obtain a canonical form of a quadratic Hamiltonian for linear waves in a weakly inhomogeneous medium. This is achieved by using the Wentzel-Kramers-Brillouin representation of wave packets. The canonical form of the Hamiltonian is obtained via the series of canonical Bogolyubov-type and near-identical transformations. Various examples of the application illustrating the main features of our approach are presented. The knowledge of the Hamiltonian structure for linear wave systems provides a basis for developing a theory of weakly nonlinear random waves in inhomogeneous media generalizing the theory of homogeneous wave turbulence.

  16. The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

    NASA Technical Reports Server (NTRS)

    Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

    1994-01-01

    The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

  17. A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity

    NASA Astrophysics Data System (ADS)

    Correggi, M.; Dell'Antonio, G.; Finco, D.; Michelangeli, A.; Teta, A.

    2015-12-01

    We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for m larger than a critical value m ∗ ≃ (13.607)-1 a self-adjoint and lower bounded Hamiltonian H 0 can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for m ∈ ( m ∗, m ∗∗), where m ∗∗ ≃ (8.62)-1, there is a further family of self-adjoint and lower bounded Hamiltonians H 0, β , β ∈ ℝ, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.

  18. Analysis of the nonlinear behavior of shear-Alfvén modes in tokamaks based on Hamiltonian mapping techniques

    SciTech Connect

    Briguglio, S. Vlad, G.; Fogaccia, G.; Di Troia, C.; Fusco, V.; Wang, X.; Zonca, F.

    2014-11-15

    We present a series of numerical simulation experiments set up to illustrate the fundamental physics processes underlying the nonlinear dynamics of Alfvénic modes resonantly excited by energetic particles in tokamak plasmas and of the ensuing energetic particle transports. These phenomena are investigated by following the evolution of a test particle population in the electromagnetic fields computed in self-consistent MHD-particle simulation performed by the HMGC code. Hamiltonian mapping techniques are used to extract and illustrate several features of wave-particle dynamics. The universal structure of resonant particle phase space near an isolated resonance is recovered and analyzed, showing that bounded orbits and untrapped trajectories, divided by the instantaneous separatrix, form phase space zonal structures, whose characteristic non-adiabatic evolution time is the same as the nonlinear time of the underlying fluctuations. Bounded orbits correspond to a net outward resonant particle flux, which produces a flattening and/or gradient inversion of the fast ion density profile around the peak of the linear wave-particle resonance. The connection of this phenomenon to the mode saturation is analyzed with reference to two different cases: a Toroidal Alfvén eigenmode in a low shear magnetic equilibrium and a weakly unstable energetic particle mode for stronger magnetic shear. It is shown that, in the former case, saturation is reached because of radial decoupling (resonant particle redistribution matching the mode radial width) and is characterized by a weak dependence of the mode amplitude on the growth rate. In the latter case, saturation is due to resonance detuning (resonant particle redistribution matching the resonance width) with a stronger dependence of the mode amplitude on the growth rate.

  19. On bounded and unbounded dynamics of the Hamiltonian system for unified scalar field cosmology

    NASA Astrophysics Data System (ADS)

    Starkov, Konstantin E.

    2016-05-01

    This paper is devoted to the research of global dynamics for the Hamiltonian system formed by the unified scalar field cosmology. We prove that this system possesses only unbounded dynamics in the space of negative curvature. It is found the invariant domain filled only by unbounded dynamics for the space with positive curvature. Further, we construct a set of polytopes depending on the Hamiltonian level surface that contain all compact invariant sets. Besides, one invariant two dimensional plane is described. Finally, we establish nonchaoticity of dynamics in one special case.

  20. Purely non-local Hamiltonian formalism, Kohno connections and ∨-systems

    SciTech Connect

    Arsie, Alessandro; Lorenzoni, Paolo

    2014-11-15

    In this paper, we extend purely non-local Hamiltonian formalism to a class of Riemannian F-manifolds, without assumptions on the semisimplicity of the product ○ or on the flatness of the connection ∇. In the flat case, we show that the recurrence relations for the principal hierarchy can be re-interpreted using a local and purely non-local Hamiltonian operators and in this case they split into two Lenard-Magri chains, one involving the even terms, the other involving the odd terms. Furthermore, we give an elementary proof that the Kohno property and the ∨-system condition are equivalent under suitable assumptions and we show how to associate a purely non-local Hamiltonian structure to any ∨-system, including degenerate ones.

  1. Numerical integration of nearly-Hamiltonian systems. [Van der Pol oscillator and perturbed Keplerian motion

    NASA Technical Reports Server (NTRS)

    Bond, V. R.

    1978-01-01

    The reported investigation is concerned with the solution of systems of differential equations which are derived from a Hamiltonian function in the extended phase space. The problem selected involves a one-dimensional perturbed harmonic oscillator. The van der Pol equation considered has an exact asymptotic value for its amplitude. Comparisons are made between a numerical solution and a known analytical solution. In addition to the van der Pol problem, known solutions regarding the restricted problem of three bodies are used as examples for perturbed Keplerian motion. The extended phase space Hamiltonian discussed by Stiefel and Scheifele (1971) is considered. A description is presented of two canonical formulations of the perturbed harmonic oscillator.

  2. Energy level structure and quantum phase transitions of spin systems with nonaxially symmetric Hamiltonians

    NASA Astrophysics Data System (ADS)

    López-Moreno, Enrique; Grether, M.; Velázquez, Víctor

    2011-11-01

    A general spin system with a nonaxially symmetric Hamiltonian containing Jx, Jz-linear and Jz-quadratic terms, widely used in many-body fermionic and bosonic systems and in molecular magnetism, is considered for the variations of general parameters describing intensity interaction changes of each of its terms. For this model Hamiltonian, a semiclassical energy surface (ES) is obtained by means of the coherent-state formalism. An analysis of this ES function, based on catastrophe theory, determines the separatrix in the control parameter space of the system Hamiltonian: the loci of singularities representing semiclassical phase transitions. Here we show that distinct regions of qualitatively different spectrum structures, as well as a singular behavior of quantum states, are ruled by this separatrix: here we show that the separatrix not only describes ground-state singularities, which have been associated with quantum phase transitions, but also reveals the structure of the excited spectrum, distinguishing different quantum phases within the parameter space. Finally, we consider magnetic susceptibility and heat capacity of the system at finite temperature, in order to study thermal properties and thermodynamical phase transitions in the perspective of the separatrix of this Hamiltonian system.

  3. Equivalence of two sets of Hamiltonians associated with the rational BCn Ruijsenaars-Schneider-van Diejen system

    NASA Astrophysics Data System (ADS)

    Görbe, T. F.; Fehér, L.

    2015-10-01

    The equivalence of two complete sets of Poisson commuting Hamiltonians of the (super)integrable rational BCn Ruijsenaars-Schneider-van Diejen system is established. Specifically, the commuting Hamiltonians constructed by van Diejen are shown to be linear combinations of the Hamiltonians generated by the characteristic polynomial of the Lax matrix obtained recently by Pusztai, and the explicit formula of this invertible linear transformation is found.

  4. Darboux integrability of 2-dimensional Hamiltonian systems with homogenous potentials of degree 3

    SciTech Connect

    Llibre, Jaume; Valls, Claudia

    2014-03-15

    We provide a characterization of all Hamiltonian systems of the form H=(p{sub 1}{sup 2}+p{sub 2}{sup 2})/2+V(q{sub 1},q{sub 2}), where V is a homogenous polynomial of degree 3 which are completely integrable with Darboux first integrals.

  5. Normal form and Nekhoroshev stability for nearly integrable hamiltonian systems with unconditionally slow aperiodic time dependence

    NASA Astrophysics Data System (ADS)

    Fortunati, Alessandro; Wiggins, Stephen

    2014-05-01

    The aim of this paper is to extend the result of Giorgilli and Zehnder for aperiodic time dependent systems to a case of nearly integrable convex analytic Hamiltonians. The existence of a normal form and then a stability result are shown in the case of a slow aperiodic time dependence that, under some smallness conditions, is independent of the size of the perturbation.

  6. A geometric Hamiltonian description of composite quantum systems and quantum entanglement

    NASA Astrophysics Data System (ADS)

    Pastorello, Davide

    2015-05-01

    Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is discussed in this paper. As summarized in the first part of this work, in the Hamiltonian formulation the phase space of a quantum system is the Kähler manifold given by the complex projective space P(H) of the Hilbert space H of the considered quantum theory. However the phase space of a bipartite system must be P(H1 ⊗ H2) and not simply P(H1) × P(H2) as suggested by the analogy with Classical Mechanics. A part of this paper is devoted to manage this problem. In the second part of the work, a definition of quantum entanglement and a proposal of entanglement measure are given in terms of a geometrical point of view (a rather studied topic in recent literature). Finally two known separability criteria are implemented in the Hamiltonian formalism.

  7. Nonlinear dynamical systems analyzer

    NASA Astrophysics Data System (ADS)

    Coffey, Adrian S.; Johnson, Martin; Jones, Robin

    1994-10-01

    Computationally intensive algorithms are an ever more common requirement of modern signal processing. Following the work of Gentleman and Kung, McWhirter, Shepherd and Proudler suggested that certain matrix-orientated algorithms can be mapped onto systolic array architectures for adaptive linear signal processing. This has been extended by Broomhead et al. to the calculation of nonlinear predictive models and applied by Jones et al. to target identification and recognition. We shall show that predictive models are extremely sharp discriminators. Our chosen problem, if implemented as a systolic array, would require 3403 processors which would result in high through-put rate at excessive cost. We are developing an efficient sub-optimally implemented systolic array; one processor servicing more than one systolic node. We describe a prototype Heuristic Processor which computes a multi- dimensional, nonlinear, predictive model. It consists of a Radial Basis Function Network and a least squares optimizer using QR decomposition. The optimized solution of a set of simultaneous equations in 81 unknowns is calculated in 150 (mu) S. The QR section emulates a triangular systolic array by the novel use of an array of 40 mature silicon DSP chips costing under DOL100 each. The DSP chips operate in synchronism at a 50 MHz clock rate passing data to each other through multi-port memories on a dead-letter box principle; there are no memory access conflicts and only two-port and three-port memories are required. The processor provides 1-GFlop of computing power per cubic-foot of electronics for a component cost of approximately DOL15,000.

  8. Canonical forms for nonlinear systems

    NASA Technical Reports Server (NTRS)

    Su, R.; Hunt, L. R.; Meyer, G.

    1983-01-01

    Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables.

  9. Expansion of the Hamiltonian of the planetary problem into the Poisson series in elements of the second Poincare system

    NASA Astrophysics Data System (ADS)

    Perminov, A. S.; Kuznetsov, E. D.

    2015-12-01

    The Hamiltonian of the N-planetary problem is written in the Jacobi coordinates using the second system of Poincare elements. The Hamiltonian is expanded into the Poisson series for the four-planet system. The computer algebra system Piranha is used for analytical transformations. Obtained expansions provide the Hamiltonian expression accuracy up to the third degree of the small parameter for giant planets of the Solar System and up to the second degree of the small parameter for extrasolar planetary systems. The ratio of sums of masses of the planets to the star mass can be selected as a small parameter.

  10. Symmetry of quantum phase space in a degenerate Hamiltonian system

    NASA Astrophysics Data System (ADS)

    Berman, G. P.; Demikhovskii, V. Ya.; Kamenev, D. I.

    2000-09-01

    The structure of the global "quantum phase space" is analyzed for the harmonic oscillator perturbed by a monochromatic wave in the limit when the perturbation amplitude is small. Usually, the phenomenon of quantum resonance was studied in nondegenerate [G. M. Zaslavsky, Chaos in Dynamic Systems (Harwood Academic, Chur, 1985)] and degenerate [Demikhovskii, Kamenev, and Luna-Acosta, Phys. Rev. E 52, 3351 (1995)] classically chaotic systems only in the particular regions of the classical phase space, such as the center of the resonance or near the separatrix. The system under consideration is degenerate, and even an infinitely small perturbation generates in the classical phase space an infinite number of the resonant cells which are arranged in the pattern with the axial symmetry of the order 2μ (where μ is the resonance number). We show analytically that the Husimi functions of all Floquet states (the quantum phase space) have the same symmetry as the classical phase space. This correspondence is demonstrated numerically for the Husimi functions of the Floquet states corresponding to the motion near the elliptic stable points (centers of the classical resonance cells). The derived results are valid in the resonance approximation when the perturbation amplitude is small enough, and the stochastic layers in the classical phase space are exponentially thin. The developed approach can be used for studying a global symmetry of more complicated quantum systems with chaotic behavior.

  11. Trace Formula for Linear Hamiltonian Systems with its Applications to Elliptic Lagrangian Solutions

    NASA Astrophysics Data System (ADS)

    Hu, Xijun; Ou, Yuwei; Wang, Penghui

    2015-04-01

    In the present paper, we build up trace formulas for both the linear Hamiltonian systems and Sturm-Liouville systems. The formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the Hessian of the action functional. A natural application is to study the non-degeneracy of linear Hamiltonian systems. Precisely, by the trace formula, we can give an estimation for the upper bound such that the non-degeneracy preserves. Moreover, we could estimate the relative Morse index by the trace formula. Consequently, a series of new stability criteria for the symmetric periodic orbits is given. As a concrete application, the trace formula is used to study the linear stability of elliptic Lagrangian solutions of the classical planar three-body problem, which depends on the mass parameter and the eccentricity . Based on the trace formula, we estimate the stable region and hyperbolic region of the elliptic Lagrangian solutions.

  12. Mechanism for stickiness suppression during extreme events in Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Krüger, Taline Suellen; Galuzio, Paulo Paneque; Prado, Thiago de Lima; Viana, Ricardo Luiz; Szezech, José Danilo; Lopes, Sergio Roberto

    2015-06-01

    In this paper we study how hyperbolic and nonhyperbolic regions in the neighborhood of a resonant island perform an important role allowing or forbidding stickiness phenomenon around islands in conservative systems. The vicinity of the island is composed of nonhyperbolic areas that almost prevent the trajectory to visit the island edge. For some specific parameters tiny channels are embedded in the nonhyperbolic area that are associated to hyperbolic fixed points localized in the neighborhood of the islands. Such channels allow the trajectory to be injected in the inner portion of the vicinity. When the trajectory crosses the barrier imposed by the nonhyperbolic regions, it spends a long time abandoning the vicinity of the island, since the barrier also prevents the trajectory from escaping from the neighborhood of the island. In this scenario the nonhyperbolic structures are responsible for the stickiness phenomena and, more than that, the strength of the sticky effect. We show that those properties of the phase space allow us to manipulate the existence of extreme events (and the transport associated to it) responsible for the nonequilibrium fluctuation of the system. In fact we demonstrate that by monitoring very small portions of the phase space (namely, ≈1 ×10-5% of it) it is possible to generate a completely diffusive system eliminating long-time recurrences that result from the stickiness phenomenon.

  13. Mechanism for stickiness suppression during extreme events in Hamiltonian systems.

    PubMed

    Krüger, Taline Suellen; Galuzio, Paulo Paneque; Prado, Thiago de Lima; Viana, Ricardo Luiz; Szezech, José Danilo; Lopes, Sergio Roberto

    2015-06-01

    In this paper we study how hyperbolic and nonhyperbolic regions in the neighborhood of a resonant island perform an important role allowing or forbidding stickiness phenomenon around islands in conservative systems. The vicinity of the island is composed of nonhyperbolic areas that almost prevent the trajectory to visit the island edge. For some specific parameters tiny channels are embedded in the nonhyperbolic area that are associated to hyperbolic fixed points localized in the neighborhood of the islands. Such channels allow the trajectory to be injected in the inner portion of the vicinity. When the trajectory crosses the barrier imposed by the nonhyperbolic regions, it spends a long time abandoning the vicinity of the island, since the barrier also prevents the trajectory from escaping from the neighborhood of the island. In this scenario the nonhyperbolic structures are responsible for the stickiness phenomena and, more than that, the strength of the sticky effect. We show that those properties of the phase space allow us to manipulate the existence of extreme events (and the transport associated to it) responsible for the nonequilibrium fluctuation of the system. In fact we demonstrate that by monitoring very small portions of the phase space (namely, ≈1×10(-5)% of it) it is possible to generate a completely diffusive system eliminating long-time recurrences that result from the stickiness phenomenon. PMID:26172768

  14. Nonlinear input-output systems

    NASA Technical Reports Server (NTRS)

    Hunt, L. R.; Luksic, Mladen; Su, Renjeng

    1987-01-01

    Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.

  15. Markov-Tree model of intrinsic transport in Hamiltonian systems

    NASA Technical Reports Server (NTRS)

    Meiss, J. D.; Ott, E.

    1985-01-01

    A particle in a chaotic region of phase space can spend a long time near the boundary of a regular region since transport there is slow. This 'stickiness' of regular regions is thought to be responsible for previous observations in numerical experiments of a long-time algebraic decay of the particle survival probability, i.e., survival probability approximately t to the (-z) power for large t. This paper presents a global model for transport in such systems and demonstrates the essential role of the infinite hierarchy of small islands interspersed in the chaotic region. Results for z are discussed.

  16. Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Chandre, C.; Jauslin, H. R.

    1998-12-01

    We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for 3 degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.

  17. Small-action Resonance in Hamiltonian Systems and Redistribution of Energetic Ions in Tokamaks

    SciTech Connect

    R.B. White; V.V. Lutsenko; Ya. I. Kolesnichenko; Yu. V. Yakovenko

    1999-07-01

    It has been found that an arbitrary small perturbation in an integrable Hamiltonian system typically leads to driven resonance in the regions of the phase space where at least one of the action variables is sufficiently small. In particular, such a small-action resonance is shown to play a dominant role in the sawtooth-crash-induced disappearance of a strongly localized gamma-ray and neutron emitting region in a tokamak plasma, which was observed experimentally.

  18. Hamiltonian quantum dynamics with separability constraints

    NASA Astrophysics Data System (ADS)

    Burić, Nikola

    2008-01-01

    Schroedinger equation on a Hilbert space H, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space PH. Separable states of a bipartite quantum system form a special submanifold of PH. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example the system of two interacting qubits. The constraints introduce nonlinearities which render the dynamics nontrivial. We show that the qualitative properties of the constrained dynamics clearly manifest the symmetry of the qubits system. In particular, if the quantum Hamilton's operator has not enough symmetry, the constrained dynamics is nonintegrable, and displays the typical features of a Hamiltonian dynamical system with mixed phase space. Possible physical realizations of the separability constraints are discussed.

  19. Variational Approach to a Class of P-T Symmetric Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Mikalopas, J.; Mancini, J. D.; Fessatidis, V.; Corvino, F. A.

    2009-03-01

    In the usual study of non-relativistic Quantum Mechanics, one chooses a real (Hermitian) potential so as to ensure a real energy spectrum for the corresponding Schr"odinger equation. In recent years, a number of authors have studied a class of complex potentials which are invariant under the combined symmetry P-T (here the operator P represents parity reflection and the operator T represents time reversal). For such P-T symmetric systems it has been shown that the energy eigenvalues of the Schr"odinger equation are real so long as the P-T symmetry is not spontaneously broken. Thus it would appear that rather than the usual demand for Hermiticity, it may be sufficient to have a P-T invariant Hamiltonian so long as the energy spectrum remains real. It should be noted however that this conjecture has not been proven, but rather has been demonstrated to be true for several sample Hamiltonian systems. Here we wish to apply a recently developed ansatz wherein a variational basis is constructed by systematically taking derivatives of an initial trial state with respect to a (set) of variational parameters. In particular we shall study the spectrum of the Hamiltonian H=p^2+x^2(ix)^α (α real) as a test case for the ansatz.

  20. Hamiltonian mechanics and planar fishlike locomotion

    NASA Astrophysics Data System (ADS)

    Kelly, Scott; Xiong, Hailong; Burgoyne, Will

    2007-11-01

    A free deformable body interacting with a system of point vortices in the plane constitutes a Hamiltonian system. A free Joukowski foil with variable camber shedding point vortices in an ideal fluid according to a periodically applied Kutta condition provides a model for fishlike locomotion which bridges the gap between inviscid analytical models that sacrifice realism for tractability and viscous computational models inaccessible to tools from nonlinear control theory. We frame such a model in the context of Hamiltonian mechanics and describe its relevance both to the study of hydrodynamic interactions within schools of fish and to the realization of model-based control laws for biomimetic autonomous robotic vehicles.

  1. The bi-Hamiltonian structure of some nonlinear fifth- and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants

    NASA Astrophysics Data System (ADS)

    Fuchssteiner, Benno; Oevel, Walter

    1982-03-01

    Using a bi-Hamiltonian formulation we give explicit formulas for the conserved quantities and infinitesimal generators of symmetries for some nonlinear fifth- and seventh-order nonlinear partial differential equations; among them, the Caudrey-Dodd-Gibbon-Sawada-Kotera equation and the Kupershmidt equation. We show that the Lie algebras of the symmetry groups of these equations are of a very special form: Among the C∞ vector fields they are generated from two given commuting vector fields by a recursive application of a single operator. Furthermore, for some higher order equations, those multisoliton solutions, which for ||t||→∞ asymptotically decompose into traveling wave solutions, are characterized as eigenvector decompositions of certain operators.

  2. The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of super Korteweg-de Vries equations

    NASA Astrophysics Data System (ADS)

    Restuccia, A.; Sotomayor, A.

    2013-11-01

    A supersymmetric breaking procedure for N = 1 super Korteweg-de Vries (KdV), using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting solitonic system of coupled KdV type system. It is shown that the Hamiltonian obtained by this procedure is bounded from below and in that sense represents a model which is physically admissible.

  3. The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of super Korteweg-de Vries equations

    SciTech Connect

    Restuccia, A.; Sotomayor, A.

    2013-11-15

    A supersymmetric breaking procedure for N= 1 super Korteweg-de Vries (KdV), using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting solitonic system of coupled KdV type system. It is shown that the Hamiltonian obtained by this procedure is bounded from below and in that sense represents a model which is physically admissible.

  4. Modeling of Nonlinear Systems using Genetic Algorithm

    NASA Astrophysics Data System (ADS)

    Hayashi, Kayoko; Yamamoto, Toru; Kawada, Kazuo

    In this paper, a newly modeling system by using Genetic Algorithm (GA) is proposed. The GA is an evolutionary computational method that simulates the mechanisms of heredity or evolution of living things, and it is utilized in optimization and in searching for optimized solutions. Most process systems have nonlinearities, so it is necessary to anticipate exactly such systems. However, it is difficult to make a suitable model for nonlinear systems, because most nonlinear systems have a complex structure. Therefore the newly proposed method of modeling for nonlinear systems uses GA. Then, according to the newly proposed scheme, the optimal structure and parameters of the nonlinear model are automatically generated.

  5. Noise in Nonlinear Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Moss, Frank; McClintock, P. V. E.

    2009-08-01

    List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.

  6. The Hamiltonian Structure and Euler-Poincare Formulation of the Valsov-Maxwell and Gyrokinetic System

    SciTech Connect

    J. Squire, H. Qin and W.M. Tang

    2012-09-25

    We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with the Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. __________________________________________________

  7. On the global structure of normal forms for slow-fast Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Avendaño Camacho, M.; Vorobiev, Yu.

    2013-04-01

    In the framework of Lie transforms and the global method of averaging, the normal forms of a multidimensional slow-fast Hamiltonian system are studied in the case when the flow of the unperturbed (fast) system is periodic and the induced {S}^1 1-action is not necessarily free and trivial. An intrinsic splitting of the second term in a {S}^1 1-invariant normal form of first order is derived in terms of the Hannay-Berry connection assigned to the periodic flow.

  8. Can model Hamiltonians describe the electron-electron interaction in π-conjugated systems?: PAH and graphene

    NASA Astrophysics Data System (ADS)

    Chiappe, G.; Louis, E.; San-Fabián, E.; Vergés, J. A.

    2015-11-01

    Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser-Parr-Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree-Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree-Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an ‘effective’ Hamiltonian including only on-site interactions (Hubbard)? The

  9. Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems

    SciTech Connect

    Oshemkov, Andrey A

    2010-10-06

    A complete invariant is constructed that is a solution of the problem of semilocal classification of saddle singularities of integrable Hamiltonian systems. Namely, a certain combinatorial object (an f{sub n}-graph) is associated with every nondegenerate saddle singularity of rank zero; as a result, the problem of semilocal classification of saddle singularities of rank zero is reduced to the problem of enumeration of the f{sub n}-graphs. This enables us to describe a simple algorithm for obtaining the lists of saddle singularities of rank zero for a given number of degrees of freedom and a given complexity. Bibliography: 24 titles.

  10. Nonlinear resonant phenomena in multilevel quantum systems

    NASA Astrophysics Data System (ADS)

    Hicke, Christian

    We study nonlinear resonant phenomena in two-level and multilevel quantum systems. Our results are of importance for applications in the areas of quantum control, quantum computation, and quantum measurement. We present a method to perform fault-tolerant single-qubit gate operations using Landau-Zener tunneling. In a single Landau-Zoner pulse, the qubit transition frequency is varied in time so that it passes through the frequency of a radiation field. We show that a simple three-pulse sequence allows eliminating errors in the gate up to the third order in errors in the qubit energies or the radiation frequency. We study the nonlinear transverse response of a spin S > 1/2 with easy-axis anisotropy. The coherent transverse response displays sharp dips or peaks when the modulation frequency is adiabatically swept through multiphoton resonance. The effect is a consequence of a certain conformal property of the spin dynamics in a magnetic field for the anisotropy energy ∝ S2z . The occurrence of the dips or peaks is determined by the spin state. Their shape strongly depends on the modulation amplitude. Higher-order anisotropy breaks the symmetry, leading to sharp steps in the transverse response as function of frequency. The results bear on the dynamics of molecular magnets in a static magnetic field. We show that a modulated large-spin system has special symmetry. In the presence of dissipation it leads to characteristic nonlinear effects. They include abrupt switching between transverse magnetization branches with varying modulating field without hysteresis and a specific pattern of switching in the presence of multistability and hysteresis. Along with steady forced vibrations the transverse spin components can display transient vibrations at a combination of the Larmor frequency and a slower frequency determined by the anisotropy energy. The analysis is based on a microscopic theory that takes into account relaxation mechanisms important for single

  11. Investigation of a Nonlinear Control System

    NASA Technical Reports Server (NTRS)

    Flugge-Lotz, I; Taylor, C F; Lindberg, H E

    1958-01-01

    A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

  12. BILL2D - A software package for classical two-dimensional Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Solanpää, J.; Luukko, P. J. J.; Räsänen, E.

    2016-02-01

    We present BILL2D, a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. BILL2D can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincaré sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a user guide, a developer's manual, and a documentation of the application program interface (API).

  13. Chaotic transport in Hamiltonian systems perturbed by a weak turbulent wave field

    SciTech Connect

    Abdullaev, S. S.

    2011-08-15

    Chaotic transport in a Hamiltonian system perturbed by a weak turbulent wave field is studied. It is assumed that a turbulent wave field has a wide spectrum containing up to thousands of modes whose phases are fluctuating in time with a finite correlation time. To integrate the Hamiltonian equations a fast symplectic mapping is derived. It has a large time-step equal to one full turn in angle variable. It is found that the chaotic transport across tori caused by the interactions of small-scale resonances have a fractal-like structure with the reduced or zero values of diffusion coefficients near low-order rational tori thereby forming transport barriers there. The density of rational tori is numerically calculated and its properties are investigated. It is shown that the transport barriers are formed in the gaps of the density of rational tori near the low-order rational tori. The dependencies of the depth and width of transport barriers on the wave field spectrum and the correlation time of fluctuating turbulent field (or the Kubo number) are studied. These numerical findings may have importance in understanding the mechanisms of transport barrier formation in fusion plasmas.

  14. Describing functions for nonlinear optical systems.

    PubMed

    Ghosh, A K

    1997-10-10

    The concept of describing functions is useful for analyzing and designing nonlinear systems. A proposal for using the idea of describing functions for studying the behavior of a nonlinear optical processing system is given. The describing function can be used in the same way that a coherent transfer function or optical transfer function is used to characterize linear, shift-invariant optical processors. Two coherent optical systems for measuring the magnitude of the describing function of nonlinear optical processors are suggested. PMID:18264243

  15. Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians

    SciTech Connect

    Buljubasich, Lisandro; Dente, Axel D.; Levstein, Patricia R.; Chattah, Ana K.; Pastawski, Horacio M.; Sánchez, Claudia M.

    2015-10-28

    We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.

  16. Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians

    NASA Astrophysics Data System (ADS)

    Buljubasich, Lisandro; Sánchez, Claudia M.; Dente, Axel D.; Levstein, Patricia R.; Chattah, Ana K.; Pastawski, Horacio M.

    2015-10-01

    We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.

  17. The Hamiltonian structure and Euler-Poincare formulation of the Vlasov-Maxwell and gyrokinetic systems

    SciTech Connect

    Squire, J.; Tang, W. M.; Qin, H.; Chandre, C.

    2013-02-15

    We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.

  18. Hamiltonian Structure of the Schrödinger Classical Dynamical System

    NASA Astrophysics Data System (ADS)

    Tessarotto, Massimo; Mond, Michael; Batic, Davide

    2016-05-01

    The connection between quantum mechanics and classical statistical mechanics has motivated in the past the representation of the Schrödinger quantum-wave equation in terms of "projections" onto the quantum configuration space of suitable phase-space asymptotic kinetic models. This feature has suggested the search of a possible exact super-dimensional classical dynamical system (CDS), denoted as Schrödinger CDS, which uniquely determines the time-evolution of the underlying quantum state describing a set of N like and mutually interacting quantum particles. In this paper the realization of the same CDS in terms of a coupled set of Hamiltonian systems is established. These are respectively associated with a quantum-hydrodynamic CDS advancing in time the quantum fluid velocity and a further one the RD-CDS, describing the relative dynamics with respect to the quantum fluid.

  19. Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity

    NASA Astrophysics Data System (ADS)

    Šepitka, Peter; Šimon Hilscher, Roman

    2016-04-01

    In this paper we derive a general limit characterization of principal solutions at infinity of linear Hamiltonian systems under no controllability assumption. The main result is formulated in terms of a limit involving antiprincipal solutions at infinity of the system. The novelty lies in the fact that the principal and antiprincipal solutions at infinity may belong to two different genera of conjoined bases, i.e., the eventual image of their first components is not required to be the same as in the known literature. For this purpose we extend the theory of genera of conjoined bases, which was recently initiated by the authors. We show that the orthogonal projector representing each genus of conjoined bases satisfies a symmetric Riccati matrix differential equation. This result then leads to an exact description of the structure of the set of all genera, in particular it forms a complete lattice. We also provide several examples, which illustrate our new theory.

  20. A canonical form for nonlinear systems

    NASA Technical Reports Server (NTRS)

    Su, R.; Hunt, L. R.

    1986-01-01

    The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.

  1. Landau-Zener problem in a three-level neutrino system with nonlinear time dependence

    SciTech Connect

    Keraenen, P.; Maalampi, J.; Myyrylaeinen, M.; Riittinen, J.

    2007-02-01

    We consider the level-crossing problem in a three-level system with nonlinearly time-varying Hamiltonian (time-dependence t{sup -3}). We study the validity of the so-called independent crossing approximation in the Landau-Zener model by making comparison with results obtained numerically in the density matrix approach. We also demonstrate the failure of the so-called 'nearest zero' approximation of the Landau-Zener level-crossing probability integral.

  2. Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory

    NASA Technical Reports Server (NTRS)

    Silva, Walter A.

    1999-01-01

    The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.

  3. Anomalous Diffusion and Mixing of Chaotic Orbits in Hamiltonian Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Ishizaki, R.; Horita, T.; Mori, H.

    1993-05-01

    Anomalous behaviors of the diffusion and mixing of chaotic orbits due to the intermittent sticking to the islands of normal tori and accelerator-mode tori in a widespread chaotic sea are studied numerically and theoretically for Hamiltonian systems with two degrees of freedom. The probability distribution functions for the coarse-grained velocity (characterizing the diffusion) and the coarse-grained expansion rate (characterizing the mixing) turn out to obey an anomalous scaling law which is quite different from the Gaussian. The scaling law is confirmed for both diffusion and mixing by numerical experiments on the heating map introduced by Karney, which exhibits remarkable statistical properties more clearly than the standard map. Its scaling exponents for the two cases, however, are found to be different from each other.

  4. Berry phase in nonlinear systems

    SciTech Connect

    Liu, J.; Fu, L. B.

    2010-05-15

    The Berry phase acquired by an eigenstate that experienced a nonlinear adiabatic evolution is investigated thoroughly. The circuit integral of the Berry connection of the instantaneous eigenstate cannot account for the adiabatic geometric phase, while the Bogoliubov excitations around the eigenstates are found to be accumulated during the nonlinear adiabatic evolution and contribute a finite phase of geometric nature. A two-mode model is used to illustrate our theory. Our theory is applicable to Bose-Einstein condensate, nonlinear light propagation, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics.

  5. Relativistic closed-form Hamiltonian for many-body gravitating systems in the post-Minkowskian approximation.

    PubMed

    Ledvinka, Tomás; Schäfer, Gerhard; Bicák, Jirí

    2008-06-27

    The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered. PMID:18643648

  6. Hamiltonian Description of Convective-cell Generation

    SciTech Connect

    J.A. Krommes and R.A. Kolesnikov

    2004-03-11

    The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted.

  7. Hamiltonian structure of the Vlasov-Einstein system and the problem of stability for spherical relativistic star clusters

    SciTech Connect

    Kandrup, H.E.; Morrison, P.J.

    1992-11-01

    The Hamiltonian formulation of the Vlasov-Einstein system, which is appropriate for collisionless, self-gravitating systems like clusters of stars that are so dense that gravity must be described by the Einstein equation, is presented. In particular, it is demonstrated explicitly in the context of a 3 + 1 splitting that, for spherically symmetric configurations, the Vlasov-Einstein system can be viewed as a Hamiltonian system, where the dynamics is generated by a noncanonical Poisson bracket, with the Hamiltonian generating the evolution of the distribution function f (a noncanonical variable) being the conserved ADM mass-energy H{sub ADM}. An explicit expression is derived for the energy {delta}({sup 2})H{sub ADM} associated with an arbitrary phase space preserving perturbation of an arbitrary spherical equilibrium, and it is shown that the equilibrium must be linearly stable if {delta}({sup 2})H{sub ADM} is positive semi-definite. Insight into the Hamiltonian reformulation is provided by a description of general finite degree of freedom systems.

  8. Hamiltonian structure of the Vlasov-Einstein system and the problem of stability for spherical relativistic star clusters

    SciTech Connect

    Kandrup, H.E. ); Morrison, P.J. . Inst. for Fusion Studies)

    1992-11-01

    The Hamiltonian formulation of the Vlasov-Einstein system, which is appropriate for collisionless, self-gravitating systems like clusters of stars that are so dense that gravity must be described by the Einstein equation, is presented. In particular, it is demonstrated explicitly in the context of a 3 + 1 splitting that, for spherically symmetric configurations, the Vlasov-Einstein system can be viewed as a Hamiltonian system, where the dynamics is generated by a noncanonical Poisson bracket, with the Hamiltonian generating the evolution of the distribution function f (a noncanonical variable) being the conserved ADM mass-energy H[sub ADM]. An explicit expression is derived for the energy [delta]([sup 2])H[sub ADM] associated with an arbitrary phase space preserving perturbation of an arbitrary spherical equilibrium, and it is shown that the equilibrium must be linearly stable if [delta]([sup 2])H[sub ADM] is positive semi-definite. Insight into the Hamiltonian reformulation is provided by a description of general finite degree of freedom systems.

  9. Hamiltonian description of the ideal fluid

    SciTech Connect

    Morrison, P.J.

    1994-01-01

    Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.

  10. Nonlinear model for building-soil systems

    SciTech Connect

    McCallen, D.B.; Romstad, K.M.

    1994-05-01

    A finite-element based, numerical analysis methodology has been developed for the nonlinear analysis of building-soil systems. The methodology utilizes a reduced-order, nonlinear continuum model to represent the building, and the soil is represented with a simple nonlinear two-dimensional plane strain finite element. The foundation of the building is idealized as a rigid block and the interface between the soil and the foundation is modeled with an interface contract element. The objectives of the current paper are to provide the theoretical development of the system model, with particular emphasis on the modeling of the foundation-soil contact, and to demonstrate the special-purpose finite-element program that has been developed for nonlinear analysis of the building-soil system. Examples are included that compare the results obtained with the special-purpose program with the results of a general-purpose nonlinear finite-element program.

  11. Explicit methods in extended phase space for inseparable Hamiltonian problems

    NASA Astrophysics Data System (ADS)

    Pihajoki, Pauli

    2015-03-01

    We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

  12. Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

    NASA Astrophysics Data System (ADS)

    Cremaschini, C.; Tessarotto, M.

    2012-01-01

    An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions ( EM-interacting N- body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie "no-interaction" theorem for the non-local Hamiltonian system considered here.

  13. Nonlinear waves in PT -symmetric systems

    NASA Astrophysics Data System (ADS)

    Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.

    2016-07-01

    Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.

  14. On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Fokas, A. S.; Anderson, R. L.

    1982-06-01

    We present an algorithmic method for obtaining an hereditary symmetry (the generalized squared-eigenfunction operator) from a given isospectral eigenvalue problem. This method is applied to the n×n eigenvalue problem considered by Ablowitz and Haberman and to the eigenvalue problem considered by Alonso. The relevant Hamiltonian formulations are also determined. Finally, an alternative method is presented in the case two evolution equations are related by a Miura type transformation and their Hamiltonian formulations are known.

  15. A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

    NASA Astrophysics Data System (ADS)

    Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

    2015-01-01

    We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

  16. Hamiltonian dynamics of vortex and magnetic lines in hydrodynamic type systems

    PubMed

    Kuznetsov; Ruban

    2000-01-01

    Vortex line and magnetic line representations are introduced for a description of flows in ideal hydrodynamics and magnetohydrodynamics (MHD), respectively. For incompressible fluids, it is shown with the help of this transformation that the equations of motion for vorticity Omega and magnetic field follow from a variational principle. By means of this representation, it is possible to integrate the hydrodynamic type system with the Hamiltonian H=integral|Omega|dr and some other systems. It is also demonstrated that these representations allow one to remove from the noncanonical Poisson brackets, defined in the space of divergence-free vector fields, the degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD, a new Weber-type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber-type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent, this transformation coincides with the Clebsch representation analog introduced by V.E. Zakharov and E. A. Kuznetsov [Dokl. Ajad. Nauk 194, 1288 (1970) [Sov. Phys. Dokl. 15, 913 (1971)

  17. Multistage slow relaxation in a Hamiltonian system: The Fermi-Pasta-Ulam model

    NASA Astrophysics Data System (ADS)

    Matsuyama, Hironori J.; Konishi, Tetsuro

    2015-08-01

    The relaxation process toward equipartition of energy among normal modes in a Hamiltonian system with many degrees of freedom, the Fermi-Pasta-Ulam (FPU) model is investigated numerically. We introduce a general indicator of relaxation σ which denotes the distance from equipartition state. In the time evolution of σ , some long-time interferences with relaxation, named "plateaus," are observed. In order to examine the details of the plateaus, relaxation time of σ and excitation time for each normal mode are measured as a function of the energy density ɛ0=E0/N . As a result, multistage relaxation is detected in the finite-size system. Moreover, by an analysis of the Lyapunov spectrum, the spectrum of mode energy occupancy, and the power spectrum of mode energy, we characterize the multistage slow relaxation, and some dynamical phases are extracted: quasiperiodic motion, stagnant motion (escaping from quasiperiodic motion), local chaos, and stronger chaos with nonthermal noise. We emphasize that the plateaus are robust against the arranging microscopic state. In other words, we can often observe plateaus and multistage slow relaxation in the FPU phase space. Slow relaxation is expected to remain or vanish in the thermodynamic limit depending on indicators.

  18. A design methodology for nonlinear systems containing parameter uncertainty: Application to nonlinear controller design

    NASA Technical Reports Server (NTRS)

    Young, G.

    1982-01-01

    A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.

  19. Markovian master equation for nonlinear systems

    NASA Astrophysics Data System (ADS)

    de los Santos-Sánchez, O.; Récamier, J.; Jáuregui, R.

    2015-06-01

    Within the f-deformed oscillator formalism, we derive a Markovian master equation for the description of the damped dynamics of nonlinear systems that interact with their environment. The applicability of this treatment to the particular case of a Morse-like oscillator interacting with a thermal field is illustrated, and the decay of quantum coherence in such a system is analyzed in terms of the evolution on phase space of its nonlinear coherent states via the Wigner function.

  20. Chaotic dynamics of weakly nonlinear systems

    SciTech Connect

    Vavriv, D.M.

    1996-06-01

    A review is given on the recent results in studying chaotic phenomena in weakly nonlinear systems. We are concerned with the class of chaotic states that can arise in physical systems with any degree of nonlinearity however small. The conditions for, and the mechanisms of, the transitions to chaos are discussed. These findings are illustrated by the results of the stability analysis of practical microwave and optical devices. {copyright} {ital 1996 American Institute of Physics.}

  1. Poincaré recurrences in Hamiltonian systems with a few degrees of freedom.

    PubMed

    Shepelyansky, D L

    2010-11-01

    Hundred twenty years after the fundamental work of Poincaré, the statistics of Poincaré recurrences in Hamiltonian systems with a few degrees of freedom is studied by numerical simulations. The obtained results show that in a regime, where the measure of stability islands is significant, the decay of recurrences is characterized by a power law at asymptotically large times. The exponent of this decay is found to be β≈1.3. This value is smaller compared to the average exponent β≈1.5 found previously for two-dimensional symplectic maps with divided phase space. On the basis of previous and present results a conjecture is put forward that, in a generic case with a finite measure of stability islands, the Poincaré exponent has a universal average value β≈1.3 being independent of number of degrees of freedom and chaos parameter. The detailed mechanisms of this slow algebraic decay are still to be determined. Poincaré recurrences in DNA are also discussed. PMID:21230536

  2. Stochastic averaging of quasi-partially integrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations

    NASA Astrophysics Data System (ADS)

    Jia, Wantao; Zhu, Weiqiu

    2014-03-01

    A stochastic averaging method for predicting the response of quasi-partially integrable and non-resonant Hamiltonian systems to combined Gaussian and Poisson white noise excitations is proposed. For the case with r (1Hamiltonian systems by using the stochastic jump-diffusion chain rule and the stochastic averaging theorem. An example is given to illustrate the applications of the proposed stochastic averaging method, and a combination of the finite difference method and the successive over-relaxation method is used to solve the reduced GFPK equation to obtain the stationary probability density of the system. The results are well verified by a Monte Carlo simulation.

  3. The effect of system nonlinearities on system noise statistics

    NASA Technical Reports Server (NTRS)

    Robinson, L. H., Jr.

    1971-01-01

    The effects are studied of nonlinearities in a baseline communications system on the system noise amplitude statistics. So that a meaningful identification of system nonlinearities can be made, the baseline system is assumed to transmit a single biphase-modulated signal through a relay satellite to the receiving equipment. The significant nonlinearities thus identified include square-law or product devices (e.g., in the carrier reference recovery loops in the receivers), bandpass limiters, and traveling wave tube amplifiers.

  4. Nonlinear dynamical system approaches towards neural prosthesis

    SciTech Connect

    Torikai, Hiroyuki; Hashimoto, Sho

    2011-04-19

    An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.

  5. Renormalization group theory of anomalous transport in systems with Hamiltonian chaos.

    PubMed

    Zaslavsky, G. M.

    1994-03-01

    We present a general scheme to describe particle kinetics in the case of incomplete Hamiltonian chaos when a set of islands of stability forms a complicated fractal space-time dynamics and when there is orbit stickiness to the islands' boundary. This kinetics is alternative to the "normal" Fokker-Planck-Kolmogorov equation. A new kinetic equation describes random wandering in the fractal space-time. Critical exponents of the anomalous kinetics are expressed through dynamical characteristics of a Hamiltonian using the renormalization group approach. Renormalization transformation has been applied simultaneously for space and time and fractional calculus has been exploited. PMID:12780083

  6. Renormalization group theory of anomalous transport in systems with Hamiltonian chaos

    NASA Astrophysics Data System (ADS)

    Zaslavsky, G. M.

    1994-03-01

    We present a general scheme to describe particle kinetics in the case of incomplete Hamiltonian chaos when a set of islands of stability forms a complicated fractal space-time dynamics and when there is orbit stickiness to the islands' boundary. This kinetics is alternative to the ``normal'' Fokker-Planck-Kolmogorov equation. A new kinetic equation describes random wandering in the fractal space-time. Critical exponents of the anomalous kinetics are expressed through dynamical characteristics of a Hamiltonian using the renormalization group approach. Renormalization transformation has been applied simultaneously for space and time and fractional calculus has been exploited.

  7. Statistical energy analysis of nonlinear vibrating systems.

    PubMed

    Spelman, G M; Langley, R S

    2015-09-28

    Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy being found in frequency bands other than those being driven by external forces. To analyse this phenomenon, a method is developed here in which the response of the structure in the frequency domain is divided into frequency bands, and the energy flow between the frequency bands is calculated. The frequency bands are assigned an energy variable to describe the mean response and the nonlinear coupling between bands is described in terms of weighted summations of the convolutions of linear modal transfer functions. This represents a nonlinear extension to an established linear theory known as statistical energy analysis (SEA). The nonlinear extension to SEA theory is presented for the case of a plate structure with quadratic and cubic nonlinearity. PMID:26303923

  8. Damage detection in initially nonlinear systems

    SciTech Connect

    Bornn, Luke; Farrar, Charles; Park, Gyuhae

    2009-01-01

    The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits, SHM has been widely studied over the past decade. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state - a condition that often does not hold in complex 'real world' systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment.

  9. A generic formulation for emittance and lattice function evolution for non-Hamiltonian systems with stochastic effects

    SciTech Connect

    Berg, J. S.

    2015-05-03

    I describe a generic formulation for the evolution of emittances and lattice functions under arbitrary, possibly non-Hamiltonian, linear equations of motion. The average effect of stochastic processes, which would include ionization interactions and synchrotron radiation, is also included. I first compute the evolution of the covariance matrix, then the evolution of emittances and lattice functions from that. I examine the particular case of a cylindrically symmetric system, which is of particular interest for ionization cooling.

  10. ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS: On Feasibility of Variable Separation Method Based on Hamiltonian System for a Class of Plate Bending Equations

    NASA Astrophysics Data System (ADS)

    Eburilitu; Alatancang

    2010-03-01

    The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy's principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations.

  11. Discrete time learning control in nonlinear systems

    NASA Technical Reports Server (NTRS)

    Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh

    1992-01-01

    In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.

  12. Impulsive synchronization of networked nonlinear dynamical systems

    NASA Astrophysics Data System (ADS)

    Jiang, Haibo; Bi, Qinsheng

    2010-06-01

    In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.

  13. Kolmogorov-Arnold-Moser renormalization-group approach to the breakup of invariant tori in Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Chandre, C.; Govin, M.; Jauslin, H. R.

    1998-02-01

    We analyze the breakup of invariant tori in Hamiltonian systems with two degrees of freedom using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We consider a class of Hamiltonians quadratic in the action variables that is invariant under the chosen KAM transformations, following the approach of Thirring. The numerical implementation of the transformation shows that the KAM iteration converges up to the critical coupling at which the torus breaks up. By combining this iteration with a renormalization, consisting of a shift of resonances and rescalings of momentum and energy, we obtain a more efficient method that allows one to determine the critical coupling with high accuracy. This transformation is based on the physical mechanism of the breakup of invariant tori. We show that the critical surface of the transformation is the stable manifold of codimension one of a nontrivial fixed point, and we discuss its universality properties.

  14. State Identification in Nonlinear Systems

    SciTech Connect

    Holloway, James Paul

    2005-02-06

    A state estimation method based on finding a system state that causes a model to match a set of system measurements is regularized by requiring that sudden changes in system state be avoided. The required optimization is accomplished by a pattern search algorithm. The method does not require derivative information or linearization of the model. Is has been applied to a 10 dimensional model of a fast reactor system.

  15. Quantum simulations with a trilinear Hamiltonian in trapped-ion system

    NASA Astrophysics Data System (ADS)

    Ding, Shiqian; Maslennikov, Gleb; Hablutzel, Roland; Matsukevich, Dzmitry

    2016-05-01

    A non-degenerate parametric oscillator, described by a trilinear Hamiltonian, is one of the most fundamental models in quantum optics. We experimentally realize this kind of interaction in fully quantum regime with three motional modes of three trapped ytterbium ions. This interaction is induced by the intrinsic anharmonicity of Coulomb potential and manifests itself by more than 100 cycles of coherent energy exchange at single quantum level between different motional modes. By exploiting this interaction, we simulate the process of non-degenerate parametric down conversion in a regime of depleted pump, demonstrate deviation from the thermal statistic for the `signal' and `idler' modes and discuss its relation with a simple model of Hawking radiation. We also present experimental results on simulation of Jaynes-Cummings model using this trilinear Hamiltonian.

  16. Quadratic boundedness of uncertain nonlinear dynamic systems

    NASA Astrophysics Data System (ADS)

    Brockman, Mark Lawrence

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

  17. Perturbation Methods and Closure Approximations in Nonlinear Systems.

    NASA Astrophysics Data System (ADS)

    Dubin, Daniel Herschel Eli

    In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, we consider the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. For small Larmor radius the equations are similar to those of Lee. Several new effects appear which are absent from conventional theories. We show that the wave kinetic equation of Galeev and Sagdeev neglects several important gyrokinetic effects. In the second section, statistical closure theories are applied to simple dynamical systems. We use the logistic map as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the Direct Interaction Approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodicity constraint on a Langevin form of the D.I.A. a new stable closure is developed. The relation between the predictability theory of Kraichnan and the theory of Liapunov exponents is considered. Realizability constraints on the moments of a distribution are formulated using Kuhn-Tucker multipliers. Results are related to the work of Sandri and Kraichnan, but the variational technique employed allows for a more elegant and general approach. The realizability criteria are

  18. Evolutionary quantitative genetics of nonlinear developmental systems.

    PubMed

    Morrissey, Michael B

    2015-08-01

    In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances. PMID:26174586

  19. Squeezing spectra for nonlinear optical systems

    NASA Technical Reports Server (NTRS)

    Collett, M. J.; Walls, D. F.

    1985-01-01

    The squeezing spectra for the output fields of several intracavity nonlinear optical systems are obtained. It is shown that at critical points, e.g., the turning points for optical bistability, the threshold for parametric oscillation, and the self-pulsing instability in second-harmonic generation, perfect squeezing in the output field is, in principle, possible.

  20. Stochastic volatility models at ρ=±1 as second class constrained Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Contreras G., Mauricio

    2014-07-01

    systems (Dirac, 1958, 1967) must be employed, and Dirac's analysis reveals that the constraints are second class. In order to obtain the transition probability density or the option price correctly, one must evaluate the propagator as a constrained Hamiltonian path-integral (Henneaux and Teitelboim, 1992), in a similar way to the high energy gauge theory models. In fact, for all stochastic volatility models, after integrating over momentum variables, one obtains an effective Euclidean Lagrangian path-integral over the volatility alone. The role of the second class constraints is determining the underlying asset price S completely in terms of volatility, so it plays no role in the path integral. In order to examine the effect of the constraints on the dynamics for both extreme limits, the probability density function is evaluated by using semi-classical arguments, in an analogous manner to that developed in Hagan et al. (2002), for the SABR model.

  1. Geometric Hamiltonian structures and perturbation theory

    SciTech Connect

    Omohundro, S.

    1984-08-01

    We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.

  2. Regularity versus randomness in matrix-element distributions in quantum nonintegrable Hamiltonian systems. II. Colored random matrix as a phenomenological model for level statistics of many-degree-of-freedom Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Shudo, Akira; Matsushita, Toshiki

    1990-02-01

    A class of colored (non-δ-correlated) random matrices composed of two independent systems of random number sequences, each of which is allocated to diagonal and off-diagonal parts of the matrices, is studied as workable models for the analysis of level statistics of sufficiently large degree-of-freedom Hamiltonian systems. In band random-matrix models, the rapid saturation toward the Wigner-type distribution as a function of the bandwidth is observed in spacing distribution patterns, suggesting that colored random matrices are capable of reproducing the non-δ-correlated random property found in level-spacing characteristics of real Hamiltonian systems. Detailed analysis reveals that at least two system parameters characterizing the colored random matrices are necessary for a workable basis of the model. The effect of the variance around the mean value of random number sequences on the spacing distribution is investigated in the small-bandwidth region, and a new type of anomalous distribution with non-Wigner-like distribution patterns is found in the small-variance limit.

  3. Non-Hermitian Hamiltonians and stability of pure states

    NASA Astrophysics Data System (ADS)

    Zloshchastiev, Konstantin G.

    2015-11-01

    We demonstrate that quantum fluctuations can cause, under certain conditions, the dynamical instability of pure states that can result in their evolution into mixed states. It is shown that the degree and type of such an instability are controlled by the environment-induced anti-Hermitian terms in Hamiltonians. Using the quantum-statistical approach for non-Hermitian Hamiltonians and related non-linear master equation, we derive the equations that are necessary to study the stability properties of any model described by a non-Hermitian Hamiltonian. It turns out that the instability of pure states is not preassigned in the evolution equation but arises as the emergent phenomenon in its solutions. In order to illustrate the general formalism and different types of instability that may occur, we perform the local stability analysis of some exactly solvable two-state models, which are being used in the theories of open quantum-optical and spin systems.

  4. Indirect learning control for nonlinear dynamical systems

    NASA Technical Reports Server (NTRS)

    Ryu, Yeong Soon; Longman, Richard W.

    1993-01-01

    In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

  5. Optimal control of open quantum systems: A combined surrogate Hamiltonian optimal control theory approach applied to photochemistry on surfaces

    SciTech Connect

    Asplund, Erik; Kluener, Thorsten

    2012-03-28

    In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ({Dirac_h}/2{pi})=m{sub e}=e=a{sub 0}= 1, have been used unless otherwise stated.

  6. Spectral decomposition of nonlinear systems with memory

    NASA Astrophysics Data System (ADS)

    Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

    2016-02-01

    We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

  7. Nonlinear dynamic macromodeling techniques for audio systems

    NASA Astrophysics Data System (ADS)

    Ogrodzki, Jan; Bieńkowski, Piotr

    2015-09-01

    This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

  8. Model reduction of systems with localized nonlinearities.

    SciTech Connect

    Segalman, Daniel Joseph

    2006-03-01

    An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.

  9. Efficient computational approaches to obtain periodic orbits in Hamiltonian systems: application to the motion of a lunar orbiter

    NASA Astrophysics Data System (ADS)

    Dena, Ángeles; Abad, Alberto; Barrio, Roberto

    2016-01-01

    In this paper, we study the problem of computing periodic orbits of Hamiltonian systems providing large families of such orbits. Periodic orbits constitute one of the most important invariants of a system, and this paper provides a comprehensive analysis of two efficient computational approaches for Hamiltonian systems. First, a new version of the grid search method, applied to problems with three degrees of freedom, has been considered to find, systematically, symmetric periodic orbits. To obtain non-symmetric periodic orbits, we use a modification of an optimization method based on an evolutionary strategy. Both methods require a great computational effort to find a big number of periodic orbits, and we apply parallelization tools to reduce the CPU time. Finally, we present a strategy to provide initial conditions of the periodic orbits with arbitrary precision. We apply all these algorithms to the problem of the motion of the lunar orbiter referred to the rotating reference frame of the Moon. The periodic orbits of this problem are very useful from the space engineering point of view because they provide low-cost orbits.

  10. Extensions of Natural Hamiltonians

    NASA Astrophysics Data System (ADS)

    Rastelli, G.

    2014-03-01

    Given an n-dimensional natural Hamiltonian L on a Riemannian or pseudo-Riemannian manifold, we call "extension" of L the n+1 dimensional Hamiltonian H = ½p2u + α(u)L + β(u) with new canonically conjugated coordinates (u,pu). For suitable L, the functions α and β can be chosen depending on any natural number m such that H admits an extra polynomial first integral in the momenta of degree m, explicitly determined in the form of the m-th power of a differential operator applied to a certain function of coordinates and momenta. In particular, if L is maximally superintegrable (MS) then H is MS also. Therefore, the extension procedure allows the creation of new superintegrable systems from old ones. For m=2, the extra first integral generated by the extension procedure determines a second-order symmetry operator of a Laplace-Beltrami quantization of H, modified by taking in account the curvature of the configuration manifold. The extension procedure can be applied to several Hamiltonian systems, including the three-body Calogero and Wolfes systems (without harmonic term), the Tremblay-Turbiner-Winternitz system and n-dimensional anisotropic harmonic oscillators. We propose here a short review of the known results of the theory and some previews of new ones.

  11. Reduction of quantum analogs of Hamiltonian systems described by Lie algebras to orbits in a coadjoint representation

    NASA Astrophysics Data System (ADS)

    Lisitsyn, Ya. V.; Shapovalov, A. V.

    1998-05-01

    A study is made of the possibility of reducing quantum analogs of Hamiltonian systems to Lie algebras. The procedure of reducing classical systems to orbits in a coadjoint representation based on Lie algebra is well-known. An analog of this procedure for quantum systems described by linear differential equations (LDEs) in partial derivatives is proposed here on the basis of the method of noncommutative integration of LDEs. As an example illustrating the procedure, an examination is made of nontrivial systems that cannot be integrated by separation of variables: the Gryachev-Chaplygin hydrostat and the Kovalevskii gyroscope. In both cases, the problem is reduced to a system with a smaller number of variables.

  12. Time-frequency characterization of nonlinear normal modes and challenges in nonlinearity identification of dynamical systems

    NASA Astrophysics Data System (ADS)

    Pai, P. Frank

    2011-10-01

    Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.

  13. Nonlinear Network Dynamics on Earthquake Fault Systems

    SciTech Connect

    Rundle, Paul B.; Rundle, John B.; Tiampo, Kristy F.; Sa Martins, Jorge S.; McGinnis, Seth; Klein, W.

    2001-10-01

    Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.

  14. Singularity perturbed zero dynamics of nonlinear systems

    NASA Technical Reports Server (NTRS)

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

    1992-01-01

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

  15. Chaotic Hamiltonian dynamics

    SciTech Connect

    Bialek, J.M.

    1988-01-01

    Chaotic behavior may be observed in deterministic Hamiltonian Systems with as few as three dimensions, i.e, X, P, and t. The amount of chaotic behavior depends on the relative influence of the integrable and non-integrable parts of the Hamiltonian. The Standard Map is such a system and the amount of chaotic behavior may be varied by adjusting a single parameter. The global phase space portrait is a complicated mixture of quiescent and chaotic regions. First a new calculational method, characterized by a Fractual Diagram, is presented. This allows the quantitative prediction of the boundaries between regular and chaotic regions in phase space. Where these barriers are located gives qualitative insight into diffusion in phase space. The method is illustrated with the Standard Map but may be applied to any Hamiltonian System. The second phenomenon is the Universal Behavior predicted to occur for all area preserving maps. As a parameter is varied causing the mapping to become more chaotic a pattern is observed in the location and stability of the fixed points of the maps. The fixed points undergo an infinite sequence of period doubling bifurcations in a finite range of the parameter. The relative locations of the fixed point bifurcation and the parameter intervals between bifurcations both asymptotically approach constants which are Universal in that the same constants keep appearing in different problems.

  16. (Investigation of transitions from order to chaos in dynamical systems)

    SciTech Connect

    Not Available

    1990-01-01

    This report discusses: torus structure in higher dimensional hamiltonian systems; particle heating and stochastic web diffusion; scaling behavior of coupled conservative nonlinear systems; box counting algorithm and dimensional analysis of a pulsar; and universality of coupled nonlinear systems. (LSP)

  17. The Bogoliubov-de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry

    SciTech Connect

    Correa, Francisco; Dunne, Gerald V.; Plyushchay, Mikhail S.

    2009-12-15

    We show that the Ginzburg-Landau expansion of the grand potential for the Bogoliubov-de Gennes Hamiltonian is determined by the integrable nonlinear equations of the AKNS hierarchy, and that this provides the natural mathematical framework for a hidden nonlinear quantum mechanical supersymmetry underlying the dynamics.

  18. Hamiltonian analysis of interacting fluids

    NASA Astrophysics Data System (ADS)

    Banerjee, Rabin; Ghosh, Subir; Mitra, Arpan Krishna

    2015-05-01

    Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed.

  19. Linear pattern dynamics in nonlinear threshold systems

    SciTech Connect

    Rundle, John B.; Klein, W.; Tiampo, Kristy; Gross, Susanna

    2000-03-01

    Complex nonlinear threshold systems frequently show space-time behavior that is difficult to interpret. We describe a technique based upon a Karhunen-Loeve expansion that allows dynamical patterns to be understood as eigenstates of suitably constructed correlation operators. The evolution of space-time patterns can then be viewed in terms of a ''pattern dynamics'' that can be obtained directly from observable data. As an example, we apply our methods to a particular threshold system to forecast the evolution of patterns of observed activity. Finally, we perform statistical tests to measure the quality of the forecasts. (c) 2000 The American Physical Society.

  20. Nonlinear Tides in Close Binary Systems

    NASA Astrophysics Data System (ADS)

    Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh

    2012-06-01

    We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' >~ 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P <~ 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the

  1. NONLINEAR TIDES IN CLOSE BINARY SYSTEMS

    SciTech Connect

    Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh

    2012-06-01

    We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' {approx}> 10-100 M{sub Circled-Plus} at orbital periods P Almost-Equal-To 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P {approx}< 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N Almost-Equal-To 10{sup 3}[P/10 days] for a solar-type star) and drives them as a single coherent unit with

  2. Nonlinear control for dual quaternion systems

    NASA Astrophysics Data System (ADS)

    Price, William D.

    The motion of rigid bodies includes three degrees of freedom (DOF) for rotation, generally referred to as roll, pitch and yaw, and 3 DOF for translation, generally described as motion along the x, y and z axis, for a total of 6 DOF. Many complex mechanical systems exhibit this type of motion, with constraints, such as complex humanoid robotic systems, multiple ground vehicles, unmanned aerial vehicles (UAVs), multiple spacecraft vehicles, and even quantum mechanical systems. These motions historically have been analyzed independently, with separate control algorithms being developed for rotation and translation. The goal of this research is to study the full 6 DOF of rigid body motion together, developing control algorithms that will affect both rotation and translation simultaneously. This will prove especially beneficial in complex systems in the aerospace and robotics area where translational motion and rotational motion are highly coupled, such as when spacecraft have body fixed thrusters. A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group SE(3). An eight dimensional representation of screw theory (combining dual numbers with traditional quaternions), dual quaternions allow for the development of control techniques for 6 DOF motion simultaneously. In this work variable structure nonlinear control methods are developed for dual quaternion systems. These techniques include use of sliding mode control. In particular, sliding mode methods are developed for use in dual quaternion systems with unknown control direction. This method, referred to as self-reconfigurable control, is based on the creation of multiple equilibrium surfaces for the system in the extended state space. Also in this work, the control problem for a class of driftless nonlinear systems is

  3. On Hamiltonian systems in two degrees of freedom with invariants quartic in the momenta of form p21p22ṡṡṡ

    NASA Astrophysics Data System (ADS)

    Evans, N. W.

    1990-03-01

    A search is made for autonomous Hamiltonian systems in two degrees of freedom which admit a second invariant quartic in the momenta with leading term p21p22/ 2. A sufficient condition for the resulting functional equation to possess solutions is deduced and a family of integrable systems is identified, which under the equivalence class of linear transformations reduce to a simpler integrable system found originally by Bozis. The method of Lax pairs is used to find further solutions to the functional equation and give new classes of integrable but nonseparable Hamiltonians.

  4. Phase space theory of quantum–classical systems with nonlinear and stochastic dynamics

    SciTech Connect

    Burić, Nikola Popović, Duška B.; Radonjić, Milan; Prvanović, Slobodan

    2014-04-15

    A novel theory of hybrid quantum–classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum–classical phase space. Both, the quantum and classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum–classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement. -- Highlights: •A novel theory of quantum–classical systems is developed. •Framework of quantum constrained dynamical systems is used. •A dynamical description of the measurement induced collapse is obtained.

  5. Constants of motion for constrained Hamiltonian systems: A particle around a charged rotating black hole

    SciTech Connect

    Igata, Takahisa; Ishihara, Hideki; Koike, Tatsuhiko

    2011-03-15

    We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint, which arises from the reparametrization invariance of the particle orbit. As the necessary and sufficient condition for the existence of a constant of motion, we obtain a set of equations with a hierarchical structure, which is understood as a generalization of the Killing tensor equation. It is also a generalization of the conventional argument in that it includes the case when the conservation condition holds only on the constraint surface in the phase space. In that case, it is shown that the constant of motion is associated with a conformal Killing tensor. We apply the hierarchical equations and find constants of motion in the case of a charged particle in an electromagnetic field in black hole spacetimes. We also demonstrate that gravitational and electromagnetic fields exist in which a charged particle has a constant of motion associated with a conformal Killing tensor.

  6. Observers for discrete-time nonlinear systems

    NASA Astrophysics Data System (ADS)

    Grossman, Walter D.

    Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. Improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed.

  7. Particle systems and nonlinear Landau damping

    SciTech Connect

    Villani, Cédric

    2014-03-15

    Some works dealing with the long-time behavior of interacting particle systems are reviewed and put into perspective, with focus on the classical Kolmogorov–Arnold–Moser theory and recent results of Landau damping in the nonlinear perturbative regime, obtained in collaboration with Clément Mouhot. Analogies are discussed, as well as new qualitative insights in the theory. Finally, the connection with a more recent work on the inviscid Landau damping near the Couette shear flow, by Bedrossian and Masmoudi, is briefly discussed.

  8. Design of suboptimal regulators for nonlinear systems

    NASA Technical Reports Server (NTRS)

    Balaram, J.; Saridis, G. N.

    1985-01-01

    An optimal feedback control law is preferred for the regulation of a deterministic nonlinear system. In this paper, a practical, iterative design method leading to a sequence of suboptimal control laws with successively improved performance is presented. The design method requires the determination of an upper bound to the performance of each successive control law. This is obtained by solving a partial differential inequality by means of a linear programming technique. Robustness properties and the application of the design method to the control of a robot manipulator arm are also presented.

  9. Output feedback adaptive fuzzy control of uncertain MIMO nonlinear systems with unknown input nonlinearities.

    PubMed

    Shahnazi, Reza

    2015-01-01

    An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations. PMID:25104646

  10. Boosted X Waves in Nonlinear Optical Systems

    SciTech Connect

    Arevalo, Edward

    2010-01-15

    X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.

  11. Impulse position control algorithms for nonlinear systems

    NASA Astrophysics Data System (ADS)

    Sesekin, A. N.; Nepp, A. N.

    2015-11-01

    The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

  12. Impulse position control algorithms for nonlinear systems

    SciTech Connect

    Sesekin, A. N.; Nepp, A. N.

    2015-11-30

    The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

  13. Parameter identification for nonlinear aerodynamic systems

    NASA Technical Reports Server (NTRS)

    Pearson, Allan E.

    1990-01-01

    Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

  14. [Investigation of transitions from order to chaos in dynamical systems]. Annual progress report

    SciTech Connect

    Not Available

    1990-12-31

    This report discusses: torus structure in higher dimensional hamiltonian systems; particle heating and stochastic web diffusion; scaling behavior of coupled conservative nonlinear systems; box counting algorithm and dimensional analysis of a pulsar; and universality of coupled nonlinear systems. (LSP)

  15. Nonlinear Mixing in Optical Multicarrier Systems

    NASA Astrophysics Data System (ADS)

    Hameed, Mahmood Abdul

    Although optical fiber has a vast spectral bandwidth, efficient use of this bandwidth is still important in order to meet the ever increased capacity demand of optical networks. In addition to wavelength division multiplexing, it is possible to partition multiple low-rate subcarriers into each high speed wavelength channel. Multicarrier systems not only ensure efficient use of optical and electrical components, but also tolerate transmission impairments. The purpose of this research is to understand the impact of mixing among subcarriers in Radio-Over-Fiber (RoF) and high speed optical transmission systems, and experimentally demonstrate techniques to minimize this impact. We also analyze impact of clipping and quantization on multicarrier signals and compare bandwidth efficiency of two popular multiplexing techniques, namely, orthogonal frequency division multiplexing (OFDM) and Nyquist modulation. For an OFDM-RoF system, we present a novel technique that minimizes the RF domain signal-signal beat interference (SSBI), relaxes the phase noise limit on the RF carrier, realizes the full potential of optical heterodyne-based RF carrier generation, and increases the performance-to-cost ratio of RoF systems. We demonstrate a RoF network that shares the same RF carrier for both downlink and uplink, avoiding the need of an additional RF oscillator in the customer unit. For multi-carrier optical transmission, we first experimentally compare performance degradations of coherent optical OFDM and single-carrier Nyquist pulse modulated systems in a nonlinear environment. We then experimentally evaluate SSBI compensation techniques in the presence of semiconductor optical amplifier (SOA) induced nonlinearities for a multicarrier optical system with direct detection. We show that SSBI contamination can be significantly reduced from the data signal when the carrier-to-signal power ratio is sufficiently low.

  16. Passive dynamic controllers for nonlinear mechanical systems

    NASA Technical Reports Server (NTRS)

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

    1991-01-01

    A methodology for model-independant controller design for controlling large angular motion of multi-body dynamic systems is outlined. The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system and at the same time suppress the vibration due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameter, even if the controlled system is nonlinear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach to a flexible six-degree-of-freedom manipulator.

  17. Nonlinear dynamic analysis of flexible multibody systems

    NASA Technical Reports Server (NTRS)

    Bauchau, Olivier A.; Kang, Nam Kook

    1991-01-01

    Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.

  18. Direct adaptive control for nonlinear uncertain dynamical systems

    NASA Astrophysics Data System (ADS)

    Hayakawa, Tomohisa

    In light of the complex and highly uncertain nature of dynamical systems requiring controls, it is not surprising that reliable system models for many high performance engineering and life science applications are unavailable. In the face of such high levels of system uncertainty, robust controllers may unnecessarily sacrifice system performance whereas adaptive controllers are clearly appropriate since they can tolerate far greater system uncertainty levels to improve system performance. In this dissertation, we develop a Lyapunov-based direct adaptive and neural adaptive control framework that addresses parametric uncertainty, unstructured uncertainty, disturbance rejection, amplitude and rate saturation constraints, and digital implementation issues. Specifically, we consider the following research topics; direct adaptive control for nonlinear uncertain systems with exogenous disturbances; robust adaptive control for nonlinear uncertain systems; adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints; adaptive reduced-order dynamic compensation for nonlinear uncertain systems; direct adaptive control for nonlinear matrix second-order dynamical systems with state-dependent uncertainty; adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia; direct adaptive control of nonnegative and compartmental dynamical systems with time delay; adaptive control for nonlinear nonnegative and compartmental dynamical systems with applications to clinical pharmacology; neural network adaptive control for nonlinear nonnegative dynamical systems; passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems; neural network adaptive dynamic output feedback control for nonlinear nonnegative systems using tapped delay memory units; Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances

  19. Application of nonlinear time series models to driven systems

    SciTech Connect

    Hunter, N.F. Jr.

    1990-01-01

    In our laboratory we have been engaged in an effort to model nonlinear systems using time series methods. Our objectives have been, first, to understand how the time series response of a nonlinear system unfolds as a function of the underlying state variables, second, to model the evolution of the state variables, and finally, to predict nonlinear system responses. We hope to address the relationship between model parameters and system parameters in the near future. Control of nonlinear systems based on experimentally derived parameters is also a planned topic of future research. 28 refs., 15 figs., 2 tabs.

  20. Lowest eigenvalues of random Hamiltonians

    SciTech Connect

    Shen, J. J.; Zhao, Y. M.; Arima, A.; Yoshinaga, N.

    2008-05-15

    In this article we study the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues is applicable to many different systems. We improve the accuracy of the formula by considering the third central moment. We show that these formulas are applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.

  1. The Hamiltonian structure of the (2+1)-dimensional Ablowitz--Kaup--Newell--Segur hierarchy

    SciTech Connect

    Athorne, C. ); Dorfman, I.Y. )

    1993-08-01

    By considering Hamiltonian theory over a suitable (noncommutative) ring the nonlinear evolution equations of the Ablowitz--Kaup--Newell--Segur (2+1) hierarchy are incorporated into a Hamiltonian framework and a modified Lenard scheme.

  2. On state representations of nonlinear implicit systems

    NASA Astrophysics Data System (ADS)

    Pereira da Silva, Paulo Sergio; Batista, Simone

    2010-03-01

    This work considers a semi-implicit system Δ, that is, a pair (S, y), where S is an explicit system described by a state representation ? , where x(t) ∈ ℝ n and u(t) ∈ ℝ m , which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) ∈ ℝ l . An input candidate is a set of functions v = (v 1, …, v s ), which may depend on time t, on x, and on u and its derivatives up to a finite order. The problem of finding a (local) proper state representation ż = g(t, z, v) with input v for the implicit system Δ is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Δ. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Lévine, Martin, and Rouchon (1999) ('A Lie-Bäcklund Approach to Equivalence and Flatness of Nonlinear Systems', IEEE Transactions on Automatic Control, 44(5), (922-937)).

  3. Bifurcations and Patterns in Nonlinear Dissipative Systems

    SciTech Connect

    Guenter Ahlers

    2005-05-27

    This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.

  4. Hamiltonian Framework for Short Optical Pulses

    NASA Astrophysics Data System (ADS)

    Amiranashvili, Shalva

    Physics of short optical pulses is an important and active research area in nonlinear optics. In this Chapter we theoretically consider the most extreme representatives of short pulses that contain only several oscillations of electromagnetic field. Description of such pulses is traditionally based on envelope equations and slowly varying envelope approximation, despite the fact that the envelope is not "slow" and, moreover, there is no clear definition of such a "fast" envelope. This happens due to another paradoxical feature: the standard (envelope) generalized nonlinear Schrödinger equation yields very good correspondence to numerical solutions of full Maxwell equations even for few-cycle pulses, the thing that should not be.In what follows we address ultrashort optical pulses using Hamiltonian framework for nonlinear waves. As it appears, the standard optical envelope equation is just a reformulation of general Hamiltonian equations. In a sense, no approximations are required, this is why the generalized nonlinear Schrödinger equation is so effective. Moreover, the Hamiltonian framework contributes greatly to our understanding of "fast" envelopes, ultrashort solitons, stability and radiation of optical pulses. Even the inclusion of dissipative terms is possible making the Hamiltonian approach an universal theoretical tool also in extreme nonlinear optics.

  5. Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings

    SciTech Connect

    Kadtke, J.B.; Bulsara, A.

    1997-12-01

    These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)

  6. Generalized hamilton-jacobi-bellman formulation -based neural network control of affine nonlinear discrete-time systems.

    PubMed

    Chen, Zheng; Jagannathan, Sarangapani

    2008-01-01

    In this paper, we consider the use of nonlinear networks towards obtaining nearly optimal solutions to the control of nonlinear discrete-time (DT) systems. The method is based on least squares successive approximation solution of the generalized Hamilton-Jacobi-Bellman (GHJB) equation which appears in optimization problems. Successive approximation using the GHJB has not been applied for nonlinear DT systems. The proposed recursive method solves the GHJB equation in DT on a well-defined region of attraction. The definition of GHJB, pre-Hamiltonian function, HJB equation, and method of updating the control function for the affine nonlinear DT systems under small perturbation assumption are proposed. A neural network (NN) is used to approximate the GHJB solution. It is shown that the result is a closed-loop control based on an NN that has been tuned a priori in offline mode. Numerical examples show that, for the linear DT system, the updated control laws will converge to the optimal control, and for nonlinear DT systems, the updated control laws will converge to the suboptimal control. PMID:18269941

  7. Spline approximations for nonlinear hereditary control systems

    NASA Technical Reports Server (NTRS)

    Daniel, P. L.

    1982-01-01

    A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

  8. Experimental nonlinear laser systems: Bigger data for better science?

    NASA Astrophysics Data System (ADS)

    Kane, D. M.; Toomey, J. P.; McMahon, C.; Noblet, Y.; Argyris, A.; Syvridis, D.

    2014-10-01

    Bigger data is supporting knowledge discovery in nonlinear laser systems as will be demonstrated with examples from three semiconductor laser based systems - one with optical feedback, a photonic integrated circuit (PIC) chaotic laser and a frequency shifted feedback laser system.

  9. Friction in a Model of Hamiltonian Dynamics

    NASA Astrophysics Data System (ADS)

    Fröhlich, Jürg; Gang, Zhou; Soffer, Avy

    2012-10-01

    We study the motion of a heavy tracer particle weakly coupled to a dense ideal Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle's trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest. "A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion."—— Aristotle

  10. Hamiltonian cosmology of bigravity

    NASA Astrophysics Data System (ADS)

    Soloviev, V. O.

    The purpose of this talk is to give an introduction both to the Hamiltonian formalism and to the cosmological equations of bigravity. In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in addressing cosmological problems.

  11. Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives

    NASA Astrophysics Data System (ADS)

    Lin-Li, Wang; Jing-Li, Fu

    2016-01-01

    In this paper, we present the fractional Hamilton’s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton’s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results. Project supported by the National Natural Science Foundation of China (Grant Nos. 11272287 and 11472247), the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT13097), and the Key Science and Technology Innovation Team Project of Zhejiang Province, China (Grant No. 2013TD18).

  12. Transport of quantum excitations coupled to spatially extended nonlinear many-body systems

    NASA Astrophysics Data System (ADS)

    Iubini, Stefano; Boada, Octavi; Omar, Yasser; Piazza, Francesco

    2015-11-01

    The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.

  13. Tensor of inertia of the collective Hamiltonian for a dinuclear system

    SciTech Connect

    Adamian, G.G.; Antonenko, N.V.; Jolos, R.V.

    1995-03-01

    The microscopic method for calculating diagonal and nondiagonal components of the tensor of inertia for a dinuclear system is proposed. The coupling between modes of motion for various mass asymmetries and fragment separations is analyzed. A neck parameter is introduced for the dinuclear system. It is shown that the coupling of the radial and mass-asymmetric modes is weak for a virtually symmetric configuration, but that it increases significantly with increasing asymmetry. 24 refs., 7 figs.

  14. Nonlinear energy transfer in classical and quantum systems.

    PubMed

    Manevitch, Leonid; Kovaleva, Agnessa

    2013-02-01

    In this paper we investigate the effect of slowly-varying parameters on the energy transfer in a weakly coupled system. For definiteness, we consider a system of two nonlinear oscillators, in which the directly excited first oscillator with constant parameter is attached to the oscillator with slowly time-varying frequency. It is proved that the equations of the slow passage through resonance in this system are identical to the equations of nonlinear Landau-Zener (LZ) tunneling. Three types of dynamical behavior are distinguished, namely, quasilinear, moderately nonlinear, and strongly nonlinear ones. Quasilinear systems exhibit a gradual energy transfer from the excited to the attached oscillator, while moderately nonlinear systems are characterized by an abrupt transition from the energy localization on the excited oscillator to the localization on the attached oscillator. In strongly nonlinear systems, the transition from the energy localization to strong energy exchange between the oscillators is revealed. Explicit approximate solutions describing the transient processes in moderately and strongly nonlinear systems are suggested. Correctness of the constructed approximations is confirmed by numerical results. The results presented in this paper, in addition to providing an analytical framework for understanding the transient dynamics, suggest an approximate procedure for solving the nonlinear LZ problem with arbitrary initial conditions over a finite time-interval. PMID:23496588

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

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

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

  16. Tools for Nonlinear Control Systems Design

    NASA Technical Reports Server (NTRS)

    Sastry, S. S.

    1997-01-01

    This is a brief statement of the research progress made on Grant NAG2-243 titled "Tools for Nonlinear Control Systems Design", which ran from 1983 till December 1996. The initial set of PIs on the grant were C. A. Desoer, E. L. Polak and myself (for 1983). From 1984 till 1991 Desoer and I were the Pls and finally I was the sole PI from 1991 till the end of 1996. The project has been an unusually longstanding and extremely fruitful partnership, with many technical exchanges, visits, workshops and new avenues of investigation begun on this grant. There were student visits, long term.visitors on the grant and many interesting joint projects. In this final report I will only give a cursory description of the technical work done on the grant, since there was a tradition of annual progress reports and a proposal for the succeeding year. These progress reports cum proposals are attached as Appendix A to this report. Appendix B consists of papers by me and my students as co-authors sorted chronologically. When there are multiple related versions of a paper, such as a conference version and journal version they are listed together. Appendix C consists of papers by Desoer and his students as well as 'solo' publications by other researchers supported on this grant similarly chronologically sorted.

  17. Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics - Monte Carlo Canonical Propagation Algorithm.

    PubMed

    Chen, Yunjie; Kale, Seyit; Weare, Jonathan; Dinner, Aaron R; Roux, Benoît

    2016-04-12

    A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method. PMID:26918826

  18. Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics — Monte Carlo Canonical Propagation Algorithm

    PubMed Central

    Weare, Jonathan; Dinner, Aaron R.; Roux, Benoît

    2016-01-01

    A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method. PMID:26918826

  19. Asymptotic Stability of Interconnected Passive Non-Linear Systems

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

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

  20. Nonlinear normal modes in electrodynamic systems: A nonperturbative approach

    NASA Astrophysics Data System (ADS)

    Kudrin, A. V.; Kudrina, O. A.; Petrov, E. Yu.

    2016-06-01

    We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.

  1. Nonlinear Optics in Novel Polymer Systems.

    NASA Astrophysics Data System (ADS)

    Li, Lian

    Polymeric nonlinear optical (NLO) materials have recently attracted considerable attention and been the subject of intensive investigations. Polymeric NLO materials possessing large second and third order NLO properties, ultrafast response times, high optical damage threshold, transparency over a broad wavelength range, and capability to be easily processed into good optical quality thin films, offer significant advantages over the traditional inorganic materials for applications in fabricating integrated optical devices, such as waveguide electro-optic (EO) modulators and optical frequency doublers, and optical signal processing devices. This dissertation presents the experimental investigations on novel NLO polymers synthesized in the Laboratory of Electronic and Photonic Materials at University of Massachusetts Lowell. Progress made for the past few years on polymeric NLO materials is reviewed, especially with regard to the second order NLO properties of the polymeric materials. Two novel stable second order NLO polymer systems, an interpenetrating polymer network (IPN) formed via thermal crosslinking and a sol-gel process, and a photocrosslinkable conducting polymer, upon poling and crosslinking, exhibited large and stable second order NLO properties measured for these polymers by using the second harmonic generation (SHG) technique. For the IPN system, the SHG measurements as a function of time at several elevated temperatures indicate the superb stability of the second order NLO properties. For the conducting NLO polymer, the NLO property of the poled and photocrosslinked polymer film is stable at room temperature. The wavelength shifting of a Q-switched Nd:YAG laser by stimulated Raman scattering is also described. Measurements were made on the third order NLO properties of a dye doped photocrosslinkable guest-host polymer system at different dye concentrations with a modified Michelson interferometer. By functionalizing the dye to make it more compatible to

  2. Energy harvesting in the nonlinear electromagnetic system

    NASA Astrophysics Data System (ADS)

    Kucab, K.; Górski, G.; Mizia, J.

    2015-11-01

    We examine the electrical response of electromagnetic device working both in the linear and nonlinear domain. The harvester is consisted of small magnet moving in isolating tube surrounded by the coil attached to the electrical circuit. In the nonlinear case the magnet vibrates in between two fixed magnets attached to the both ends of the tube. Additionally we use two springs which limit the movement of the small magnet. The linear case is when the moving magnet is attached to the repelling springs, and the static magnets have been replaced by the non-magnetic material. The potentials and forces were calculated using both the analytical expressions and the finite elements method. We compare the results for energy harvesting obtained in these two cases. The generated output power in the linear case reaches the peak value 80 mW near the resonance frequency ω0 for maximum base acceleration considered by us, whereas in the non-linear case the corresponding outpot power has the peak value 95 mW and additionally relatively high values in the excitation frequencies range up to ω = 1.2ω0. The numerical results also show that the power efficiency in the nonlinear case exceeds the corresponding efficiency in the linear case at relatively high values of base accelerations greater than 5 g. The results show the increase of harvested energy in the broad band of excitation frequencies in the nonlinear case.

  3. Nonlinear dynamics in tunable graphene nanoelectromechanical systems

    NASA Astrophysics Data System (ADS)

    Guan, Fen; Kumaravadivel, Piranavan; Averin, Dmitri; Du, Xu

    2015-03-01

    We report the fabrication and characterization of graphene nanoelectromechanical resonators (GNEMR) on flexible substrates. The intrinsic stain in graphene is tuned by bending the substrate, during which a transition from hardening to softening resonance behavior and a minimum resonance frequency are observed. To explain these observations, a resonator model taking into account the intrinsic strain and electrostatic force is developed. Including higher-order nonlinear terms, a minimum frequency is obtained analytically from the model and matches with experimental data. Results from numerical simulation demonstrate also the transition in the nonlinear behavior. Additionally, the model-based fittings determine the intrinsic strain and mass of graphene samples accurately. Our devices allow thorough exploration of the nonlinear dynamics in GNEMR and may help further study of the intrinsic electrical properties of the materials under strain.

  4. Analysis and design of robust decentralized controllers for nonlinear systems

    SciTech Connect

    Schoenwald, D.A.

    1993-07-01

    Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.

  5. An experimental study of nonlinear dynamic system identification

    NASA Technical Reports Server (NTRS)

    Stry, Greselda I.; Mook, D. Joseph

    1990-01-01

    A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

  6. An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension

    NASA Astrophysics Data System (ADS)

    Kaloshin, Vadim; Saprykina, Maria

    2012-11-01

    The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers. Vol 2, New York: Dover, pp 462-465, 1968) stated the quasi-ergodic hypothesis claiming that a typical Hamiltonian on a typical energy surface has a dense orbit. This question is wide open. Herman (Proceedings of the International Congress of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin: Int Math Union, pp 797-808, 1998) proposed to look for an example of a Hamiltonian near {H_0(I)= < I, I rangle/2} with a dense orbit on the unit energy surface. In this paper we construct a Hamiltonian {H_0(I)+\\varepsilon H_1(θ , I , \\varepsilon)} which has an orbit dense in a set of maximal Hausdorff dimension equal to 5 on the unit energy surface.

  7. Computational studies of nonlinear dispersive plasma systems

    NASA Astrophysics Data System (ADS)

    Qian, Xin

    Plasma systems with dispersive waves are ubiquitous. Dispersive waves have the property that their wave velocity depends on the wave number of the wave. These waves show up in weakly as well as strongly coupled plasmas, and play a significant role in the underlying plasma dynamics. Dispersive waves bring new challenges to the computer simulation of nonlinear phenomena. The goal of this thesis is to discuss two computational studies of plasma phenomena, one drawn from strongly coupled complex or dusty plasmas, and the other from weakly coupled hydrogen plasmas. In the realm of dusty plasmas, we focus on the problem of three-dimensional (3D) Mach cones which we study by means of Molecular Dynamics (MD) simulations, assuming that the dust particles interact via a Yukawa potential. While laboratory and MD simulations have explored thoroughly the properties of Mach cones in 2D, elucidating the important role of dispersive waves in the formation of multiple cones, the simulations presented in this thesis represent the first 3D MD studies of Mach cones in strongly coupled dusty plasmas. These results have qualitative similarities with experimental observations on 3D Mach cones from the PK-3 plus project, which studies complex plasmas under microgravity conditions aboard the International Space station. In the realm of weakly coupled plasmas, we present results on the application of non-oscillatory central schemes to Hall MHD reconnection problems, in which the presence of dispersive whistler waves presents a formidable challenge for numerical algorithms that rely on explicit time-stepping schemes. In particular, we focus on the semi-discrete central formulation of Kurganov and Tadmor (2000), which has the advantage that it allow for larger time steps, and with significantly smaller numerical viscosity, than fully discrete schemes. We implement the Hall MHD equations through the CentPACK software package that implements the Kurganov-Tadmor formulation for a wide range of

  8. Pseudo Hermitian formulation of the quantum Black-Scholes Hamiltonian

    NASA Astrophysics Data System (ADS)

    Jana, T. K.; Roy, P.

    2012-04-01

    We show that the non-Hermitian Black-Scholes Hamiltonian and its various generalizations are η-pseudo Hermitian. The metric operator η is explicitly constructed for this class of Hamiltonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system.

  9. An experimental study of nonlinear dynamic system identification

    NASA Technical Reports Server (NTRS)

    Stry, Greselda I.; Mook, D, Joseph

    1991-01-01

    A technique based on the Minimum Model Error optimal estimation approach is employed for robust identification of a nonlinear dynamic system. A simple harmonic oscillator with quadratic position feedback was simulated on an analog computer. With the aid of analog measurements and an assumed linear model, the Minimum Model Error Algorithm accurately identifies the quadratic nonlinearity. The tests demonstrate that the method is robust with respect to prior ignorance of the nonlinear system model and with respect to measurement record length, regardless of initial conditions.

  10. Self-characterization of linear and nonlinear adaptive optics systems.

    PubMed

    Hampton, Peter J; Conan, Rodolphe; Keskin, Onur; Bradley, Colin; Agathoklis, Pan

    2008-01-10

    We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM. PMID:18188192

  11. Applications of nonlinear systems theory to control design

    NASA Technical Reports Server (NTRS)

    Hunt, L. R.; Villarreal, Ramiro

    1988-01-01

    For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.

  12. On-line robust nonlinear state estimators for nonlinear bioprocess systems

    NASA Astrophysics Data System (ADS)

    Iratni, A.; Katebi, R.; Mostefai, M.

    2012-04-01

    This paper presents the design of a new robust nonlinear estimator for estimation of states of nonlinear systems. Two approaches are considered based on the state-dependent Riccati equation formulation and the technique of H-infinity control design. The proposed method differs from other well-known state estimators, because not only nonlinear dynamics but also the robustness is taken into account. The proposed method is implemented and tested on a biological wastewater system. The simulation study compares the Extended Kalman Estimator ( EKE), the State-Dependent Riccati Estimator ( SDRE), and the Extended H-infinity Estimator ( EHE) with a new proposed State Dependent H-infinity Estimator ( SDHE). The results are compared for different weather conditions, i.e. dry, rain and storm, showing a superior performance of the proposed method.

  13. Nonlinear dynamic phenomena in the space shuttle thermal protection system

    NASA Technical Reports Server (NTRS)

    Housner, J. M.; Edighoffer, H. H.; Park, K. C.

    1981-01-01

    The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

  14. Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.

    PubMed

    Jiang, Yu; Jiang, Zhong-Ping

    2014-05-01

    This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system. PMID:24808035

  15. Dynamical supersymmetric Dirac Hamiltonians

    SciTech Connect

    Ginocchio, J.N.

    1986-01-01

    Using the language of quantum electrodynamics, the Dirac Hamiltonian of a neutral fermion interacting with a tensor field is examined. A supersymmetry found for a general Dirac Hamiltonian of this type is discussed, followed by consideration of the special case of a harmonic electric potential. The square of the Dirac Hamiltonian of a neutral fermion interacting via an anomalous magnetic moment in an electric potential is shown to be equivalent to a three-dimensional supersymmetric Schroedinger equation. It is found that for a potential that grows as a power of r, the lowest energy of the Hamiltonian equals the rest mass of the fermion, and the Dirac eigenfunction has only an upper component which is normalizable. It is also found that the higher energy states have upper and lower components which form a supersymmetric doublet. 15 refs. (LEW)

  16. Impact of nonlinear and polarization effects in coherent systems.

    PubMed

    Xie, Chongjin

    2011-12-12

    Coherent detection with digital signal processing (DSP) significantly changes the ways impairments are managed in optical communication systems. In this paper, we review the recent advances in understanding the impact of fiber nonlinearities, polarization-mode dispersion (PMD), and polarization-dependent loss (PDL) in coherent optical communication systems. We first discuss nonlinear transmission performance of three coherent optical communication systems, homogeneous polarization-division-multiplexed (PDM) quadrature-phase-shift-keying (QPSK), hybrid PDM-QPSK and on/off keying (OOK), and PDM 16-ary quadrature-amplitude modulation (QAM) systems. We show that while the dominant nonlinear effects in coherent optical communication systems without optical dispersion compensators (ODCs) are intra-channel nonlinearities, the dominant nonlinear effects in dispersion-managed (DM) systems with inline dispersion compensation fiber (DCF) are different when different modulation formats are used. In DM coherent optical communication systems using modulation formats of constant amplitude, the dominant nonlinear effect is nonlinear polarization scattering induced by cross-polarization modulation (XPolM), whereas when modulation formats of non-constant amplitude are used, the impact of inter-channel cross-phase modulation (XPM) is much larger than XPolM. We then describe the effects of PMD and PDL in coherent systems. We show that although in principle PMD can be completely compensated in a coherent optical receiver, a real coherent receiver has limited tolerance to PMD due to hardware limitations. Two PDL models used to evaluate PDL impairments are discussed. We find that a simple lumped model significantly over-estimates PDL impairments and show that a distributed model has to be used in order to accurately evaluate PDL impairments. Finally, we apply system outage considerations to coherent systems, taking into account the statistics of polarization effects in fiber. PMID

  17. A Student's Guide to Lagrangians and Hamiltonians

    NASA Astrophysics Data System (ADS)

    Hamill, Patrick

    2013-11-01

    Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.

  18. Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

    SciTech Connect

    Barnich, Glenn; Troessaert, Cedric

    2009-04-15

    In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

  19. Nonlinear signal processing using neural networks: Prediction and system modelling

    SciTech Connect

    Lapedes, A.; Farber, R.

    1987-06-01

    The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.

  20. Effective Hamiltonians for Rapidly Driven Many-Body Lattice Systems: Induced Exchange Interactions and Density-Dependent Hoppings

    NASA Astrophysics Data System (ADS)

    Itin, A. P.; Katsnelson, M. I.

    2015-08-01

    We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g., Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered, where our corrections play an essential role.

  1. Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems

    PubMed Central

    Lü, Xin-You; Zhang, Wei-Min; Ashhab, Sahel; Wu, Ying; Nori, Franco

    2013-01-01

    We investigate a hybrid electro-optomechanical system that allows us to realize controllable strong Kerr nonlinearities even in the weak-coupling regime. We show that when the controllable electromechanical subsystem is close to its quantum critical point, strong photon-photon interactions can be generated by adjusting the intensity (or frequency) of the microwave driving field. Nonlinear optical phenomena, such as the appearance of the photon blockade and the generation of nonclassical states (e.g., Schrödinger cat states), are demonstrated in the weak-coupling regime, making the observation of strong Kerr nonlinearities feasible with currently available optomechanical technology. PMID:24126279

  2. Code System for Solving Nonlinear Systems of Equations via the Gauss-Newton Method.

    Energy Science and Technology Software Center (ESTSC)

    1981-08-31

    Version 00 REGN solves nonlinear systems of numerical equations in difficult cases: high nonlinearity, poor initial approximations, a large number of unknowns, ill condition or degeneracy of a problem.

  3. Development of a nonlinear optical measurement-4 coherent imaging system

    NASA Astrophysics Data System (ADS)

    Chen, Xiaojun; Song, Yinglin; Gu, Jihua; Yang, Junyi; Shui, Min; Hou, Dengke; Zhu, Zongjie

    2009-07-01

    After the nonlinear optical phenomena were discovered, people began to research the techniques to detect the optical nonlinearities of materials. In this paper, a new optical nonlinear measurement technique-4f coherent imaging system is recommended. The system has many advantages: single shot real-time measurement, simple experimental apparatus, high sensitivity, being able to detect the magnitude and sign of both nonlinear absorption and refraction at the same time, low requirement of beam spatial distribution, and so on. This paper introduces the theory of the 4f system and makes a detailed review and expounds development and application of the 4f coherent image system. The nerve of the experiment is improving the phase diaphragm. The shape of the diaphragm from the double-slits to the small rectangular object, and transition to a circular aperture, finally forming a circular phase diaphragm, which is a circular aperture in the center add a phase object. Following these diaphragm changes, the sensitivity of the system is greatly improved. The latest developments of the system are series-wound double 4f coherent imaging technique and the time-resolved pump-probe system based on NIT-PO. The time-resolved pump-probe system based on NIT-PO can be used to measure the dynamic characteristics of excited states nonlinear absorption and refraction.

  4. Applications of nonlinear system identification to structural health monitoring.

    SciTech Connect

    Farrar, C. R.; Sohn, H.; Robertson, A. N.

    2004-01-01

    The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). In many cases damage causes a structure that initially behaves in a predominantly linear manner to exhibit nonlinear response when subject to its operating environment. The formation of cracks that subsequently open and close under operating loads is an example of such damage. The damage detection process can be significantly enhanced if one takes advantage of these nonlinear effects when extracting damage-sensitive features from measured data. This paper will provide an overview of nonlinear system identification techniques that are used for the feature extraction process. Specifically, three general approaches that apply nonlinear system identification techniques to the damage detection process are discussed. The first two approaches attempt to quantify the deviation of the system from its initial linear characteristics that is a direct result of damage. The third approach is to extract features from the data that are directly related to the specific nonlinearity associated with the damaged condition. To conclude this discussion, a summary of outstanding issues associated with the application of nonlinear system identification techniques to the SHM problem is presented.

  5. Damage detection in nonlinear systems using multiple system augmentations and matrix updating

    NASA Astrophysics Data System (ADS)

    D'Souza, Kiran; Epureanu, Bogdan I.

    2006-03-01

    Recently, a damage detection method for nonlinear systems using model updating has been developed by the authors. The method uses an augmented linear model of the system, which is determined from the functional form of the nonlinearities and a nonlinear discrete model of the system. The modal properties of the augmented system after the onset of damage are extracted from the system using a modal analysis technique that uses known but not prescribed forcing. Minimum Rank Perturbation Theory was generalized so that damage location and extent could be determined using the augmented modal properties. The method was demonstrated previously for cubic springs and Coulomb friction nonlinearities. In this work, the methodology is extended to handle large systems where only the first few of the augmented eigenvectors are known. The methodology capitalizes on the ability to create multiple augmentations for a single nonlinear system. Cubic spring nonlinearities are explored within a nonlinear 3-bay truss structure for various damage scenarios simulated numerically.

  6. Non-linear system identification in flow-induced vibration

    SciTech Connect

    Spanos, P.D.; Zeldin, B.A.; Lu, R.

    1996-12-31

    The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.

  7. Simulation program of nonlinearities applied to telecommunication systems

    NASA Technical Reports Server (NTRS)

    Thomas, C.

    1979-01-01

    In any satellite communication system, the problems of distorsion created by nonlinear devices or systems must be considered. The subject of this paper is the use of the Fast Fourier Transform (F.F.T.) in the prediction of the intermodulation performance of amplifiers, mixers, filters. A nonlinear memory-less model is chosen to simulate amplitude and phase nonlinearities of the device in the simulation program written in FORTRAN 4. The experimentally observed nonlinearity parameters of a low noise 3.7-4.2 GHz amplifier are related to the gain and phase coefficients of Fourier Service Series. The measured results are compared with those calculated from the simulation in the cases where the input signal is composed of two, three carriers and noise power density.

  8. Aeroelasticity of Nonlinear Tail / Rudder Systems with Freeplay

    NASA Astrophysics Data System (ADS)

    Rishel, Evan

    This thesis details the development of a linear/nonlinear three degree of freedom aeroelastic system designed and manufactured at the University of Washington (UW). Describing function analysis was carried out in the frequency domain. Time domain simulations were carried out to account for all types of motion. Nonlinear aeroelastic behavior may lead to limit cycles which can be captured in the frequency domain using describing function approximation and numerically using Runga-Kutta integration. Linear and nonlinear aeroelastic tests were conducted in the UW 3x3 low-speed wind tunnel to determine the linear flutter speed and frequency of the system as well as its nonlinear behavior when freeplay is introduced. The test data is presented along with the results of the MATLAB-based simulations. The correlation between test and numerical results is very high.

  9. Diagnosis of nonlinear systems using time series analysis

    SciTech Connect

    Hunter, N.F. Jr.

    1991-01-01

    Diagnosis and analysis techniques for linear systems have been developed and refined to a high degree of precision. In contrast, techniques for the analysis of data from nonlinear systems are in the early stages of development. This paper describes a time series technique for the analysis of data from nonlinear systems. The input and response time series resulting from excitation of the nonlinear system are embedded in a state space. The form of the embedding is optimized using local canonical variate analysis and singular value decomposition techniques. From the state space model, future system responses are estimated. The expected degree of predictability of the system is investigated using the state transition matrix. The degree of nonlinearity present is quantified using the geometry of the transfer function poles in the z plane. Examples of application to a linear single-degree-of-freedom system, a single-degree-of-freedom Duffing Oscillator, and linear and nonlinear three degree of freedom oscillators are presented. 11 refs., 9 figs.

  10. 3-D Mesh Generation Nonlinear Systems

    Energy Science and Technology Software Center (ESTSC)

    1994-04-07

    INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surfacemore » equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.« less

  11. Variational principle for nonlinear wave propagation in dissipative systems.

    PubMed

    Dierckx, Hans; Verschelde, Henri

    2016-02-01

    The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time. PMID:26986334

  12. Chaotic and hyperchaotic attractors of a complex nonlinear system

    NASA Astrophysics Data System (ADS)

    Mahmoud, Gamal M.; Al-Kashif, M. A.; Farghaly, A. A.

    2008-02-01

    In this paper, we introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.

  13. Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.

    PubMed

    Zhang, Yanjun; Tao, Gang; Chen, Mou

    2016-09-01

    This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method. PMID:26285223

  14. Experimental nonlinear laser systems: Bigger data for better science?

    SciTech Connect

    Kane, D. M.; Toomey, J. P.; McMahon, C.; Noblet, Y.; Argyris, A.; Syvridis, D.

    2014-10-06

    Bigger data is supporting knowledge discovery in nonlinear laser systems as will be demonstrated with examples from three semiconductor laser based systems – one with optical feedback, a photonic integrated circuit (PIC) chaotic laser and a frequency shifted feedback laser system.

  15. Hamiltonian Analysis of the Particle Motion in an Accelerator with the Longitudinal Magnetic Field

    SciTech Connect

    Reva, V. B.

    2006-03-20

    The particle motion at a presence of a large magnetic field directed along the particle trajectory demands the special description. This article deals with the decomposition of the Hamiltonian on the two parts: fast and slow motion. The first part describes the fast rotation around the magnetic line of longitudinal field. The second part describes the slow drift of rotation center from one magnetic line to another. The supposed method enables to write the simple Hamiltonian to each motion type and to formulate the matrix formalism for any element of an accelerator device (quadruple, skew- quadruple, drift gap, bend with a filed index). The Hamiltonian decomposition has physical clearness when the longitudinal field is larger than another fields but it is correct for the arbitrary parameters. At the small longitudinal field the coupling term in Hamiltonian between two modes is essential. The dispersion property of fast and slow modes is derived easy from Hamiltonian also. This method expands easily for nonlinear motion of such modes. This results may be used at analyzed the electron motion in the cooling device, the muon motion in the muon ionization cooler or another system with strong solenoidal coupling.

  16. Geometric nonlinear formulation for thermal-rigid-flexible coupling system

    NASA Astrophysics Data System (ADS)

    Fan, Wei; Liu, Jin-Yang

    2013-10-01

    This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.

  17. Geometric nonlinear formulation for thermal-rigid-flexible coupling system

    NASA Astrophysics Data System (ADS)

    Fan, Wei; Liu, Jin-Yang

    2013-09-01

    This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.

  18. Hamiltonian time integrators for Vlasov-Maxwell equations

    SciTech Connect

    He, Yang; Xiao, Jianyuan; Zhang, Ruili; Liu, Jian; Qin, Hong; Sun, Yajuan

    2015-12-15

    Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.

  19. Robust Online Hamiltonian Learning

    NASA Astrophysics Data System (ADS)

    Granade, Christopher; Ferrie, Christopher; Wiebe, Nathan; Cory, David

    2013-05-01

    In this talk, we introduce a machine-learning algorithm for the problem of inferring the dynamical parameters of a quantum system, and discuss this algorithm in the example of estimating the precession frequency of a single qubit in a static field. Our algorithm is designed with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online, during experimental data collection, or can be used as a tool for post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. Finally, we discuss the performance of the our algorithm by appeal to the Cramer-Rao bound. This work was financially supported by the Canadian government through NSERC and CERC and by the United States government through DARPA. NW would like to acknowledge funding from USARO-DTO.

  20. A nonlinear complementarity approach for the national energy modeling system

    SciTech Connect

    Gabriel, S.A.; Kydes, A.S.

    1995-03-08

    The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP.

  1. w-REXAMD: A Hamiltonian Replica Exchange Approach to Improve Free Energy Calculations for Systems with Kinetically Trapped Conformations

    PubMed Central

    2012-01-01

    Free energy governs the equilibrium extent of many biological processes. High barriers separating free energy minima often limit the sampling in molecular dynamics (MD) simulations, leading to inaccurate free energies. Here, we demonstrate enhanced sampling and improved free energy calculations, relative to conventional MD, using windowed accelerated MD within a Hamiltonian replica exchange framework (w-REXAMD). We show that for a case in which multiple conformations are separated by large free energy barriers, w-REXAMD is a useful enhanced sampling technique, without any necessary reweighting. PMID:23316122

  2. Energy transfer in systems with random forcing and nonlinear dissipation

    NASA Astrophysics Data System (ADS)

    Pignol, Ricardo Jorge

    The purpose of this thesis is to study energy transfer in nonlinear systems. In the first part, I focus on a model of two nonlinearly coupled (complex) oscillators subject to stochastic forcing and nonlinear dissipation. This model arises from isolating an individual resonant quartet in a general dispersive system, and reducing it further by exploiting some of the system's symmetries. It turns out that the reduced model exhibits a rich and complex behavior encountered in far larger systems, with two qualitatively distinct regimes arising as one varies the system's single non-dimensional parameter: one that can be characterized as a perturbation of thermal equilibrium, and another highly constrained state, with phase and amplitude locking , and singular invariant measures. The relative simplicity of the reduced model allows a thorough numerical and theoretical treatment (including a closed expression for the system's invariant measures) that furnishes valuable insight on the energy transfer process in systems with much higher dimensionality. In the second part, the damped oscillator is replaced by an individual mode of the inviscid Burgers equation. Here, the dissipation occurs through shocks. Despite the complexity resulting from the inclusion of a nonlinear partial differential equation, I show that much of this system's behavior can be inferred precisely from a reduction to one of the cases studied in the first part.

  3. Numerical studies of identification in nonlinear distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.

    1989-01-01

    An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

  4. Applications of equivalent linearization approaches to nonlinear piping systems

    SciTech Connect

    Park, Y.; Hofmayer, C.; Chokshi, N.

    1997-04-01

    The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA`s are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations.

  5. Dynamic analysis of nonlinear rotor-housing systems

    NASA Technical Reports Server (NTRS)

    Noah, Sherif T.

    1988-01-01

    Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

  6. Nonlinear control structures based on embedded neural system models.

    PubMed

    Lightbody, G; Irwin, G W

    1997-01-01

    This paper investigates in detail the possible application of neural networks to the modeling and adaptive control of nonlinear systems. Nonlinear neural-network-based plant modeling is first discussed, based on the approximation capabilities of the multilayer perceptron. A structure is then proposed to utilize feedforward networks within a direct model reference adaptive control strategy. The difficulties involved in training this network, embedded within the closed-loop are discussed and a novel neural-network-based sensitivity modeling approach proposed to allow for the backpropagation of errors through the plant to the neural controller. Finally, a novel nonlinear internal model control (IMC) strategy is suggested, that utilizes a nonlinear neural model of the plant to generate parameter estimates over the nonlinear operating region for an adaptive linear internal model, without the problems associated with recursive parameter identification algorithms. Unlike other neural IMC approaches the linear control law can then be readily designed. A continuous stirred tank reactor was chosen as a realistic nonlinear case study for the techniques discussed in the paper. PMID:18255659

  7. Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

    NASA Astrophysics Data System (ADS)

    Baykara, N. A.

    2015-12-01

    Recent studies on quantum evolutionary problems in Demiralp's group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.

  8. Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

    SciTech Connect

    Baykara, N. A.

    2015-12-31

    Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.

  9. Nonlinear system guidance in the presence of transmission zero dynamics

    NASA Technical Reports Server (NTRS)

    Meyer, G.; Hunt, L. R.; Su, R.

    1995-01-01

    An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.

  10. Accurate Effective Hamiltonians via Unitary Flow in Floquet Space

    NASA Astrophysics Data System (ADS)

    Verdeny, Albert; Mielke, Andreas; Mintert, Florian

    2013-10-01

    We present a systematic construction of effective Hamiltonians of periodically driven quantum systems. Because of an equivalence between the time dependence of a Hamiltonian and an interaction in its Floquet operator, flow equations, that permit us to decouple interacting quantum systems, allow us to identify time-independent Hamiltonians for driven systems. With this approach, we explain the experimentally observed deviation of expected suppression of tunneling in ultracold atoms.

  11. Nonperturbative embedding for highly nonlocal Hamiltonians

    NASA Astrophysics Data System (ADS)

    Subaşı, Yiǧit; Jarzynski, Christopher

    2016-07-01

    The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l system plus ancilla qubits (possibly using a gate-based device), then evolve with a new Hamiltonian which is more local than the original one (using an analog device), and finally reverse the unitary transformation. The net effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.

  12. Perturbation analysis of a clearance-type nonlinear system

    NASA Astrophysics Data System (ADS)

    Zhu, Farong; Parker, Robert G.

    2006-05-01

    This study applies the method of multiple scales to obtain periodic solutions of a two-pulley belt system with clearance-type nonlinearity. The purpose is to explain the published numerical results and clarify how design parameters affect the system dynamics. The validity of the perturbation method for such strong nonlinearity is evaluated. The closed-form frequency-response relation is determined at the first order, and an implicit expression is obtained for the second-order approximation. The preload applied to the accessory determines the softening level of the nonlinearity. Larger preload leads to less disengagement and less softening. For a considerable range of practical parameter values, the analytical solutions well approximate the numerical results from harmonic balance.

  13. A simple approach to nonlinear estimation of physical systems

    USGS Publications Warehouse

    Christakos, G.

    1988-01-01

    Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared. ?? 1988.

  14. Parameter identification for nonlinear aerodynamic systems

    NASA Technical Reports Server (NTRS)

    Pearson, Allan E.

    1991-01-01

    Work continues on frequency analysis for transfer function identification, both with respect to the continued development of the underlying algorithms and in the identification study of two physical systems. Some new results of a theoretical nature were recently obtained that lend further insight into the frequency domain interpretation of the research. Progress in each of those areas is summarized. Although not related to the system identification problem, some new results were obtained on the feedback stabilization of linear time lag systems.

  15. Microscopic plasma Hamiltonian

    NASA Technical Reports Server (NTRS)

    Peng, Y.-K. M.

    1974-01-01

    A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.

  16. The coupled nonlinear dynamics of a lift system

    NASA Astrophysics Data System (ADS)

    Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan

    2014-12-01

    Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.

  17. The coupled nonlinear dynamics of a lift system

    SciTech Connect

    Crespo, Rafael Sánchez E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Picton, Phil E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk

    2014-12-10

    Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.

  18. Non-linear dynamic analysis of geared systems, part 2

    NASA Technical Reports Server (NTRS)

    Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

    1990-01-01

    A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

  19. Transient stability and control of renewable generators based on Hamiltonian surface shaping and power flow control. Part II, analysis.

    SciTech Connect

    Robinett, Rush D., III; Wilson, David Gerald

    2010-11-01

    The swing equations for renewable generators connected to the grid are developed and a wind turbine is used as an example. The swing equations for the renewable generators are formulated as a natural Hamiltonian system with externally applied non-conservative forces. A two-step process referred to as Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) is used to analyze and design feedback controllers for the renewable generators system. This formulation extends previous results on the analytical verification of the Potential Energy Boundary Surface (PEBS) method to nonlinear control analysis and design and justifies the decomposition of the system into conservative and non-conservative systems to enable a two-step, serial analysis and design procedure. The first step is to analyze the system as a conservative natural Hamiltonian system with no externally applied non-conservative forces. The Hamiltonian surface of the swing equations is related to the Equal-Area Criterion and the PEBS method to formulate the nonlinear transient stability problem. This formulation demonstrates the effectiveness of proportional feedback control to expand the stability region. The second step is to analyze the system as natural Hamiltonian system with externally applied non-conservative forces. The time derivative of the Hamiltonian produces the work/rate (power flow) equation which is used to ensure balanced power flows from the renewable generators to the loads. The Second Law of Thermodynamics is applied to the power flow equations to determine the stability boundaries (limit cycles) of the renewable generators system and enable design of feedback controllers that meet stability requirements while maximizing the power generation and flow to the load. Necessary and sufficient conditions for stability of renewable generators systems are determined based on the concepts of Hamiltonian systems, power flow, exergy (the maximum work that can be extracted from an energy flow) rate

  20. The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

    NASA Astrophysics Data System (ADS)

    Benioff, Paul

    1980-05-01

    In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each number N and Turing machine Q there exists a Hamiltonian H N Q and a class of appropriate initial states such that if c is such an initial state, then ψ Q N (t)=exp(-1 H N Q t) ψ Q N (0) correctly describes at times t 3, t 6,⋯, t 3N model states that correspond to the completion of the first, second, ⋯, Nth computation step of Q. The model parameters can be adjusted so that for an arbitrary time interval Δ around t 3, t 6,⋯, t 3N, the "machine" part of ψ Q N (t) is stationary.

  1. Simple nonlinear systems and navigating catastrophes

    NASA Astrophysics Data System (ADS)

    Harré, Michael S.; Atkinson, Simon R.; Hossain, Liaquat

    2013-06-01

    Tipping points are a common occurrence in complex adaptive systems. In such systems feedback dynamics strongly influence equilibrium points and they are one of the principal concerns of research in this area. Tipping points occur as small changes in system parameters result in disproportionately large changes in the global properties of the system. In order to show how tipping points might be managed we use the Maximum Entropy (MaxEnt) method developed by Jaynes to find the fixed points of an economic system in two different ways. In the first, economic agents optimise their choices based solely on their personal benefits. In the second they optimise the total benefits of the system, taking into account the effects of all agent's actions. The effect is to move the game from a recently introduced dual localised Lagrangian problem to that of a single global Lagrangian. This leads to two distinctly different but related solutions where localised optimisation provides more flexibility than global optimisation. This added flexibility allows an economic system to be managed by adjusting the relationship between macro parameters, in this sense such manipulations provide for the possibility of "steering" an economy around potential disasters.

  2. Terminal Sliding Modes In Nonlinear Control Systems

    NASA Technical Reports Server (NTRS)

    Venkataraman, Subramanian T.; Gulati, Sandeep

    1993-01-01

    Control systems of proposed type called "terminal controllers" offers increased precision and stability of robotic operations in presence of unknown and/or changing parameters. Systems include special computer hardware and software implementing novel control laws involving terminal sliding modes of motion: closed-loop combination of robot and terminal controller converge, in finite time, to point of stable equilibrium in abstract space of velocity and/or position coordinates applicable to particular control problem.

  3. Passive dynamic controllers for non-linear mechanical systems

    NASA Technical Reports Server (NTRS)

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

    1992-01-01

    The objective is to develop active model-independent controllers for slewing and vibration control of nonlinear multibody flexible systems, including flexible robots. The topics are presented in viewgraph form and include: passive stabilization; work-energy rate principle; Liapunov theory; displacement feedback; dynamic controller; displacement and acceleration feedback; velocity feedback; displacement feedback; physical interaction; a 6-DOF robot; and simulation results.

  4. Application of dynamical systems theory to nonlinear aircraft dynamics

    NASA Technical Reports Server (NTRS)

    Culick, Fred E. C.; Jahnke, Craig C.

    1988-01-01

    Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

  5. Arithmetic coding as a non-linear dynamical system

    NASA Astrophysics Data System (ADS)

    Nagaraj, Nithin; Vaidya, Prabhakar G.; Bhat, Kishor G.

    2009-04-01

    In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.

  6. On stability theory. [of nonlinear feedback control systems

    NASA Technical Reports Server (NTRS)

    Safonov, M. G.; Athans, M.

    1979-01-01

    It is found that under mild assumptions, feedback system stability can be concluded if one can 'topologically separate' the infinite-dimensional function space containing the system's dynamical input-output relations into two regions, one region containing the dynamical input-output relation of the 'feedforward' element of the system and the other region containing the dynamical output-input relation of the 'feedback' element. Nonlinear system stability criteria of both the input-output type and the state-space (Liapunov) type are interpreted in this context. The abstract generality and conceptual simplicity afforded by the topological separation perspective clarifies some of the basic issues underlying stability theory and serves to suggest improvements in existing stability criteria. A generalization of Zames' (1966) conic-relation stability criterion is proved, laying the foundation for improved multivariable generalizations of the frequency-domain circle stability criterion for nonlinear systems.

  7. Nonlinear Dynamics, Chaotic and Complex Systems

    NASA Astrophysics Data System (ADS)

    Infeld, E.; Zelazny, R.; Galkowski, A.

    2011-04-01

    Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet

  8. Nonlinear dynamics of fluid-structure systems. Annual technical report

    SciTech Connect

    Moon, F.C.; Muntean, G.

    1994-01-01

    We are investigating the nonlinear dynamics of a row of cylindrical tubes excited by the cross flow of fluid. Both experimental and analytical/numerical studies have been conducted. The goal of this research is to look for low dimensional dynamic models in flow- induced vibrations using modern methods of dynamical systems and chaos theory. The experimental study uses a 25 cm {times} 25 cm wind tunnel with flow velocity in the range of 15 m/sec. The use of a wind tunnel to explore dynamic phenomenon compliments the work of Chen at Argonne National Laboratory who also is conducting experiments with a water tunnel. The principal nonlinearities studies are impact constraints due to gaps in the cylinder supports and nonlinear fluid forces.

  9. Nonlinearity as a resource for nonclassicality in anharmonic systems

    NASA Astrophysics Data System (ADS)

    Albarelli, Francesco; Ferraro, Alessandro; Paternostro, Mauro; Paris, Matteo G. A.

    2016-03-01

    Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macroscopic quantum coherence. Considering various exactly solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the entropic nonlinearity of the considered potentials and their ground-state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing, which is not captured by the negativity of the Wigner function, we focus on the Glauber-Sudarshan P function and address the nonclassicality-nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators.

  10. Synchronised output regulation of nonlinear multi-agent systems

    NASA Astrophysics Data System (ADS)

    Xiang, Ji; Li, Yanjun; Wei, Wei

    2015-01-01

    This paper considers a synchronised output regulation (SOR) problem of nonlinear multi-agent systems with switching graph. The SOR means that all agents have their outputs synchronised but also ultimately evolve on a manifold determined by a predefined exosystem. Each agent constructs its local copy of the predefined exosystem and exchanges the state information of the local exosystem to realise the synchronisation of local exosystem. A controller based on the nonlinear output regulation theory is then presented to force the agent's output track the output of local exosystem. It is shown that the SOR is solvable under the assumptions same as that for nonlinear output regulation of a single agent, if the switching graph satisfies the bounded interconnectivity times condition. Both state feedback and output feedback are addressed. A numerical simulation is made to show the efficacy of the analytic results.

  11. On discrete control of nonlinear systems with applications to robotics

    NASA Technical Reports Server (NTRS)

    Eslami, Mansour

    1989-01-01

    Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.

  12. A nonlinear model for gas chromatograph systems

    NASA Technical Reports Server (NTRS)

    Feinberg, M. P.

    1975-01-01

    Fundamental engineering design techniques and concepts were studied for the optimization of a gas chromatograph-mass spectrometer chemical analysis system suitable for use on an unmanned, Martian roving vehicle. Previously developed mathematical models of the gas chromatograph are found to be inadequate for predicting peak heights and spreading for some experimental conditions and chemical systems. A modification to the existing equilibrium adsorption model is required; the Langmuir isotherm replaces the linear isotherm. The numerical technique of Crank-Nicolson was studied for use with the linear isotherm to determine the utility of the method. Modifications are made to the method eliminate unnecessary calculations which result in an overall reduction of the computation time of about 42 percent. The Langmuir isotherm is considered which takes into account the composition-dependent effects on the thermodynamic parameter, mRo.

  13. Laser vibrometry for measurement of nonlinear distortions in the vibration of weakly nonlinear slowly time-varying systems

    NASA Astrophysics Data System (ADS)

    Aerts, Johan R. M.; de Greef, Daniël; Peacock, John; Dirckx, Joris J. J.

    2011-08-01

    Recently, a new signal analysis method was developed to detect small non-linear distortions in weakly non-linear systems using specially designed broadband excitation signals, i.e. odd random phase multisines. The method allows the detection and quantification of the system response, noise level and both odd and even degree nonlinear distortions over an extensive frequency range from one single short-term measurement. Here, this method is implemented in an opto-acoustical set-up to detect small non-linearities in the response of vibrating structures. Because of the highly linear response achievable with heterodyne vibrometry, it is possible to detect non-linearities in the system under test with extremely high sensitivity. Non-linear behaviour is very common in biomechanical systems, but their dynamics and thus response might change over time. This leads to measurement artifacts that cause an overestimation of the noise level. A correction algorithm can be applied to remove the effect of these time variations, so that heterodyne vibrometry also allows the detection and quantification of non-linearities in unstable biomechanical systems. In this paper the technique is demonstrated with a measurement of the non-linear distortions in the vibration of the gerbil middle ear, where the use of a non-contact optical detection method is essential to not disturb the tiny vibrating structures.

  14. Parameter identification for nonlinear aerodynamic systems

    NASA Technical Reports Server (NTRS)

    Pearson, Allan E.

    1993-01-01

    This final technical report covers a three and one-half year period preceding February 28, 1993 during which support was provided under NASA Grant NAG-1-1065. Following a general description of the system identification problem and a brief survey of methods to attack it, the basic ideas behind the approach taken in this research effort are presented. The results obtained are described with reference to the published work, including the five semiannual progress reports previously submitted and two interim technical reports.

  15. Dissipative control for a class of nonlinear descriptor systems

    NASA Astrophysics Data System (ADS)

    Zhou, Juan; Zhang, Qingling; Li, Jinghao; Men, Bo; Ren, Junchao

    2016-04-01

    This paper is concerned with the dissipative control problem for a class of nonlinear descriptor systems. Based on Lyapunov stability theory, sufficient conditions are derived, which guarantee that the underlying systems are strictly dissipative. Then, the design method for a state feedback controller is provided. All the conditions can be expressed via linear matrix inequalities. Finally, a numerical example is presented to demonstrate the validity of the proposed methods.

  16. Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

    SciTech Connect

    Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.; Chandrasekar, V. K.

    2015-01-15

    We consider the problem of removal of ordering ambiguity in position dependent mass quantum systems characterized by a generalized position dependent mass Hamiltonian which generalizes a number of Hermitian as well as non-Hermitian ordered forms of the Hamiltonian. We implement point canonical transformation method to map one-dimensional time-independent position dependent mass Schrödinger equation endowed with potentials onto constant mass counterparts which are considered to be exactly solvable. We observe that a class of mass functions and the corresponding potentials give rise to solutions that do not depend on any particular ordering, leading to the removal of ambiguity in it. In this case, it is imperative that the ordering is Hermitian. For non-Hermitian ordering, we show that the class of systems can also be exactly solvable and is also shown to be iso-spectral using suitable similarity transformations. We also discuss the normalization of the eigenfunctions obtained from both Hermitian and non-Hermitian orderings. We illustrate the technique with the quadratic Liénard type nonlinear oscillators, which admit position dependent mass Hamiltonians.

  17. Adaptive Neural Output Feedback Control of Output-Constrained Nonlinear Systems With Unknown Output Nonlinearity.

    PubMed

    Liu, Zhi; Lai, Guanyu; Zhang, Yun; Chen, Chun Lung Philip

    2015-08-01

    This paper addresses the problem of adaptive neural output-feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states. A modified Bouc-Wen model is first employed to capture the output hysteresis phenomenon in the design procedure. For its fusion with the neural networks and the Nussbaum-type function, two key lemmas are established using some extended properties of this model. To avoid the bad system performance caused by the output nonlinearity, a barrier Lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error. In addition, a robust filtering method is designed to cancel the restriction that all the system states require to be measured. Based on the Lyapunov synthesis, a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system. Simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper. PMID:25915964

  18. Nonlinear Network Dynamics on Earthquake Fault Systems

    NASA Astrophysics Data System (ADS)

    Rundle, P. B.; Rundle, J. B.; Tiampo, K. F.

    2001-12-01

    Understanding the physics of earthquakes is essential if large events are ever to be forecast. Real faults occur in topologically complex networks that exhibit cooperative, emergent space-time behavior that includes precursory quiescence or activation, and clustering of events. The purpose of this work is to investigate the sensitivity of emergent behavior of fault networks to changes in the physics on the scale of single faults or smaller. In order to investigate the effect of changes at small scales on the behavior of the network, we need to construct models of earthquake fault systems that contain the essential physics. A network topology is therefore defined in an elastic medium, the stress Green's functions (i.e. the stress transfer coefficients) are computed, frictional properties are defined and the system is driven via the slip deficit as defined below. The long-range elastic interactions produce mean-field dynamics in the simulations. We focus in this work on the major strike-slip faults in Southern California that produce the most frequent and largest magnitude events. To determine the topology and properties of the network, we used the tabulation of fault properties published in the literature. We have found that the statistical distribution of large earthquakes on a model of a topologically complex, strongly correlated real fault network is highly sensitive to the precise nature of the stress dissipation properties of the friction laws associated with individual faults. These emergent, self-organizing space-time modes of behavior are properties of the network as a whole, rather than of the individual fault segments of which the network is comprised (ref: PBR et al., Physical Review Letters, in press, 2001).

  19. From nonlinear Schroedinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

    SciTech Connect

    Yang Xiao; Du Dianlou

    2010-08-15

    The Poisson structure on C{sup N}xR{sup N} is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schroedinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

  20. From nonlinear Schrödinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

    NASA Astrophysics Data System (ADS)

    Yang, Xiao; Du, Dianlou

    2010-08-01

    The Poisson structure on CN×RN is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schrödinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

  1. Hamiltonian spinfoam gravity

    NASA Astrophysics Data System (ADS)

    Wieland, Wolfgang M.

    2014-01-01

    This paper presents a Hamiltonian formulation of spinfoam gravity, which leads to a straightforward canonical quantization. To begin with, we derive a continuum action adapted to a simplicial decomposition of space-time. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise—in the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may still miss an additional constraint. Finally, we canonically quantize and recover the EPRL (Engle-Pereira-Rovelli-Livine) face amplitudes. Communicated by P R L V Moniz

  2. Predicting catastrophes in nonlinear dynamical systems by compressive sensing

    PubMed Central

    Wang, Wen-Xu; Yang, Rui; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso

    2013-01-01

    An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea and potential challenges are discussed. PMID:21568562

  3. Hamiltonian description of closed configurations of the vacuum magnetic field

    NASA Astrophysics Data System (ADS)

    Skovoroda, A. A.

    2015-05-01

    Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov'ev, and V.D. Shafranov.

  4. Action with Acceleration i: Euclidean Hamiltonian and Path Integral

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2013-10-01

    An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.

  5. Hamiltonian description of closed configurations of the vacuum magnetic field

    SciTech Connect

    Skovoroda, A. A.

    2015-05-15

    Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov.

  6. Tensor methods for large sparse systems of nonlinear equations

    SciTech Connect

    Bouaricha, A.; Schnabel, R.B.

    1996-12-31

    This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.

  7. Nonlinear stability of discrete shocks for systems of conservation laws

    NASA Astrophysics Data System (ADS)

    Liu, Jian-Guo; Xin, Zhouping

    1993-09-01

    In this paper we study the asymptotic nonlinear stability of discrete shocks for the Lax-Friedrichs scheme for approximating general m×m systems of nonlinear hyperbolic conservation laws. It is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the L p-norm for all p ≧ 1, provided that the sums of the initial perturbations equal zero. These results should shed light on the convergence of the numerical solution constructed by the Lax-Friedrichs scheme for the single-shock solution of system of hyperbolic conservation laws. If the Riemann solution corresponding to the given far-field states is a superposition of m single shocks from each characteristic family, we show that the corresponding multiple discrete shocks are nonlinearly stable in L p (P ≧ 2). These results are proved by using both a weighted estimate and a characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.

  8. PVODE and KINSOL: parallel software for differential and nonlinear systems

    SciTech Connect

    Hindmarsh, A.C.; Taylor, A.G.

    1998-02-01

    In this project, parallel general-purpose software for two classes of mathematical problems has been developed. PVODE is a portable solver for ordinary differential equation systems, based on robustmathematical algorithms, and targeted at large systems on parallel machines. It is the parallel extension of the earlier sequential solver CVODE. A related solver called KINSOL has been developed for systems of nonlinear algebraic equations. KINSOL was first developed as a sequential solver, on a design that permitted extending it to a parallel version with fairly minimal additions. Both PVODE and KINSOL are being used within a parallel version of the tokamak edge plasma model UEDGE. KINSOL is also being applied in the ParFlow groundwater flow model to solve a nonlinear pressure equation.

  9. Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems

    SciTech Connect

    Williams, Rube B.

    2004-02-04

    Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.

  10. Digital self-triggered robust control of nonlinear systems

    NASA Astrophysics Data System (ADS)

    Di Benedetto, M. D.; Di Gennaro, S.; D'Innocenzo, A.

    2013-09-01

    In this paper, we develop novel results on self-triggered control of nonlinear systems, subject to perturbations, and sensing/computation/actuation delays. First, considering an unperturbed nonlinear system with bounded delays, we provide conditions that guarantee the existence of a self-triggered control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances and bounded delays, we provide conditions guaranteeing the existence of a self-triggered strategy that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach in terms of energy consumption with respect to control algorithms based on a constant sampling with a sensible reduction of the average sampling time.

  11. Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1988-01-01

    An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

  12. Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems

    NASA Astrophysics Data System (ADS)

    Williams, Rube B.

    2004-02-01

    Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.

  13. Digital simulation and modeling of nonlinear stochastic systems

    SciTech Connect

    Richardson, J M; Rowland, J R

    1981-04-01

    Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.

  14. Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems.

    PubMed

    Li, Jianfeng; Huang, Zhitong; Liu, Xiaoshuang; Ji, Yuefeng

    2015-01-12

    A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (N-TDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced. PMID:25835706

  15. Hamiltonian deformations of Gabor frames: First steps

    PubMed Central

    de Gosson, Maurice A.

    2015-01-01

    Gabor frames can advantageously be redefined using the Heisenberg–Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed – as the title suggests – as the very first steps towards a general deformation theory for Gabor frames. PMID:25892903

  16. Observer-based controller for nonlinear analytical systems

    NASA Astrophysics Data System (ADS)

    Elloumi, S.; Belhouane, M. M.; Benhadj Braiek, N.

    2016-06-01

    In this paper, we propose to design a polynomial observer-based control for nonlinear systems and to determine sufficient linear matrix inequality (LMI) global stabilisation conditions of the polynomial controlled system augmented by its observer. The design of the observer-based control leverages some notations from the Kronecker product and the power of matrices properties for the state space description of polynomial systems. The stability study of the polynomial controlled system augmented by its observer is based on the Lyapunov stability direct method. Intensive simulations are performed to illustrate the validity and the effectiveness of the polynomial approach used to design the control.

  17. On the orthogonalised reverse path method for nonlinear system identification

    NASA Astrophysics Data System (ADS)

    Muhamad, P.; Sims, N. D.; Worden, K.

    2012-09-01

    The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.

  18. Numerical analysis of nonlinear properties of rail fastening systems

    NASA Astrophysics Data System (ADS)

    Liu, Y.; Luo, Y.; Yin, H. P.

    2014-10-01

    Higher demand on vibration isolation of track structure in nowadays leads to a trend of lower stiffness of rail fastening system accompanied with larger deformation of its rubber component. Nonlinear properties of rubber material under large deformation thus should be taken into account. Uniaxial tension, uniaxial compression and planar tension experiments of a rubber material were carried out to defined mathematical material models by using Abaqus. Accuracy of the material model and model coefficients were supported by good agreement between measured and simulated results. A shear type and a bonded compressed type of rail fastening system are designed and produced with the same rubber material. Quasi-static experiment of these two rail fastening systems were performed and simulated as well. Predictions of the preload dependent nonlinear properties of the two different rail fastening systems by Abaqus were found to be in good agreement with experiments. Nonlinearities of the two specimens, due both to the intrinsic rubber material properties and the geometric characteristics, were well analyzed and explained. This is believed to contribute to product designing and geometrical optimization with rubber component under general or local large deformation.

  19. Multi-scale energy exchanges between a nonlinear oscillator of Bouc-Wen type and another coupled nonlinear system

    NASA Astrophysics Data System (ADS)

    Lamarque, C.-H.; Ture Savadkoohi, A.; Naudan, M.

    2013-09-01

    The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.

  20. Adaptive control of nonlinear systems using multistage dynamic neural networks

    NASA Astrophysics Data System (ADS)

    Gupta, Madan M.; Rao, Dandina H.

    1992-11-01

    In this paper we present a new architecture of neuron, called the dynamic neural unit (DNU). The topology of the proposed neuronal model embodies delay elements, feedforward and feedback signals weighted by the synaptic weights and a time-varying nonlinear activation function, and is thus different from the conventionally and assumed architecture of neurons. The learning algorithm for the proposed neuronal structure and the corresponding implementation scheme are presented. A multi-stage dynamic neural network is developed using the DNU as the basic processing element. The performance evaluation of the dynamic neural network is presented for nonlinear dynamic systems under various situations. The capabilities of the proposed neural network model not only account for the learning and control actions emulating some of the biological control functions, but also provide a promising parallel-distributed intelligent control scheme for large-scale complex dynamic systems.

  1. The relative degree enhancement problem for MIMO nonlinear systems

    SciTech Connect

    Schoenwald, D.A.; Oezguener, Ue.

    1995-07-01

    The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for a completely decentralized feedback linearization result for at least one input-output channel.

  2. Adaptive control of Hammerstein-Wiener nonlinear systems

    NASA Astrophysics Data System (ADS)

    Zhang, Bi; Hong, Hyokchan; Mao, Zhizhong

    2016-07-01

    The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.

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

    NASA Astrophysics Data System (ADS)

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

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

  4. Fractional Hamiltonian monodromy from a Gauss-Manin monodromy

    SciTech Connect

    Sugny, D.; Jauslin, H. R.; Mardesic, P.; Pelletier, M.; Jebrane, A.

    2008-04-15

    Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskii, and Zhilinskii, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); and Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m:-n resonant systems.

  5. A method for Hamiltonian truncation: a four-wave example

    NASA Astrophysics Data System (ADS)

    Viscondi, Thiago F.; Caldas, Iberê L.; Morrison, Philip J.

    2016-04-01

    A method for extracting finite-dimensional Hamiltonian systems from a class of 2 + 1 Hamiltonian mean field theories is presented. These theories possess noncanonical Poisson brackets, which normally resist Hamiltonian truncation, but a process of beatification by coordinate transformation near a reference state is described in order to perturbatively overcome this difficulty. Two examples of four-wave truncation of Euler’s equation for scalar vortex dynamics are given and compared: one a direct non-Hamiltonian truncation of the equations of motion, the other obtained by beatifying the Poisson bracket and then truncating.

  6. Global nonexistence for nonlinear Kirchhoff systems with memory term

    NASA Astrophysics Data System (ADS)

    Liu, Gongwei; Hou, Changshun; Guo, Xiulan

    2014-10-01

    The initial boundary value problem for nonlinear wave equations of Kirchhoff systems with memory type in a bounded domain is considered. By modifying the method introduced in a work by Autuori et al. (Arch Rational Mech Anal 196:489-516, 2010), we establish the nonexistence result of global solutions with the initial energy controlled above by a critical value, that is, when the initial data belong to a specific region in the phase plane. This improves earlier results in the literatures.

  7. On the Davey-Stewartson system with competing nonlinearities

    NASA Astrophysics Data System (ADS)

    Zhu, Shihui

    2016-03-01

    This paper is concerned with the blow-up solutions for the Davey-Stewartson system with competing nonlinearities, which results in the loss of scaling invariance. The best constant of a new gG-N type inequality is given to find the sharp threshold mass of blow-up and global existence. Moreover, under the sharp threshold mass, the dynamical behavior of blow-up solutions is investigated, including L2-concentration, L2 weak limits, and limiting profile.

  8. An iterative method for systems of nonlinear hyperbolic equations

    NASA Technical Reports Server (NTRS)

    Scroggs, Jeffrey S.

    1989-01-01

    An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented.

  9. Method of Conjugate Radii for Solving Linear and Nonlinear Systems

    NASA Technical Reports Server (NTRS)

    Nachtsheim, Philip R.

    1999-01-01

    This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

  10. Bandlimited computerized improvements in characterization of nonlinear systems with memory

    NASA Astrophysics Data System (ADS)

    Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

    2016-05-01

    The present article discusses some inroads in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] over many years of developmental research. The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order in order to combat and reasonably alleviate the curse of dimensionality.

  11. Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

    NASA Astrophysics Data System (ADS)

    Mikhlin, Yu V.; Perepelkin, N. V.; Klimenko, A. A.; Harutyunyan, E.

    2012-08-01

    Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

  12. Decentralized robust nonlinear model predictive controller for unmanned aerial systems

    NASA Astrophysics Data System (ADS)

    Garcia Garreton, Gonzalo A.

    The nonlinear and unsteady nature of aircraft aerodynamics together with limited practical range of controls and state variables make the use of the linear control theory inadequate especially in the presence of external disturbances, such as wind. In the classical approach, aircraft are controlled by multiple inner and outer loops, designed separately and sequentially. For unmanned aerial systems in particular, control technology must evolve to a point where autonomy is extended to the entire mission flight envelope. This requires advanced controllers that have sufficient robustness, track complex trajectories, and use all the vehicles control capabilities at higher levels of accuracy. In this work, a robust nonlinear model predictive controller is designed to command and control an unmanned aerial system to track complex tight trajectories in the presence of internal and external perturbance. The Flight System developed in this work achieves the above performance by using: 1. A nonlinear guidance algorithm that enables the vehicle to follow an arbitrary trajectory shaped by moving points; 2. A formulation that embeds the guidance logic and trajectory information in the aircraft model, avoiding cross coupling and control degradation; 3. An artificial neural network, designed to adaptively estimate and provide aerodynamic and propulsive forces in real-time; and 4. A mixed sensitivity approach that enhances the robustness for a nonlinear model predictive controller overcoming the effect of un-modeled dynamics, external disturbances such as wind, and measurement additive perturbations, such as noise and biases. These elements have been integrated and tested in simulation and with previously stored flight test data and shown to be feasible.

  13. Neural networks for feedback feedforward nonlinear control systems.

    PubMed

    Parisini, T; Zoppoli, R

    1994-01-01

    This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method. PMID:18267810

  14. Reduced bases for nonlinear structural dynamic systems: A comparative study

    NASA Astrophysics Data System (ADS)

    Lülf, Fritz Adrian; Tran, Duc-Minh; Ohayon, Roger

    2013-07-01

    The presented work provides an overview of some commonly used approaches for generating reduced bases for discrete nonlinear dynamic systems. It investigates the performance and the robustness of these bases if they are applied in a reduction-by-projection procedure on different test cases. The bases are created from the Linear Normal Modes, the Ritz-vectors, the Proper and the Smooth Orthogonal Decomposition method, the A Priori Reduction, the Centroidal Voronoi Tessellation and the Local Equivalent Linear Stiffness Method. Second-Order Terms and an Enhanced Proper Orthogonal Decomposition formulation are included as variants. The test cases are small dimensional, locally or entirely nonlinear system subjected to a harmonic or an impulse force excitation. The double objective of this numerical study is, first, to determine which bases are most adequate for a given combination of nonlinearity and excitation and, second, to which extend the bases exhibit an inherent robustness if the parameterisation of the excitation is changed. A specific multicriteria decision analysis score is developed to assess the bases' performance. As a major result, a strong dependence of the performance of the bases on the type of excitation is established and thus some bases become more adequate for a certain situation than others. Also a lack of robustness for all considered bases can be observed. This situation improves in most cases if the basis is generated with the most critical values of the parameter.

  15. Telescopic systems with dynamic nonlinear optical correction for distortions

    SciTech Connect

    Vasil'ev, Michail V; Venediktov, Vladimir Yu; Leshchev, Alexey A

    2001-01-31

    The review of basic achievements in the field of non-linear adaptive optics is presented. In particular, schematics and properties of adaptive optical telescopes considered in which the image distortions introduced by defects of the primary mirror and other optical elements are compensated by nonlinear optical methods. The conventional methods of laser optics, such as phase conjugation and dynamic holography, make it possible both to solve the problems of classical (imaging) optics related to the building of telescopes for imaging remote objects with high resolution, which are based on large, light-weight or sectional mirrors, and create the systems that produce laser beams with the high-quality wave front. The basic designs of such telescopes are considered and the possibilities of corrections for distortions in them are analysed and confirmed by experiments. (review)

  16. Autonomous navigation system using a fuzzy adaptive nonlinear H∞ filter.

    PubMed

    Outamazirt, Fariz; Li, Fu; Yan, Lin; Nemra, Abdelkrim

    2014-01-01

    Although nonlinear H∞ (NH∞) filters offer good performance without requiring assumptions concerning the characteristics of process and/or measurement noises, they still require additional tuning parameters that remain fixed and that need to be determined through trial and error. To address issues associated with NH∞ filters, a new SINS/GPS sensor fusion scheme known as the Fuzzy Adaptive Nonlinear H∞ (FANH∞) filter is proposed for the Unmanned Aerial Vehicle (UAV) localization problem. Based on a real-time Fuzzy Inference System (FIS), the FANH∞ filter continually adjusts the higher order of the Taylor development thorough adaptive bounds  and adaptive disturbance attenuation , which significantly increases the UAV localization performance. The results obtained using the FANH∞ navigation filter are compared to the NH∞ navigation filter results and are validated using a 3D UAV flight scenario. The comparison proves the efficiency and robustness of the UAV localization process using the FANH∞ filter. PMID:25244587

  17. Swarming behaviors in multi-agent systems with nonlinear dynamics

    SciTech Connect

    Yu, Wenwu; Chen, Guanrong; Cao, Ming; Lü, Jinhu; Zhang, Hai-Tao

    2013-12-15

    The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.

  18. Hamiltonian dynamics for complex food webs.

    PubMed

    Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

    2016-03-01

    We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity. PMID:27078396

  19. Chaotic maps, Hamiltonian flows, and Holographic methods.

    SciTech Connect

    Curtright, T. L.; Zachos, C. K.; High Energy Physics; Univ. of Miami

    2010-01-01

    Holographic functional methods are introduced as probes of discrete time-stepped maps that lead to chaotic behavior. The methods provide continuous time interpolation between the time steps, thereby revealing the maps to be quasi-Hamiltonian systems underlain by novel potentials that govern the motion of a perceived point particle. Between turning points, the particle is strictly driven by Hamiltonian dynamics, but at each encounter with a turning point the potential changes abruptly, loosely analogous to the switchbacks on a mountain road. A sequence of successively deepening switchback potentials explains, in physical terms, the frequency cascade and trajectory folding that occur on the particular route to chaos revealed by the logistic map.

  20. Ostrogradski Hamiltonian approach for geodetic brane gravity

    SciTech Connect

    Cordero, Ruben; Molgado, Alberto

    2010-12-07

    We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.

  1. Hamiltonian dynamics for complex food webs

    NASA Astrophysics Data System (ADS)

    Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

    2016-03-01

    We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

  2. Hamiltonian Dynamics of Protein Filament Formation

    NASA Astrophysics Data System (ADS)

    Michaels, Thomas C. T.; Cohen, Samuel I. A.; Vendruscolo, Michele; Dobson, Christopher M.; Knowles, Tuomas P. J.

    2016-01-01

    We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.

  3. Hamiltonian dynamics of the parametrized electromagnetic field

    NASA Astrophysics Data System (ADS)

    Barbero G, J. Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.

    2016-06-01

    We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.

  4. Quantum control by means of hamiltonian structure manipulation.

    PubMed

    Donovan, A; Beltrani, V; Rabitz, H

    2011-04-28

    A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited

  5. Effective Hamiltonians for correlated narrow energy band systems and magnetic insulators: Role of spin-orbit interactions in metal-insulator transitions and magnetic phase transitions.

    PubMed

    Chakraborty, Subrata; Vijay, Amrendra

    2016-04-14

    Using a second-quantized many-electron Hamiltonian, we obtain (a) an effective Hamiltonian suitable for materials whose electronic properties are governed by a set of strongly correlated bands in a narrow energy range and (b) an effective spin-only Hamiltonian for magnetic materials. The present Hamiltonians faithfully include phonon and spin-related interactions as well as the external fields to study the electromagnetic response properties of complex materials and they, in appropriate limits, reduce to the model Hamiltonians due to Hubbard and Heisenberg. With the Hamiltonian for narrow-band strongly correlated materials, we show that the spin-orbit interaction provides a mechanism for metal-insulator transition, which is distinct from the Mott-Hubbard (driven by the electron correlation) and the Anderson mechanism (driven by the disorder). Next, with the spin-only Hamiltonian, we demonstrate the spin-orbit interaction to be a reason for the existence of antiferromagnetic phase in materials which are characterized by a positive isotropic spin-exchange energy. This is distinct from the Néel-VanVleck-Anderson paradigm which posits a negative spin-exchange for the existence of antiferromagnetism. We also find that the Néel temperature increases as the absolute value of the spin-orbit coupling increases. PMID:27083708

  6. Effective Hamiltonians for correlated narrow energy band systems and magnetic insulators: Role of spin-orbit interactions in metal-insulator transitions and magnetic phase transitions

    NASA Astrophysics Data System (ADS)

    Chakraborty, Subrata; Vijay, Amrendra

    2016-04-01

    Using a second-quantized many-electron Hamiltonian, we obtain (a) an effective Hamiltonian suitable for materials whose electronic properties are governed by a set of strongly correlated bands in a narrow energy range and (b) an effective spin-only Hamiltonian for magnetic materials. The present Hamiltonians faithfully include phonon and spin-related interactions as well as the external fields to study the electromagnetic response properties of complex materials and they, in appropriate limits, reduce to the model Hamiltonians due to Hubbard and Heisenberg. With the Hamiltonian for narrow-band strongly correlated materials, we show that the spin-orbit interaction provides a mechanism for metal-insulator transition, which is distinct from the Mott-Hubbard (driven by the electron correlation) and the Anderson mechanism (driven by the disorder). Next, with the spin-only Hamiltonian, we demonstrate the spin-orbit interaction to be a reason for the existence of antiferromagnetic phase in materials which are characterized by a positive isotropic spin-exchange energy. This is distinct from the Néel-VanVleck-Anderson paradigm which posits a negative spin-exchange for the existence of antiferromagnetism. We also find that the Néel temperature increases as the absolute value of the spin-orbit coupling increases.

  7. Nonlinear dynamics of global atmospheric and earth system processes

    NASA Technical Reports Server (NTRS)

    Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu

    1995-01-01

    During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.

  8. Discrete-time ? filtering for nonlinear polynomial systems

    NASA Astrophysics Data System (ADS)

    Basin, M. V.; Hernandez-Gonzalez, M.

    2016-07-01

    This paper presents a suboptimal ? filtering problem solution for a class of discrete-time nonlinear polynomial systems over linear observations. The solution is obtained splitting the whole problem into finding a-priori and a-posteriori equations for state estimates and gain matrices. The closed-form filtering equations for the state estimate and gain matrix are obtained in case of a third-degree polynomial system. Numerical simulations are carried out to show effectiveness of the proposed filter. The obtained filter is compared to the extended Kalman-like ? filter.

  9. Global adaptive control for uncertain nonaffine nonlinear hysteretic systems.

    PubMed

    Liu, Yong-Hua; Huang, Liangpei; Xiao, Dongming; Guo, Yong

    2015-09-01

    In this paper, the global output tracking is investigated for a class of uncertain nonlinear hysteretic systems with nonaffine structures. By combining the solution properties of the hysteresis model with the novel backstepping approach, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The proposed control scheme is further modified to tackle the bounded disturbances by adaptively estimating their bounds. It is rigorously proven that the designed adaptive controllers can guarantee global stability of the closed-loop system. Two numerical examples are provided to show the effectiveness of the proposed control schemes. PMID:26169122

  10. Temporal and spatial structures of nonlinear dynamical systems

    NASA Astrophysics Data System (ADS)

    Purwins, Hans-Georg; Klempt, Günter; Berkemeier, Jürgen

    The present article contains the description of simple experiments mounted for a demonstration of temporal and spatial structures of dissipative nonlinear dynamical systems. The systematic approach possible to systems with few degrees of freedom is described on an elementary level showing experiments on a rotating nonlinear oscillator. The temporal structure elements are those contained in the stationary, periodic, quasi-periodic, and chaotic motion. Structures of systems with many degrees of freedom are demonstrated by showing experiments on real spatially extended electronic circuits and gas discharge systems both described by reaction diffusion equations. Such systems have a complexity and richness of structures far beyond what can be described systematically by current techniques. However, for special cases a quantitative understanding is possible. Also filaments of rather well defined size and shape observed in our experiments can be considered as simple elements building up a variety of spatial patterns. We also show that noise is decisive in many cases for the formation and the nonreproducibility of stationary structures. Finally, we stress some features common to reaction diffusion systems and living beings.

  11. Optimal spatiotemporal reduced order modeling for nonlinear dynamical systems

    NASA Astrophysics Data System (ADS)

    LaBryer, Allen

    Proposed in this dissertation is a novel reduced order modeling (ROM) framework called optimal spatiotemporal reduced order modeling (OPSTROM) for nonlinear dynamical systems. The OPSTROM approach is a data-driven methodology for the synthesis of multiscale reduced order models (ROMs) which can be used to enhance the efficiency and reliability of under-resolved simulations for nonlinear dynamical systems. In the context of nonlinear continuum dynamics, the OPSTROM approach relies on the concept of embedding subgrid-scale models into the governing equations in order to account for the effects due to unresolved spatial and temporal scales. Traditional ROMs neglect these effects, whereas most other multiscale ROMs account for these effects in ways that are inconsistent with the underlying spatiotemporal statistical structure of the nonlinear dynamical system. The OPSTROM framework presented in this dissertation begins with a general system of partial differential equations, which are modified for an under-resolved simulation in space and time with an arbitrary discretization scheme. Basic filtering concepts are used to demonstrate the manner in which residual terms, representing subgrid-scale dynamics, arise with a coarse computational grid. Models for these residual terms are then developed by accounting for the underlying spatiotemporal statistical structure in a consistent manner. These subgrid-scale models are designed to provide closure by accounting for the dynamic interactions between spatiotemporal macroscales and microscales which are otherwise neglected in a ROM. For a given resolution, the predictions obtained with the modified system of equations are optimal (in a mean-square sense) as the subgrid-scale models are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. Methods are suggested for efficient model construction, appraisal, error measure, and implementation with a couple of well-known time

  12. Nonlinear stochastic system identification of skin using volterra kernels.

    PubMed

    Chen, Yi; Hunter, Ian W

    2013-04-01

    Volterra kernel stochastic system identification is a technique that can be used to capture and model nonlinear dynamics in biological systems, including the nonlinear properties of skin during indentation. A high bandwidth and high stroke Lorentz force linear actuator system was developed and used to test the mechanical properties of bulk skin and underlying tissue in vivo using a non-white input force and measuring an output position. These short tests (5 s) were conducted in an indentation configuration normal to the skin surface and in an extension configuration tangent to the skin surface. Volterra kernel solution methods were used including a fast least squares procedure and an orthogonalization solution method. The practical modifications, such as frequency domain filtering, necessary for working with low-pass filtered inputs are also described. A simple linear stochastic system identification technique had a variance accounted for (VAF) of less than 75%. Representations using the first and second Volterra kernels had a much higher VAF (90-97%) as well as a lower Akaike information criteria (AICc) indicating that the Volterra kernel models were more efficient. The experimental second Volterra kernel matches well with results from a dynamic-parameter nonlinearity model with fixed mass as a function of depth as well as stiffness and damping that increase with depth into the skin. A study with 16 subjects showed that the kernel peak values have mean coefficients of variation (CV) that ranged from 3 to 8% and showed that the kernel principal components were correlated with location on the body, subject mass, body mass index (BMI), and gender. These fast and robust methods for Volterra kernel stochastic system identification can be applied to the characterization of biological tissues, diagnosis of skin diseases, and determination of consumer product efficacy. PMID:23264003

  13. Develop advanced nonlinear signal analysis topographical mapping system

    NASA Technical Reports Server (NTRS)

    1994-01-01

    The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of

  14. Develop advanced nonlinear signal analysis topographical mapping system

    NASA Technical Reports Server (NTRS)

    Jong, Jen-Yi

    1993-01-01

    The SSME has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) Develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system. (2) Develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amounts of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. A high compression ratio can be achieved to allow the minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities. (3) Integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for a quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate

  15. Stability of dithered non-linear systems with backlash or hysteresis

    NASA Technical Reports Server (NTRS)

    Desoer, C. A.; Shahruz, S. M.

    1986-01-01

    A study is conducted of the effect of dither on the nonlinear element of a single-input single-outout feedback system. Nonlinearities are considered with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system.

  16. Turing pattern formation in the Brusselator system with nonlinear diffusion

    NASA Astrophysics Data System (ADS)

    Gambino, G.; Lombardo, M. C.; Sammartino, M.; Sciacca, V.

    2013-10-01

    In this work we investigate the effect of density-dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in one-dimensional and two-dimensional spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover, we consider traveling patterning waves: When the domain size is large, the pattern forms sequentially and traveling wave fronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and, through a matching procedure, we construct the outer amplitude equation and the inner core solution.

  17. Stochastic resonance in a nonlinear mechanical vibration isolation system

    NASA Astrophysics Data System (ADS)

    Lu, Zeqi; Chen, Li-Qun; Brennan, Michael J.; Yang, Tiejun; Ding, Hu; Liu, Zhigang

    2016-05-01

    This paper concerns the effect that a stochastic resonance can have on a vibration isolation system. Rather than reducing the transmitted force, it is shown that it is possible to significantly mask the component of the force transmitted though the isolator, when the system is excited harmonically. This can be achieved by adding a very low intensity of random noise to the harmonic excitation force. The nonlinear mechanical vibration isolation system used in the study consists of a vertical linear spring in parallel with two horizontal springs, which are configured so that the potential energy of the system has a double-well. Prior to the analytical and numerical study, an experiment to demonstrate stochastic resonance in a mechanical system is described.

  18. Quantised consensus of multi-agent systems with nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Zhu, Yunru; Zheng, Yuanshi; Wang, Long

    2015-08-01

    This paper studies the consensus problem of first-order and second-order multi-agent systems with nonlinear dynamics and quantised interactions. Continuous-time and impulsive control inputs are designed for the multi-agent systems on the logarithmic quantised relative state measurements of agents, respectively. By using nonsmooth analysis tools, we get some sufficient conditions for the consensus of multi-agent systems under the continuous-time inputs. Compared with continuous-time control inputs, impulsive distributed control inputs just use the state variables of the systems at discrete-time instances. Based on impulsive control theory, we prove that the multi-agent systems can reach consensus by choosing proper control gains and impulsive intervals. The simulation results are given to verify the effectiveness of the theoretical results.

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

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Martin, Corless

    2004-01-01

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

  20. General purpose nonlinear system solver based on Newton-Krylov method.

    Energy Science and Technology Software Center (ESTSC)

    2013-12-01

    KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

  1. Peregrine rogue wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity

    NASA Astrophysics Data System (ADS)

    Gupta, Samit Kumar; Sarma, Amarendra K.

    2016-07-01

    In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Ablowitz and Musslimani, (2013) [31]) continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrödinger system with PT-symmetric nonlinearity also admits Peregrine soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.

  2. On the transmissibilities of nonlinear vibration isolation system

    NASA Astrophysics Data System (ADS)

    Lu, Zeqi; Brennan, Michael J.; Chen, Li-Qun

    2016-08-01

    Transmissibility is a key parameter to quantify the effectiveness of a vibration isolation system. Under harmonic excitation, the force transmissibility of a linear vibration isolation system is defined as the ratio between the amplitude of the force transmitted to the host structure and the excitation force amplitude, and the displacement transmissibility is the ratio between the displacement amplitude of the payload and that of the base. For a nonlinear vibration isolation system, the force or the displacement responses usually have more frequency components than the excitation. For a harmonic excitation, the response may be periodic, quasi-periodic or chaotic. Therefore, the amplitude ratio cannot well define the transmissibility. The root-mean-square ratio of the response to the excitation is suggested to define the transmissibility. The significance of the modified transmissibility is highlighted in a nonlinear two-stage vibration isolation system consisting of two linear spring connected linear vibration isolators with two additional horizontal linear springs. Harmonic balance method (HBM) is applied to determine the responses with the fundamental and third harmonic. Numerical simulations reveal that chaos may occur in the responses. In both cases, the modified transmissibility works while the original definition cannot be applied to chaotic response.

  3. Hamiltonian Formulation for Wave-Current Interactions in Stratified Rotational Flows

    NASA Astrophysics Data System (ADS)

    Constantin, A.; Ivanov, R. I.; Martin, C.-I.

    2016-09-01

    We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.

  4. Investigation of non-Hermitian Hamiltonians in the Heisenberg picture

    NASA Astrophysics Data System (ADS)

    Miao, Yan-Gang; Xu, Zhen-Ming

    2016-05-01

    The Heisenberg picture for non-Hermitian but η-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but η-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order Heisenberg equations of motion are complex, we can construct a Hermitian counterpart that gives the same second order equations of motion. In terms of a similarity transformation we verify the iso-spectral property of the Hermitian and non-Hermitian Hamiltonians and obtain the related eigenfunctions. This feature can be used to determine real eigenvalues for such non-Hermitian Hamiltonian systems. As an application, two new non-Hermitian Hamiltonians are constructed and investigated, where one is non-Hermitian and non-PT-symmetric and the other is non-Hermitian but PT-symmetric. Moreover, the complementarity and compatibility between our treatment and the PT symmetry are discussed.

  5. FINDS: A fault inferring nonlinear detection system. User's guide

    NASA Technical Reports Server (NTRS)

    Lancraft, R. E.; Caglayan, A. K.

    1983-01-01

    The computer program FINDS is written in FORTRAN-77, and is intended for operation on a VAX 11-780 or 11-750 super minicomputer, using the VMS operating system. The program detects, isolates, and compensates for failures in navigation aid instruments and onboard flight control and navigation sensors of a Terminal Configured Vehicle aircraft in a Microwave Landing System environment. In addition, FINDS provides sensor fault tolerant estimates for the aircraft states which are then used by an automatic guidance and control system to land the aircraft along a prescribed path. FINDS monitors for failures by evaluating all sensor outputs simultaneously using the nonlinear analytic relationships between the various sensor outputs arising from the aircraft point mass equations of motion. Hence, FINDS is an integrated sensor failure detection and isolation system.

  6. A universal approach to the study of nonlinear systems

    NASA Astrophysics Data System (ADS)

    Hwa, Rudolph C.

    2004-07-01

    A large variety of nonlinear systems have been treated by a common approach that emphasizes the fluctuation of spatial patterns. By using the same method of analysis it is possible to discuss the chaotic behaviors of quark jets and logistic map in the same language. Critical behaviors of quark-hadron phase transition in heavy-ion collisions and of photon production at the threshold of lasing can also be described by a common scaling behavior. The universal approach also makes possible an insight into the recently discovered phenomenon of wind reversal in cryogenic turbulence as a manifestation of self-organized criticality.

  7. Limits of localized control in extended nonlinear systems

    NASA Astrophysics Data System (ADS)

    Handel, Andreas

    We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under

  8. Drift Hamiltonian in magnetic coordinates

    SciTech Connect

    White, R.B.; Boozer, A.H.; Hay, R.

    1982-02-01

    A Hamiltonian formulation of the guiding-center drift in arbitrary, steady state, magnetic and electric fields is given. The canonical variables of this formulation are simply related to the magnetic coordinates. The modifications required to treat ergodic magnetic fields using magnetic coordinates are explicitly given in the Hamiltonian formulation.

  9. Nonlinear dynamics of a simplified engine-propeller system

    NASA Astrophysics Data System (ADS)

    Yu, S. D.; Warwick, S. A.; Zhang, X.

    2009-07-01

    This paper presents a procedure for studying dynamical behaviors of a simplified engine-propeller dynamical system consisting of a number of bodies of plane motions. The equation of motion of the complex system is obtained using the Lagrange equation and solved numerically using the 4th order Runge-Kutta method. Various simulations were performed to investigate the transient and steady state behaviors of the multiple body system while taking into consideration the engine pressure pulsations, nonlinear inertia of moving bodies, and nonlinear aerodynamic load. Sub-harmonics and super harmonics in the steady state responses for different power and propeller pitch settings are obtained using the fast Fourier transform. Numerical simulations indicate that the 1.5 order is the dominant order of harmonics in the steady state oscillatory motion of the crankshaft. The findings and procedure presented in the paper are useful to the aerospace industry in certifying reciprocating engines and propellers. The crankshaft oscillatory velocities obtained from the simplified rigid body model are in good agreement with the experimental data for a SAITO-450 engine and a SOLO propeller at a 6″ pitch setting.

  10. Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

    PubMed

    Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

    2015-11-01

    The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness. PMID:26277007

  11. Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Agarwal, S.; Wettlaufer, J. S.

    2014-12-01

    We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

  12. Practical application of equivalent linearization approaches to nonlinear piping systems

    SciTech Connect

    Park, Y.J.; Hofmayer, C.H.

    1995-05-01

    The use of mechanical energy absorbers as an alternative to conventional hydraulic and mechanical snubbers for piping supports has attracted a wide interest among researchers and practitioners in the nuclear industry. The basic design concept of energy absorbers (EA) is to dissipate the vibration energy of piping systems through nonlinear hysteretic actions of EA!s under design seismic loads. Therefore, some type of nonlinear analysis needs to be performed in the seismic design of piping systems with EA supports. The equivalent linearization approach (ELA) can be a practical analysis tool for this purpose, particularly when the response approach (RSA) is also incorporated in the analysis formulations. In this paper, the following ELA/RSA methods are presented and compared to each other regarding their practice and numerical accuracy: Response approach using the square root of sum of squares (SRSS) approximation (denoted RS in this paper). Classical ELA based on modal combinations and linear random vibration theory (denoted CELA in this paper). Stochastic ELA based on direct solution of response covariance matrix (denoted SELA in this paper). New algorithms to convert response spectra to the equivalent power spectral density (PSD) functions are presented for both the above CELA and SELA methods. The numerical accuracy of the three EL are studied through a parametric error analysis. Finally, the practicality of the presented analysis is demonstrated in two application examples for piping systems with EA supports.

  13. Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities

    SciTech Connect

    Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Konotop, Vladimir V.

    2008-04-25

    Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schroedinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.

  14. General formalism for singly thermostated Hamiltonian dynamics.

    PubMed

    Ramshaw, John D

    2015-11-01

    A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed. PMID:26651677

  15. Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Kulikov, G. Yu.

    2015-06-01

    A technique for constructing nested implicit Runge-Kutta methods in the class of mono-implicit formulas of this type is studied. These formulas are highly efficient in practice, since the dimension of the original system of differential equations is preserved, which is not possible in the case of implicit multistage Runge-Kutta formulas of the general from. On the other hand, nested implicit Runge-Kutta methods inherit all major properties of general formulas of this form, such as A-stability, symmetry, and symplecticity in a certain sense. Moreover, they can have sufficiently high stage and classical orders and, without requiring high extra costs, can ensure dense output of integration results of the same accuracy as the order of the underlying method. Thus, nested methods are efficient when applied to the numerical integration of differential equations of various sorts, including stiff and nonstiff problems, Hamiltonian systems, and invertible equations. In this paper, previously proposed nested methods based on the Gauss quadrature formulas are generalized to Lobatto-type methods. Additionally, a unified technique for constructing all such methods is proposed. Its performance is demonstrated as applied to embedded examples of nested implicit formulas of various orders. All the methods constructed are supplied with tools for local error estimation and automatic variable-stepsize mesh generation based on an optimal stepsize selection. These numerical methods are verified by solving test problems with known solutions. Additionally, a comparative analysis of these methods with Matlab built-in solvers is presented.

  16. Memristive non-linear system and hidden attractor

    NASA Astrophysics Data System (ADS)

    Saha, P.; Saha, D. C.; Ray, A.; Chowdhury, A. R.

    2015-07-01

    Effects of memristor on non-linear dynamical systems exhibiting chaos are analysed both form the view point of theory and experiment. It is observed that the memristive system has always fewer number of fixed points than the original one. Sometimes there is no fixed point in the memristive system. But its chaotic properties are retained. As such we have a situation known as hidden attractor because if it is a stable fixed point then the attractor does not evolve from its basin of attraction(obtained from its stable fixed point) or if there is no fixed point, the question of basin of attraction from fixed point does not arise at all [1, 2]. Our analysis gives a detailed accounts of properties related to its chaotic behavior. Important observations are also obtained with the help of electronic circuits to support the numerical simulations.

  17. THz impulse radar for biomedical sensing: nonlinear system behavior

    NASA Astrophysics Data System (ADS)

    Brown, E. R.; Sung, Shijun; Grundfest, W. S.; Taylor, Z. D.

    2014-03-01

    The THz impulse radar is an "RF-inspired" sensor system that has performed remarkably well since its initial development nearly six years ago. It was developed for ex vivo skin-burn imaging, and has since shown great promise in the sensitive detection of hydration levels in soft tissues of several types, such as in vivo corneal and burn samples. An intriguing aspect of the impulse radar is its hybrid architecture which combines the high-peak-power of photoconductive switches with the high-responsivity and -bandwidth (RF and video) of Schottky-diode rectifiers. The result is a very sensitive sensor system in which the post-detection signal-to-noise ratio depends super-linearly on average signal power up to a point where the diode is "turned on" in the forward direction, and then behaves quasi-linearly beyond that point. This paper reports the first nonlinear systems analysis done on the impulse radar using MATLAB.

  18. Fuzzy fractional order sliding mode controller for nonlinear systems

    NASA Astrophysics Data System (ADS)

    Delavari, H.; Ghaderi, R.; Ranjbar, A.; Momani, S.

    2010-04-01

    In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PDα, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.

  19. Dynamics of large constrained nonlinear systems -- A taxonomy theory

    SciTech Connect

    Venkatasubramanian, V.; Schaettler, H.; Zaborszky, J.

    1995-11-01

    This paper provides an overview of the taxonomy theory which has been proposed as a fundamental platform for solving practical stability related problems in large constrained nonlinear systems such as the electric power system. The theory reveals a two-level intertwined cellular nature of the constrained system dynamics which serves as a unifying structure, a taxonomy, for analyzing nonlinear phenomena in large system models. These broadly divide into the state space aspects (related to dynamic stability issues among others) and the parameter space aspects (connected with bifurcation phenomena among others). In the state-space formulation, the boundary of the region of attraction for the operating point is shown (under certain Morse-Smale like assumptions) to be composed of stable manifolds of certain anchors and portions of the singularity surface. Such boundary characterization provides the foundation for rigorous Lyapunov theoretic transient stability methods. In the parameter space analysis, the feasibility region which is bounded by the feasibility boundary provides a safe operating region for guaranteeing local stability at the equilibrium under slow parametric variations. The feasibility boundary where the operating point undergoes loss of local stability is characterized in the form of three principal bifurcations including a new bifurcation called the singularity induced bifurcation. An overview of the recent results which prove that the two-level structure exists even in nonsmooth models that incorporate the effects of system hard limits is also included. Specifically hard limits induce a number of new bifurcations. This natural taxonomy of the system dynamics stands as the backbone for developing practical and rigorous computational techniques in detecting diverse instability mechanisms.

  20. Transient dynamics and nonlinear stability of spatially extended systems.

    PubMed

    Handel, Andreas; Grigoriev, Roman O

    2006-09-01

    As studies of various systems have shown, the sole focus on the eigenvalues in a linear stability analysis can be misleading, especially when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilization process. The critical noise level leading to destabilization is often found to scale as a power of the magnitude of transient amplification. In what follows we show that the power law exponent sensitively depends on the type of nonlinear terms and their potential for generating self-sustaining noise amplification cycles (bootstrapping). We find, however, that the exponents are not universal and also depend on the more subtle details of the transient dynamics. We also show that the basin of attraction of a spatially uniform state is bounded by the stable manifold(s) of nearby saddle(s) which play a major role in the transition. PMID:17025738

  1. Simulating typical entanglement with many-body Hamiltonian dynamics

    SciTech Connect

    Nakata, Yoshifumi; Murao, Mio

    2011-11-15

    We study the time evolution of the amount of entanglement generated by one-dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.

  2. Nonlinear modeling and predictive functional control of Hammerstein system with application to the turntable servo system

    NASA Astrophysics Data System (ADS)

    Zhang, Qian; Wang, Qunjing; Li, Guoli

    2016-05-01

    This article deals with the identification of nonlinear model and Nonlinear Predictive Functional Controller (NPFC) design based on the Hammerstein structure for the turntable servo system. As a mechanism with multi-mass rotational system, nonlinearities significantly influence the system operation, especially when the turntable is in the states of zero-crossing distortion or rapid acceleration/deceleration, etc. The field data from identification experiments are processed by Comprehensive Learning Particle Swarm Optimization (CLPSO). As a result, Hammerstein model can be derived to describe the input-output relationship globally, considering all the linear and nonlinear factors of the turntable system. Cross validation results demonstrate good correspondence between the real equipment and the identified model. In the second part of this manuscript, a nonlinear control strategy based on the genetic algorithm and predictive control is developed. The global nonlinear predictive controller is carried out by two steps: (i) build the linear predictive functional controller with state space equations for the linear subsystem of Hammerstein model, and (ii) optimize the global control variable by minimizing the cost function through genetic algorithm. On the basis of distinguish model for turntable and the effectiveness of NPFC, the good performance of tracking ability is achieved in the simulation results.

  3. Adaptive RSOV filter using the FELMS algorithm for nonlinear active noise control systems

    NASA Astrophysics Data System (ADS)

    Zhao, Haiquan; Zeng, Xiangping; He, Zhengyou; Li, Tianrui

    2013-01-01

    This paper presents a recursive second-order Volterra (RSOV) filter to solve the problems of signal saturation and other nonlinear distortions that occur in nonlinear active noise control systems (NANC) used for actual applications. Since this nonlinear filter based on an infinite impulse response (IIR) filter structure can model higher than second-order and third-order nonlinearities for systems where the nonlinearities are harmonically related, the RSOV filter is more effective in NANC systems with either a linear secondary path (LSP) or a nonlinear secondary path (NSP). Simulation results clearly show that the RSOV adaptive filter using the multichannel structure filtered-error least mean square (FELMS) algorithm can further greatly reduce the computational burdens and is more suitable to eliminate nonlinear distortions in NANC systems than a SOV filter, a bilinear filter and a third-order Volterra (TOV) filter.

  4. A Nonlinear Elastic Beam System with Inelastic Contact Constraints

    SciTech Connect

    Russell, D.L. White, L.W.

    2002-12-19

    In this paper we study freely propagating inertial, i.e., unforced, waves, in an elastic beam constrained so that all motion takes place above and on a flat, rigid support surface, subject to a gravitational force and a compressive longitudinal load. Contact between the beam and the support surface is assumed to be completely inelastic. A nonlinear beam model is used, incorporating a quartic extension of the familiar quadratic potential energy functional for the standard Euler-Bernoulli model. After briefly reviewing the rationale for the model and some of its properties, as developed in earlier articles, we present existence and uniqueness results for the constrained system obtained with the use of a 'penalty function' approach involving the addition of a 'uni-directional friction' dissipative term, active only when the constraint is violated, to the unconstrained system.

  5. One-Time Pad as a nonlinear dynamical system

    NASA Astrophysics Data System (ADS)

    Nagaraj, Nithin

    2012-11-01

    The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding - a scheme for joint compression and encryption.

  6. A globalization procedure for solving nonlinear systems of equations

    NASA Astrophysics Data System (ADS)

    Shi, Yixun

    1996-09-01

    A new globalization procedure for solving a nonlinear system of equationsF(x)D0 is proposed based on the idea of combining Newton step and the steepest descent step WITHIN each iteration. Starting with an arbitrary initial point, the procedure converges either to a solution of the system or to a local minimizer off(x)D1/2F(x)TF(x). Each iteration is chosen to be as close to a Newton step as possible and could be the Newton step itself. Asymptotically the Newton step will be taken in each iteration and thus the convergence is quadratic. Numerical experiments yield positive results. Further generalizations of this procedure are also discussed in this paper.

  7. Inverse problem of nonlinear dynamical systems: a constructive approach

    SciTech Connect

    Gonzalez-Gascon, F.; Moreno-Insertis, F.; Rodriguez-Camino, E.

    1980-08-01

    A quite simple and practical method is developed for the construction of two dimensional nonlinear dynamical systems (plane vector fields) possessing an arbitrary number of given limit cycles. The method is applied to the construction of n-dimensional dynamical systems (R/sup n/ vector fields) possessing at least one limit cycle and, under certain circumstances, more than one, or even a numerable infinity. Interesting open problems arise when n is greater than two, or where more than one limit cycle appears. Our constructive algorithm for this type of inverse problem is also applied to the construction of second order differential equations (Newtonian differential equations) possessing a finite or infinite number of invariant speeds. This last problem is relevant for certain aspects of the special theory of relativity.

  8. Using Numerical Solutions in the Fourier Method for the Fokker-Planck-Kolmogorov Equation in the Analysis of First-Order Stochastic Nonlinear Systems for Nonlinear Detectors

    NASA Astrophysics Data System (ADS)

    Nevolin, V. I.

    2003-04-01

    We present a method for analyzing the characteristics of nonlinear detectors using the algorithms of first-order nonlinear differential equations. This method is based on numerical solutions of the Fokker-Planck-Kolmogorov (FPK) equations in the form of series of functions over Hermite-Chebyshev polynomials for both nonlinear systems and their linear counterparts. The results of the solutions for the linear case are extended to nonlinear systems in a recurrent way.

  9. Expansion Hamiltonian model for a diatomic molecule adsorbed on a surface: Vibrational states of the CO/Cu(100) system including surface vibrations

    NASA Astrophysics Data System (ADS)

    Meng, Qingyong; Meyer, Hans-Dieter

    2015-10-01

    Molecular-surface studies are often done by assuming a corrugated, static (i.e., rigid) surface. To be able to investigate the effects that vibrations of surface atoms may have on spectra and cross sections, an expansion Hamiltonian model is proposed on the basis of the recently reported [R. Marquardt et al., J. Chem. Phys. 132, 074108 (2010)] SAP potential energy surface (PES), which was built for the CO/Cu(100) system with a rigid surface. In contrast to other molecule-surface coupling models, such as the modified surface oscillator model, the coupling between the adsorbed molecule and the surface atoms is already included in the present expansion SAP-PES model, in which a Taylor expansion around the equilibrium positions of the surface atoms is performed. To test the quality of the Taylor expansion, a direct model, that is avoiding the expansion, is also studied. The latter, however, requests that there is only one movable surface atom included. On the basis of the present expansion and direct models, the effects of a moving top copper atom (the one to which CO is bound) on the energy levels of a bound CO/Cu(100) system are studied. For this purpose, the multiconfiguration time-dependent Hartree calculations are carried out to obtain the vibrational fundamentals and overtones of the CO/Cu(100) system including a movable top copper atom. In order to interpret the results, a simple model consisting of two coupled harmonic oscillators is introduced. From these calculations, the vibrational levels of the CO/Cu(100) system as function of the frequency of the top copper atom are discussed.

  10. Expansion Hamiltonian model for a diatomic molecule adsorbed on a surface: Vibrational states of the CO/Cu(100) system including surface vibrations

    SciTech Connect

    Meng, Qingyong; Meyer, Hans-Dieter

    2015-10-28

    Molecular-surface studies are often done by assuming a corrugated, static (i.e., rigid) surface. To be able to investigate the effects that vibrations of surface atoms may have on spectra and cross sections, an expansion Hamiltonian model is proposed on the basis of the recently reported [R. Marquardt et al., J. Chem. Phys. 132, 074108 (2010)] SAP potential energy surface (PES), which was built for the CO/Cu(100) system with a rigid surface. In contrast to other molecule-surface coupling models, such as the modified surface oscillator model, the coupling between the adsorbed molecule and the surface atoms is already included in the present expansion SAP-PES model, in which a Taylor expansion around the equilibrium positions of the surface atoms is performed. To test the quality of the Taylor expansion, a direct model, that is avoiding the expansion, is also studied. The latter, however, requests that there is only one movable surface atom included. On the basis of the present expansion and direct models, the effects of a moving top copper atom (the one to which CO is bound) on the energy levels of a bound CO/Cu(100) system are studied. For this purpose, the multiconfiguration time-dependent Hartree calculations are carried out to obtain the vibrational fundamentals and overtones of the CO/Cu(100) system including a movable top copper atom. In order to interpret the results, a simple model consisting of two coupled harmonic oscillators is introduced. From these calculations, the vibrational levels of the CO/Cu(100) system as function of the frequency of the top copper atom are discussed.

  11. Nonlinear observer designs for fuel cell power systems

    NASA Astrophysics Data System (ADS)

    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

  12. Reduction of nonlinear phase noise using optical phase conjugation in quasi-linear optical transmission systems.

    PubMed

    Kumar, Shiva; Liu, Ling

    2007-03-01

    An analytical expression for the variance of nonlinear phase noise for a quasi-linear system using the midpoint optical phase conjugation (OPC) is obtained. It is shown that the the system with OPC and dispersion inversion (DI) can exactly cancel the nonlinear phase noise up to the first order in nonlinear coefficient if the amplifier and the end point of the system are equidistant from the OPC. It is found that the nonlinear phase noise variance of the midpoint phase-conjugated optical transmission system with DI is smaller than that of the system without DI. PMID:19532453

  13. An approximation theory for the identification of nonlinear distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1990-01-01

    An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato appproximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

  14. An approximation theory for the identification of nonlinear distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1988-01-01

    An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

  15. Predictability of extremes in non-linear hierarchically organized systems

    NASA Astrophysics Data System (ADS)

    Kossobokov, V. G.; Soloviev, A.

    2011-12-01

    Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare

  16. Appropriate time scales for nonlinear analyses of deterministic jump systems

    NASA Astrophysics Data System (ADS)

    Suzuki, Tomoya

    2011-06-01

    In the real world, there are many phenomena that are derived from deterministic systems but which fluctuate with nonuniform time intervals. This paper discusses the appropriate time scales that can be applied to such systems to analyze their properties. The financial markets are an example of such systems wherein price movements fluctuate with nonuniform time intervals. However, it is common to apply uniform time scales such as 1-min data and 1-h data to study price movements. This paper examines the validity of such time scales by using surrogate data tests to ascertain whether the deterministic properties of the original system can be identified from uniform sampled data. The results show that uniform time samplings are often inappropriate for nonlinear analyses. However, for other systems such as neural spikes and Internet traffic packets, which produce similar outputs, uniform time samplings are quite effective in extracting the system properties. Nevertheless, uniform samplings often generate overlapping data, which can cause false rejections of surrogate data tests.

  17. Optimum Damping in a Non-Linear Base Isolation System

    NASA Astrophysics Data System (ADS)

    Jangid, R. S.

    1996-02-01

    Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations; i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping.

  18. The Hamiltonian property of the flow of singular trajectories

    NASA Astrophysics Data System (ADS)

    Lokutsievskiy, L. V.

    2014-03-01

    Pontryagin's maximum principle reduces optimal control problems to the investigation of Hamiltonian systems of ordinary differential equations with discontinuous right-hand side. An optimal synthesis is the totality of solutions to this system with a fixed terminal (or initial) condition, which fill a region in the phase space one-to-one. In the construction of optimal synthesis, singular trajectories that go along the discontinuity surface N of the right-hand side of the Hamiltonian system of ordinary differential equations, are crucial. The aim of the paper is to prove that the system of singular trajectories makes up a Hamiltonian flow on a submanifold of N. In particular, it is proved that the flow of singular trajectories in the problem of control of the magnetized Lagrange top in a variable magnetic field is completely Liouville integrable and can be embedded in the flow of a smooth superintegrable Hamiltonian system in the ambient space. Bibliography: 17 titles.

  19. Dispersion and nonlinear effects in OFDM-RoF system

    NASA Astrophysics Data System (ADS)

    Alhasson, Bader H.; Bloul, Albe M.; Matin, M.

    2010-08-01

    The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.

  20. Nonlinear disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition

    NASA Astrophysics Data System (ADS)

    Yang, Jun; Li, Shihua; Chen, Wen-Hua

    2012-08-01

    For a multi-input multi-output (MIMO) nonlinear system, the existing disturbance observer-based control (DOBC) only provides solutions to those whose disturbance relative degree (DRD) is higher than or equal to its input relative degree. By designing a novel disturbance compensation gain matrix, a generalised nonlinear DOBC method is proposed in this article to solve the disturbance attenuation problem of the MIMO nonlinear system with arbitrary DRD. It is shown that the disturbances are able to be removed from the output channels by the proposed method with appropriately chosen control parameters. The property of nominal performance recovery, which is the major merit of the DOBCs, is retained with the proposed method. The feasibility and effectiveness of the proposed method are demonstrated by simulation studies of both the numerical and application examples.

  1. Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians

    NASA Astrophysics Data System (ADS)

    Subasi, Yigit; Jarzynski, Christopher

    The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary k-body interactions, their use is limited to small k because the strength of interaction is k'th order in perturbation theory. Here we develop a nonperturbative technique for obtaining effective k-body interactions using Hamiltonians consisting of at most l-body interactions with l < k . This technique works best for Hamiltonians with a few interactions with very large k and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme. We gratefully acknowledge financial support from the Lockheed Martin Corporation under Contract U12001C.

  2. Noise in Nonlinear Dynamical Systems 3 Volume Paperback Set

    NASA Astrophysics Data System (ADS)

    Moss, Frank; McClintock, P. V. E.

    2011-11-01

    Volume 1: List of contributors; Preface; Introduction to volume one; 1. Noise-activated escape from metastable states: an historical view Rolf Landauer; 2. Some Markov methods in the theory of stochastic processes in non-linear dynamical systems R. L. Stratonovich; 3. Langevin equations with coloured noise J. M. Sancho and M. San Miguel; 4. First passage time problems for non-Markovian processes Katja Lindenberg, Bruce J. West and Jaume Masoliver; 5. The projection approach to the Fokker-Planck equation: applications to phenomenological stochastic equations with coloured noises Paolo Grigolini; 6. Methods for solving Fokker-Planck equations with applications to bistable and periodic potentials H. Risken and H. D. Vollmer; 7. Macroscopic potentials, bifurcations and noise in dissipative systems Robert Graham; 8. Transition phenomena in multidimensional systems - models of evolution W. Ebeling and L. Schimansky-Geier; 9. Coloured noise in continuous dynamical systems: a functional calculus approach Peter Hanggi; Appendix. On the statistical treatment of dynamical systems L. Pontryagin, A. Andronov and A. Vitt; Index. Volume 2: List of contributors; Preface; Introduction to volume two; 1. Stochastic processes in quantum mechanical settings Ronald F. Fox; 2. Self-diffusion in non-Markovian condensed-matter systems Toyonori Munakata; 3. Escape from the underdamped potential well M. Buttiker; 4. Effect of noise on discrete dynamical systems with multiple attractors Edgar Knobloch and Jeffrey B. Weiss; 5. Discrete dynamics perturbed by weak noise Peter Talkner and Peter Hanggi; 6. Bifurcation behaviour under modulated control parameters M. Lucke; 7. Period doubling bifurcations: what good are they? Kurt Wiesenfeld; 8. Noise-induced transitions Werner Horsthemke and Rene Lefever; 9. Mechanisms for noise-induced transitions in chemical systems Raymond Kapral and Edward Celarier; 10. State selection dynamics in symmetry-breaking transitions Dilip K. Kondepudi; 11. Noise in a

  3. Nonlinear dynamics of global atmospheric and Earth-system processes

    NASA Technical Reports Server (NTRS)

    Saltzman, Barry; Ebisuzaki, Wesley; Maasch, Kirk A.; Oglesby, Robert; Pandolfo, Lionel

    1990-01-01

    Researchers are continuing their studies of the nonlinear dynamics of global weather systems. Sensitivity analyses of large-scale dynamical models of the atmosphere (i.e., general circulation models i.e., GCM's) were performed to establish the role of satellite-signatures of soil moisture, sea surface temperature, snow cover, and sea ice as crucial boundary conditions determining global weather variability. To complete their study of the bimodality of the planetary wave states, they are using the dynamical systems approach to construct a low-order theoretical explanation of this phenomenon. This work should have important implications for extended range forecasting of low-frequency oscillations, elucidating the mechanisms for the transitions between the two wave modes. Researchers are using the methods of jump analysis and attractor dimension analysis to examine the long-term satellite records of significant variables (e.g., long wave radiation, and cloud amount), to explore the nature of mode transitions in the atmosphere, and to determine the minimum number of equations needed to describe the main weather variations with a low-order dynamical system. Where feasible they will continue to explore the applicability of the methods of complex dynamical systems analysis to the study of the global earth-system from an integrative viewpoint involving the roles of geochemical cycling and the interactive behavior of the atmosphere, hydrosphere, and biosphere.

  4. Third-order nonlinear optical response of energy transfer systems

    NASA Astrophysics Data System (ADS)

    Yang, Mino; Fleming, Graham R.

    1999-07-01

    The third-order nonlinear optical response of energy transfer systems is theoretically investigated. A system composed of two chromophores having the same electronic transition energies is considered. The dynamics of energy transfer between the two chromophores is assumed to occur via a hopping (incoherent) mechanism. We introduce new types of pathways incorporating the hopping processes occurring while the system is in population states and reconstruct a third-order response function which is computationally viable. The nuclear propagators in the electronic population states are written as convolution integrals between those of the nonreactive two-state system weighted by some factors for the energy transfer. The response function is given by multitime correlation functions and these are analyzed by the cumulant expansion method. Based on this approach, the three-pulse photon echo peak shift for several models of energy transfer systems is discussed. It is shown that the rephasing capability of the induced signal is reduced by the memory loss due to resonant energy transfer. A previous model which incorporates resonant energy transfers in an intuitive way is reviewed and modified to supplement the loss of dynamic correlation of nuclear motion within the framework of the theory. The response function obtained by our new approach gives a more accurate description than the existing theory and a comparative discussion is given. The effect of inhomogeneity in rate constants on the third-order signal is discussed and the temperature dependence of the echo signal is examined.

  5. Equations for Nonlinear MHD Convection in Shearless Magnetic Systems

    SciTech Connect

    Pastukhov, V.P.

    2005-07-15

    A closed set of reduced dynamic equations is derived that describe nonlinear low-frequency flute MHD convection and resulting nondiffusive transport processes in weakly dissipative plasmas with closed or open magnetic field lines. The equations obtained make it possible to self-consistently simulate transport processes and the establishment of the self-consistent plasma temperature and density profiles for a large class of axisymmetric nonparaxial shearless magnetic devices: levitated dipole configurations, mirror systems, compact tori, etc. Reduced equations that are suitable for modeling the long-term evolution of the plasma on time scales comparable to the plasma lifetime are derived by the method of the adiabatic separation of fast and slow motions.

  6. Method and system for non-linear motion estimation

    NASA Technical Reports Server (NTRS)

    Lu, Ligang (Inventor)

    2011-01-01

    A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.

  7. Exploring lipids with nonlinear optical microscopy in multiple biological systems

    NASA Astrophysics Data System (ADS)

    Alfonso-Garcia, Alba

    Lipids are crucial biomolecules for the well being of humans. Altered lipid metabolism may give rise to a variety of diseases that affect organs from the cardiovascular to the central nervous system. A deeper understanding of lipid metabolic processes would spur medical research towards developing precise diagnostic tools, treatment methods, and preventive strategies for reducing the impact of lipid diseases. Lipid visualization remains a complex task because of the perturbative effect exerted by traditional biochemical assays and most fluorescence markers. Coherent Raman scattering (CRS) microscopy enables interrogation of biological samples with minimum disturbance, and is particularly well suited for label-free visualization of lipids, providing chemical specificity without compromising on spatial resolution. Hyperspectral imaging yields large datasets that benefit from tailored multivariate analysis. In this thesis, CRS microscopy was combined with Raman spectroscopy and other label-free nonlinear optical techniques to analyze lipid metabolism in multiple biological systems. We used nonlinear Raman techniques to characterize Meibum secretions in the progression of dry eye disease, where the lipid and protein contributions change in ratio and phase segregation. We employed similar tools to examine lipid droplets in mice livers aboard a spaceflight mission, which lose their retinol content contributing to the onset of nonalcoholic fatty-liver disease. We also focused on atherosclerosis, a disease that revolves around lipid-rich plaques in arterial walls. We examined the lipid content of macrophages, whose variable phenotype gives rise to contrasting healing and inflammatory activities. We also proposed new label-free markers, based on lifetime imaging, for macrophage phenotype, and to detect products of lipid oxidation. Cholesterol was also detected in hepatitis C virus infected cells, and in specific strains of age-related macular degeneration diseased cells by

  8. Time-dependent drift Hamiltonian

    SciTech Connect

    Boozer, A.H.

    1983-03-01

    The lowest-order drift equations are given in a canonical magnetic coordinate form for time-dependent magnetic and electric fields. The advantages of the canonical Hamiltonian form are also discussed.

  9. Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

    NASA Technical Reports Server (NTRS)

    Devasia, Santosh

    1996-01-01

    The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.

  10. Modeling and detecting localized nonlinearity in continuum systems with a multistage transform.

    PubMed

    Bryant, Paul H; Nichols, J M

    2010-02-01

    A general method is presented for modeling spatially extended systems that may contain a localized source of nonlinearity. It has direct applications to structural health monitoring (SHM) where physical damage may cause such nonlinearity and also communications channels which may exhibit localized nonlinearity due to bad electrical contacts or component nonlinearity. The method uses a multistage nonlinear transform in order to model the system dynamics. We discuss the application to SHM and provide a preliminary test of the method with experimental data from a randomly shaken beam with loose bolts. We discuss the application to telecommunications, provide an experimental observation of symmetric nonlinearity in a "bad" electrical contact, and provide a preliminary test of using this method to remove nonlinear echo (and thereby improve data rate) on a telephone line used for data transmission. PMID:20365640

  11. Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory

    NASA Astrophysics Data System (ADS)

    Bona, J. L.; Chen, M.; Saut, J.-C.

    2004-05-01

    In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283-318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to arise in other physical settings where the dominant aspects of propagation are a balance between the nonlinear effects of convection and the linear effects of frequency dispersion. In addition to deriving these systems, we determined in part I exactly which of them are linearly well posed in various natural function classes. It was argued that linear well-posedness is a natural necessary requirement for the possible physical relevance of the model in question. In this paper, it is shown that the first-order correct models that are linearly well posed are in fact locally nonlinearly well posed. Moreover, in certain specific cases, global well-posedness is established for physically relevant initial data. In part I, higher-order correct models were also derived. A preliminary analysis of a promising subclass of these models shows them to be well posed.

  12. Macrosimulation of nonlinear dynamic systems for wave-shaping applications

    NASA Astrophysics Data System (ADS)

    Ogrodzki, Jan; Bieńkowski, Piotr

    2014-11-01

    Macromodeling is a technique widely used in circuits simulation. Macromodels usually describe complex, repetitive parts of large systems. They are often created on the base of original circuits by their simplification, e.g. macromodels of operational amplifiers. Another group of macromodels makes use of the circuit response approximation. This approach is called behavioral macromodeling. Low numerical complexity of behavioral macromodels is especially useful in CAD systems where circuit simulation must be run many times. In this paper the behavioral macromodeling technique has been applied to the whole circuit not to its part. This technique may be understood as shaping of the circuit output response and so belongs to a class of wave-shaping methods. We have used it to nonlinear, dynamic circuits with periodic signals of finite spectra, as e.g. in audio systems. The macromodels shape their frequency and spectral characteristics with a sufficient simplicity to omit unwanted distortions and with a sufficient efficiency to run the simulator in real time. Elaboration of this wave-shaping simulator is based on dynamic circuits identification, Fourier approximation of signals and harmonic balance technique. The obtained macromodel can be run as a software substitute for a hardware audio system.

  13. Nonlinear Dynamics of Extended Hydrologic Systems over long time scales

    NASA Astrophysics Data System (ADS)

    Lall, Upmanu

    2014-05-01

    We often view our knowledge of hydrology and hence of nature as intransient, at least over the time scales over which we study processes we wish to predict and understand. Over the last few decades, this assumption has come under question, largely because of the vocal expression of a changing climate, but also the recurrent demonstration of significant land use change, both of which significantly affect the boundary conditions for terrestrial hydrology that is our forte. Most recently, the concepts of hydromorphology and social hydrology have entered the discussion, and the notion that climate and hydrology influence human action, which in turn shapes hydrology, is being recognized. Finally, as a field, we seem to be coming to the conclusion that the hydrologic system is an open system, whose boundaries evolve in time, and that the hydrologic system, at many scales, has a profound effect on the systems that drive it -- whether they be the ecological and climatic systems, or the social system. What a mess! Complexity! Unpredictability! At a certain level of abstraction, one can consider the evolution of these coupled systems with nonlinear feedbacks and ask what types of questions are relevant in terms of such a coupled evolution? What are their implications at the planetary scale? What are their implications for a subsistence farmer in an arid landscape who may under external influence achieve a new transient hydro-ecological equilibrium? What are the implications for the economy and power of nations? In this talk, I will try to raise some of these questions and also provide some examples with very simple dynamical systems that suggest ways of thinking about some practical issues of feedback across climate, hydrology and human behavior.

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

    NASA Technical Reports Server (NTRS)

    Fitzjerrell, D. G.

    1974-01-01

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

  15. Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems

    EPA Science Inventory

    Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...

  16. A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems

    ERIC Educational Resources Information Center

    Stavrou, D.; Duit, R.; Komorek, M.

    2008-01-01

    A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…

  17. Conformal killing tensors and covariant Hamiltonian dynamics

    SciTech Connect

    Cariglia, M.; Gibbons, G. W.; Holten, J.-W. van; Horvathy, P. A.; Zhang, P.-M.

    2014-12-15

    A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.

  18. The Impact of Fiber Nonlinearities on Digital Optical Communication Systems

    NASA Astrophysics Data System (ADS)

    Chiang, Ting-Kuang

    Wavelength-division multiplexing (WDM) enables high throughput fiber-optic networks by sending several optical channels through a single fiber. Even though the bandwidth of optical fibers is over 25 THz, fiber nonlinearities can limit the capacity of WDM communication systems. Cross -phase modulation (XPM) is one of the nonlinear effects that affect WDM systems. This thesis provides an in-depth understanding of the properties of XPM-induced phase shift and suggests techniques to suppress XPM in long-distance WDM optical networks. In this thesis, XPM is theoretically and experimentally investigated in fiber links with optical amplifiers and dispersion compensators. The theoretical analysis suggests that the XPM effect can be modeled as a phase modulator with inputs from the intensity of co-propagating waves. The frequency response of the phase modulator depends on fiber dispersion, wavelength separation, and fiber length. In non-dispersive fibers, XPM is frequency-independent; in dispersive fibers, the response is approximately inversely proportional to modulation frequency, fiber dispersion, and wavelength separation. In N-segment amplified links with no dispersion compensators, the XPM frequency response is increased N -fold, but only in very narrow frequency bands. In most other frequency bands, the increase is limited and almost independent of N. However, in N-segment amplified links with dispersion compensators, the frequency response of XPM is increased N-fold at all frequencies if the dispersion is compensated for within each fiber segment. The XPM-induced sensitivity penalty in multichannel continuous-phase frequency-shift-keying optical communication systems is investigated by theoretical analysis, computer simulations, and experimental measurements. It is shown that high-frequency components in the XPM-induced phase shift play a more important role in determining the sensitivity penalty than the low-frequency components. The XPM-induced sensitivity penalty

  19. Dynamics and bifurcations in a Dn-symmetric Hamiltonian network. Application to coupled gyroscopes

    NASA Astrophysics Data System (ADS)

    Buono, Pietro-Luciano; Chan, Bernard S.; Palacios, Antonio; In, Visarath

    2015-01-01

    The advent of novel engineered or smart materials, whose properties can be significantly altered in a controlled fashion by external stimuli, has stimulated the design and fabrication of smaller, faster, and more energy-efficient devices. As the need for even more powerful devices grows, networks have become popular alternatives to advance the fundamental limits of performance of individual units. In many cases, the collective rhythmic behavior of a network can be studied through the classical theory of nonlinear oscillators or through the more recent development of the coupled cell formalism. However, the current theory does not account yet for networks in which cells, or individual units, possess a Hamiltonian structure. One such example is a ring array of vibratory gyroscopes, where certain network topologies favor stable synchronized oscillations. Previous perturbation-based studies have shown that synchronized oscillations may, in principle, increase performance by reducing phase drift. The governing equations for larger array sizes are, however, not amenable to similar analysis. To circumvent this problem, the model equations are now reformulated in a Hamiltonian structure and the corresponding normal forms are derived. Through a normal form analysis, we investigate the effects of various coupling schemes and unravel the nature of the bifurcations that lead a ring of gyroscopes of any size into and out of synchronization. The Hamiltonian approach can, in principle, be readily extended to other symmetry-related systems.

  20. Stability of Gabor Frames Under Small Time Hamiltonian Evolutions

    NASA Astrophysics Data System (ADS)

    de Gosson, Maurice A.; Gröchenig, Karlheinz; Romero, José Luis

    2016-05-01

    We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability of the frame property for small times and Hamiltonians consisting of a quadratic polynomial plus a potential in the Sjöstrand class with bounded second-order derivatives. This answers a question raised in de Gosson (Appl Comput Harmonic Anal 38(2):196-221, 2015)

  1. An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator

    NASA Astrophysics Data System (ADS)

    Masterov, Ivan

    2016-01-01

    Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [7] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais-Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N = 2 supersymmetric Pais-Uhlenbeck oscillator.

  2. Stability of Gabor Frames Under Small Time Hamiltonian Evolutions

    NASA Astrophysics Data System (ADS)

    de Gosson, Maurice A.; Gröchenig, Karlheinz; Romero, José Luis

    2016-06-01

    We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability of the frame property for small times and Hamiltonians consisting of a quadratic polynomial plus a potential in the Sjöstrand class with bounded second-order derivatives. This answers a question raised in de Gosson (Appl Comput Harmonic Anal 38(2):196-221, 2015)

  3. Linear versus nonlinear response of a forced wave turbulence system.

    PubMed

    Cadot, Olivier; Touzé, Cyril; Boudaoud, Arezki

    2010-10-01

    A vibrating plate is set into a chaotic state of wave turbulence by a forcing having periodic and random components. Both components are weighted in order to explore continuously intermediate forcing from the periodic to the random one, but keeping constant its rms value. The transverse velocity of the plate is measured at the application point of the force. It is found that whatever the detail of the forcing is, the velocity spectra exhibit a universal cascade for frequencies larger than the forcing frequency range. In contrast, the velocity spectra strongly depend on the nature of the forcing within the range of forcing frequencies. The coherence function is used to extract the contribution of the velocity fluctuations that display a linear relationship with the forcing. The nonlinear contribution to the velocity fluctuations is found to be almost constant, about 55% of the total velocity fluctuations whatever the nature of the forcing from random to periodic. On the other hand, the nonlinear contribution to the fluctuations of the injected power depends on the nature of the forcing; it is significantly larger for the periodic forcing (60%) and decreases continuously as the randomness is increased, reaching a value of 40% for the pure random forcing. For all the cases of intermediate forcing from random to periodic, a simple model of the velocity response recovers in a fairly good agreement the probability density function of the injected power. The consequence of the existence of a linear-response component is discussed in the context of the fluctuation-dissipation theorem validation in experiments of out-of-equilibrium systems. PMID:21230369

  4. Hamiltonian theory of guiding-center motion

    SciTech Connect

    Littlejohn, R.G.

    1980-05-01

    A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.

  5. Nonlinear Network Modes in Cyclic Systems with Applications to Connected Vehicles

    NASA Astrophysics Data System (ADS)

    Avedisov, Sergei S.; Orosz, Gábor

    2015-08-01

    In this paper, we propose a novel technique to decompose networked systems with cyclic structure into nonlinear modes and apply these ideas to a system of connected vehicles. We perform linear and nonlinear transformations that exploit the network structure and lead to nonlinear modal equations that are decoupled. Each mode can be obtained by solving a small set of algebraic equations without deriving the coefficients for any other mode. By focusing on the mode that is loosing stability, bifurcation analysis can be carried out. The techniques developed are applied to evaluate the impact of connected cruise control on the nonlinear dynamics of a connected vehicle system.

  6. A new method of modelling and numerical simulation of nonlinear dynamical systems

    SciTech Connect

    Colosi, T.; Codreanu, S.

    1996-06-01

    This work presents the most significant aspects of an original method of modelling and numerical simulation of nonlinear (linear) dynamical systems (1) it assures the local-iterative linearization (LIL) of nonlinear (linear) differential equations and transforms them, in the close proximity of a pivot moment, into algebraic equations. The use of this method is illustrated in the study of a particular nonlinear dynamical systems. The conclusions highlight the advantages of the proposed procedure. {copyright} {ital 1996 American Institute of Physics.}

  7. Nonlinear Bogolyubov-Valatin transformations: Two modes

    SciTech Connect

    Scharnhorst, K.; Holten, J.-W. van

    2011-11-15

    Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper, we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes, which can be implemented by means of unitary SU(2{sup n}=4) transformations, is isomorphic to SO(6;R)/Z{sub 2}. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (linear combinations of products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington's E-numbers and can be understood in terms of the tensor product of two commuting copies of the division algebra of quaternions H. From a physical point of view, we present a method to diagonalize any arbitrary two-fermion Hamiltonians. Relying on Jordan-Wigner transformations for two-spin-1/2 and single-spin-3/2 systems, we also study nonlinear spin transformations and the related problem of diagonalizing arbitrary two-spin-1/2 and single-spin-3/2 Hamiltonians. Finally, from a calculational point of view, we pay due attention to explicit parametrizations of SU(4) and SO(6;R) matrices (of respective sizes 4x4 and 6x6) and their mutual relation. - Highlights: > Reveals the structure of nonlinear canonical transformations for two fermionic modes. > Studies nonlinear basis transformations in a Clifford algebra. > Focuses on methodological and structural aspects. > Presents a new approach to the diagonalization of 4x4 matrix Hamiltonians. > Presents the relation between

  8. Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS

    NASA Astrophysics Data System (ADS)

    Horwitz, Lawrence; Gershon, Avi; Schiffer, Marcelo

    2011-01-01

    It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual by means of a conformal map. This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system. We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence in this way with another Hamiltonian with conformally modified metric. Such a construction could account for part of the requirements of Bekenstein for achieving the MOND theory of Milgrom in the post-Newtonian limit. The constraints on the MOND theory imposed by the galactic rotation curves, through this correspondence, would then imply constraints on the structure of the world scalar field. We then use the fact that a Hamiltonian with vector gauge fields results, through such a conformal map, in a Kaluza-Klein type theory, and indicate how the TeVeS structure of Bekenstein and Saunders can be put into this framework. We exhibit a class of infinitesimal gauge transformations on the gauge fields {mathcal{U}}_{μ}(x) which preserve the Bekenstein-Sanders condition {mathcal{U}}_{μ}{mathcal{U}}^{μ}=-1. The underlying quantum structure giving rise to these gauge fields is a Hilbert bundle, and the gauge transformations induce a non-commutative behavior to the fields, i.e. they become of Yang-Mills type. Working in the infinitesimal gauge neighborhood of the initial Abelian theory we show that in the Abelian limit the Yang-Mills field equations provide residual nonlinear terms which may avoid the caustic singularity found by Contaldi et al.

  9. Robust Control Design for Uncertain Nonlinear Dynamic Systems

    NASA Technical Reports Server (NTRS)

    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.

  10. Nonlinear dynamics of global atmospheric and Earth system processes

    NASA Technical Reports Server (NTRS)

    Saltzman, Barry

    1993-01-01

    During the past eight years, we have been engaged in a NASA-supported program of research aimed at establishing the connection between satellite signatures of the earth's environmental state and the nonlinear dynamics of the global weather and climate system. Thirty-five publications and four theses have resulted from this work, which included contributions in five main areas of study: (1) cloud and latent heat processes in finite-amplitude baroclinic waves; (2) application of satellite radiation data in global weather analysis; (3) studies of planetary waves and low-frequency weather variability; (4) GCM studies of the atmospheric response to variable boundary conditions measurable from satellites; and (5) dynamics of long-term earth system changes. Significant accomplishments from the three main lines of investigation pursued during the past year are presented and include the following: (1) planetary atmospheric waves and low frequency variability; (2) GCM studies of the atmospheric response to changed boundary conditions; and (3) dynamics of long-term changes in the global earth system.

  11. Adaptation with disturbance attenuation in nonlinear control systems

    SciTech Connect

    Basar, T.

    1997-12-31

    We present an optimization-based adaptive controller design for nonlinear systems exhibiting parametric as well as functional uncertainty. The approach involves the formulation of an appropriate cost functional that places positive weight on deviations from the achievement of desired objectives (such as tracking of a reference trajectory while the system exhibits good transient performance) and negative weight on the energy of the uncertainty. This cost functional also translates into a disturbance attenuation inequality which quantifies the effect of the presence of uncertainty on the desired objective, which in turn yields an interpretation for the optimizing control as one that optimally attenuates the disturbance, viewed as the collection of unknown parameters and unknown signals entering the system dynamics. In addition to this disturbance attenuation property, the controllers obtained also feature adaptation in the sense that they help with identification of the unknown parameters, even though this has not been set as the primary goal of the design. In spite of this adaptation/identification role, the controllers obtained are not of certainty-equivalent type, which means that the identification and the control phases of the design are not decoupled.

  12. Nonlinear damage identification of breathing cracks in Truss system

    NASA Astrophysics Data System (ADS)

    Zhao, Jie; DeSmidt, Hans

    2014-03-01

    The breathing cracks in truss system are detected by Frequency Response Function (FRF) based damage identification method. This method utilizes damage-induced changes of frequency response functions to estimate the severity and location of structural damage. This approach enables the possibility of arbitrary interrogation frequency and multiple inputs/outputs which greatly enrich the dataset for damage identification. The dynamical model of truss system is built using the finite element method and the crack model is based on fracture mechanics. Since the crack is driven by tensional and compressive forces of truss member, only one damage parameter is needed to represent the stiffness reduction of each truss member. Assuming that the crack constantly breathes with the exciting frequency, the linear damage detection algorithm is developed in frequency/time domain using Least Square and Newton Raphson methods. Then, the dynamic response of the truss system with breathing cracks is simulated in the time domain and meanwhile the crack breathing status for each member is determined by the feedback from real-time displacements of member's nodes. Harmonic Fourier Coefficients (HFCs) of dynamical response are computed by processing the data through convolution and moving average filters. Finally, the results show the effectiveness of linear damage detection algorithm in identifying the nonlinear breathing cracks using different combinations of HFCs and sensors.

  13. Multi-agent motion planning for nonlinear Gaussian systems

    NASA Astrophysics Data System (ADS)

    Postlethwaite, Ian; Kothari, Mangal

    2013-11-01

    In this paper, a multi-agent motion planner is developed for nonlinear Gaussian systems using a combination of probabilistic approaches and a rapidly exploring random tree (RRT) algorithm. A closed-loop model consisting of a controller and estimation loops is used to predict future distributions to manage the level of uncertainty in the path planner. The closed-loop model assumes the existence of a feedback control law that drives the actual system towards a nominal system. This ensures the uncertainty in the evolution does not grow significantly and the tracking errors are bounded. To trade conservatism with the risk of infeasibility and failure, we use probabilistic constraints to limit the probability of constraint violation. The probability of leaving the configuration space is included by using a chance constraint approach and the probability of closeness between two agents is imposed using an overlapping coefficient approach. We augment these approaches with the RRT algorithm to develop a robust path planner. Conflict among agents is resolved using a priority-based technique. Numerical results are presented to demonstrate the effectiveness of the planner.

  14. Classical Histories in Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Kouletsis, Ioannis

    2001-08-01

    The incompatibility between the treatment of time in the classical and in the quantum theory results in the so-called problem of time in canonical quantum gravity. For this reason, attempts have been made to devise algorithms of quantization which accomodate the covariance of the classical theory from the outset. One of the most prominent of these attempts is based on the notion of continuous histories (Isham and Linden) in the context of the consistent histories approach to quantum theory (Griffiths, Omnes, Gell-Mann and Hartle). By the term continuous histories it is implied that the canonical fields and the symplectic structure of the theory depend on time as well as space. The aim of this thesis (in the form it was submitted to the University of London, February 2000) is to show that, even at the purely classical level, a history approach has several advantages (compared to its equal-time counterpart) when it comes to discussing spacetime issues. This is illustrated here by reframing and generalizing the derivation of geometrodynamics from first principles (Hojman, Kuchar, Teitelboim) in the language of the history phase space.

  15. Some Thoughts on Stability in Nonlinear Periodic Focusing Systems

    DOE R&D Accomplishments Database

    McMillan, E. M.

    1967-09-05

    A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.

  16. Projection methods for solving nonlinear systems of equations

    SciTech Connect

    Brown, P.N. ); Saad, Y. . Ames Research Center)

    1990-04-01

    This paper describes several nonlinear projection methods based on Krylov subspaces and analyzes their convergence. The prototype of these methods is a technique that generalizes the conjugate direction method by minimizing the norm of the function F over some subspace. The emphasis of this paper is on nonlinear least squares problems which can also be handled by this general approach.

  17. Overview of nonlinear dynamical systems and complexity theory

    SciTech Connect

    Herbert, D.E.

    1996-06-01

    A brief overview is presented of the principal elements of {open_quote}{open_quote}nonlinear dynamics{close_quote}{close_quote}: catastrophes, fractals, chaos, solitary waves, and coherent and dissipative structures. The text is followed by a set of 10 portraits of the strange and violent world of nonlinear dynamics. {copyright} {ital 1996 American Institute of Physics.}

  18. Nonlinear phase field model for electrodeposition in electrochemical systems

    SciTech Connect

    Liang, Linyun; Chen, Long-Qing

    2014-12-29

    A nonlinear phase-field model has been developed for describing the electrodeposition process in electrochemical systems that are highly out of equilibrium. Main thermodynamic driving forces for the electrode-electrolyte interface (EEI) evolution are limited to local variations of overpotential and ion concentration. Application of the model to Li-ion batteries describes the electrode interface motion and morphology change caused by charge mass transfer in the electrolyte, an electrochemical reaction at the EEI and cation deposition on the electrode surface during the charging operation. The Li electrodeposition rate follows the classical Butler-Volmer kinetics with exponentially and linearly depending on local overpotential and cation concentration at the electrode surface, respectively. Simulation results show that the Li deposit forms a fiber-like shape and grows parallel to the electric field direction. The longer and thicker deposits are observed both for higher current density and larger rate constant where the surface reaction rate is expected to be high. The proposed diffuse interface model well captures the metal electrodeposition phenomena in plenty of non-equilibrium electrochemical systems.

  19. Controlling Spatiotemporal Chaos in Active Dissipative-Dispersive Nonlinear Systems

    NASA Astrophysics Data System (ADS)

    Gomes, Susana; Pradas, Marc; Kalliadasis, Serafim; Papageorgiou, Demetrios; Pavliotis, Grigorios

    2015-11-01

    We present a novel generic methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. The methodology is exemplified with the generalized Kuramoto-Sivashinsky equation, the simplest possible prototype that retains that fundamental elements of any nonlinear process involving wave evolution. The equation is applicable on a wide variety of systems including falling liquid films and plasma waves with dispersion due to finite banana width. We show that applying the appropriate choice of time-dependent feedback controls via blowing and suction, we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, travelling waves and spatiotemporal chaos, but also use the controls obtained to stabilize the solutions to more general long wave models. We acknowledge financial support from Imperial College through a Roth PhD studentship, Engineering and Physical Sciences Research Council of the UK through Grants No. EP/H034587, EP/J009636, EP/K041134, EP/L020564 and EP/L024926 and European Research Council via Advanced Grant No. 247031.

  20. Thermostatistics of small nonlinear systems: Poissonian athermal bath

    NASA Astrophysics Data System (ADS)

    Morgado, Welles A. M.; Queirós, Sílvio M. Duarte

    2016-01-01

    We extend an earlier study [W. A. M. Morgado and S. M. Duarte Queirós, Phys. Rev. E 90, 022110 (2014), 10.1103/PhysRevE.90.022110] to the case of a small system subject to nonlinear interaction and in contact with an athermal shot-noise reservoir. We first focus on steady state properties, namely, on the impact of the singular measure of the reservoir in the steady state energy. We introduce the concept of temperatures of higher order, which aim to represent the effect produced by the cumulants of the noise of order larger than 2 in the form of sources of energy of higher order and new response functions such as high-order specific heats that zero out when the system is thermal or linear. Afterwards, we study the effect of the nature of the noise in the heat and energy fluxes and determine asymptotic expressions for its large deviation functions. Finally, by analyzing the probabilistics of the injected power, we verify that the exponential form of its fluctuation relation is only asymptotically valid, whereas in the thermal case it is valid for the injected power at all times.

  1. Limit cycle analysis of active disturbance rejection control system with two nonlinearities.

    PubMed

    Wu, Dan; Chen, Ken

    2014-07-01

    Introduction of nonlinearities to active disturbance rejection control algorithm might have high control efficiency in some situations, but makes the systems with complex nonlinearity. Limit cycle is a typical phenomenon that can be observed in the nonlinear systems, usually causing failure or danger of the systems. This paper approaches the problem of the existence of limit cycles of a second-order fast tool servo system using active disturbance rejection control algorithm with two fal nonlinearities. A frequency domain approach is presented by using describing function technique and transfer function representation to characterize the nonlinear system. The derivations of the describing functions for fal nonlinearities and treatment of two nonlinearities connected in series are given to facilitate the limit cycles analysis. The effects of the parameters of both the nonlinearity and the controller on the limit cycles are presented, indicating that the limit cycles caused by the nonlinearities can be easily suppressed if the parameters are chosen carefully. Simulations in the time domain are performed to assess the prediction accuracy based on the describing function. PMID:24795034

  2. Estimation of a general time-dependent Hamiltonian for a single qubit.

    PubMed

    de Clercq, L E; Oswald, R; Flühmann, C; Keitch, B; Kienzler, D; Lo, H-Y; Marinelli, M; Nadlinger, D; Negnevitsky, V; Home, J P

    2016-01-01

    The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control. PMID:27075230

  3. Estimation of a general time-dependent Hamiltonian for a single qubit

    NASA Astrophysics Data System (ADS)

    de Clercq, L. E.; Oswald, R.; Flühmann, C.; Keitch, B.; Kienzler, D.; Lo, H.-Y.; Marinelli, M.; Nadlinger, D.; Negnevitsky, V.; Home, J. P.

    2016-04-01

    The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.

  4. Estimation of a general time-dependent Hamiltonian for a single qubit

    PubMed Central

    de Clercq, L. E.; Oswald, R.; Flühmann, C.; Keitch, B.; Kienzler, D.; Lo, H. -Y.; Marinelli, M.; Nadlinger, D.; Negnevitsky, V.; Home, J. P.

    2016-01-01

    The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control. PMID:27075230

  5. Hamiltonian Dynamics of Protein Filament Formation.

    PubMed

    Michaels, Thomas C T; Cohen, Samuel I A; Vendruscolo, Michele; Dobson, Christopher M; Knowles, Tuomas P J

    2016-01-22

    We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils. PMID:26849615

  6. Identification of limit cycles in multi-nonlinearity, multiple path systems

    NASA Technical Reports Server (NTRS)

    Mitchell, J. R.; Barron, O. L.

    1979-01-01

    A method of analysis which identifies limit cycles in autonomous systems with multiple nonlinearities and multiple forward paths is presented. The FORTRAN code for implementing the Harmonic Balance Algorithm is reported. The FORTRAN code is used to identify limit cycles in multiple path and nonlinearity systems while retaining the effects of several harmonic components.

  7. On the estimation of the attainability set of nonlinear control systems

    SciTech Connect

    Ekimov, A.V.; Balykina, Yu.E.; Svirkin, M.V.

    2015-03-10

    Analysis of the attainability set and construction of its estimates greatly facilitates the solution of a variety of problems in mathematical control theory. In the paper, the problem of boundedness of the integral funnel of nonlinear controlled system is considered. Some estimates of the attainability sets for a nonlinear controlled system are presented. Theorems on the boundedness of considered integral funnels are proved.

  8. Hamiltonian approach to the magnetostatic equilibrium problem

    SciTech Connect

    Tessarotto, M.; Zheng, Lin Jin; Johnson, J.L.

    1995-02-01

    The purpose of this paper is to investigate the classical scalar-pressure magnetostatic equilibrium problem for non-symmetric configurations in the framework of a Hamiltonian approach. Requiring that the equilibrium admits locally, in a suitable subdomain, a family of nested toroidal magnetic surfaces, the Hamiltonian equations describing the magnetic flux lines in such a subdomain are obtained for general curvilinear coordinate systems. The properties of such Hamiltonian system are investigated. A representation of the magnetic field in terms of arbitrary general curvilinear coordinates is thus obtained. Its basic feature is that the magnetic field must fulfill suitable periodicity constraints to be imposed on arbitrary rational magnetic surfaces for general non-symmetric toroidal equilibria, i.e., it is quasi-symmetric. Implications for the existence of magnetostatic equilibria are pointed out. In particular, it is proven that a generalized equilibrium equation exists for such quasi-symmetric equilibria, which extends the Grad-Shafranov equation to fully three-dimensional configurations. As an application, the case is considered of quasi-helical equilibria, i.e., displaying a magnetic field magnitude depending on the poloidal ({chi}) and toroidal ({var_theta}) angles only in terms of {alpha}={chi}-N{theta} with N an arbitrary integer.

  9. Self-synchronization in an ensemble of nonlinear oscillators.

    PubMed

    Ostrovsky, L A; Galperin, Y V; Skirta, E A

    2016-06-01

    The paper describes the results of study of a system of coupled nonlinear, Duffing-type oscillators, from the viewpoint of their self-synchronization, i.e., generation of a coherent field (order parameter) via instability of an incoherent (random-phase) initial state. We consider both the cases of dissipative coupling (e.g., via the joint radiation) and reactive coupling in a Hamiltonian system. PMID:27368772

  10. Hamiltonian formalism and path entropy maximization

    NASA Astrophysics Data System (ADS)

    Davis, Sergio; González, Diego

    2015-10-01

    Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the second law of thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the second law is a fundamental property of plausible inference.

  11. Identification of nonlinear dynamic systems using functional link artificial neural networks.

    PubMed

    Patra, J C; Pal, R N; Chatterji, B N; Panda, G

    1999-01-01

    We have presented an alternate ANN structure called functional link ANN (FLANN) for nonlinear dynamic system identification using the popular backpropagation algorithm. In contrast to a feedforward ANN structure, i.e., a multilayer perceptron (MLP), the FLANN is basically a single layer structure in which nonlinearity is introduced by enhancing the input pattern with nonlinear functional expansion. With proper choice of functional expansion in a FLANN, this network performs as good as and in some cases even better than the MLP structure for the problem of nonlinear system identification. PMID:18252296

  12. Develop Advanced Nonlinear Signal Analysis Topographical Mapping System

    NASA Technical Reports Server (NTRS)

    Jong, Jen-Yi

    1997-01-01

    During the development of the SSME, a hierarchy of advanced signal analysis techniques for mechanical signature analysis has been developed by NASA and AI Signal Research Inc. (ASRI) to improve the safety and reliability for Space Shuttle operations. These techniques can process and identify intelligent information hidden in a measured signal which is often unidentifiable using conventional signal analysis methods. Currently, due to the highly interactive processing requirements and the volume of dynamic data involved, detailed diagnostic analysis is being performed manually which requires immense man-hours with extensive human interface. To overcome this manual process, NASA implemented this program to develop an Advanced nonlinear signal Analysis Topographical Mapping System (ATMS) to provide automatic/unsupervised engine diagnostic capabilities. The ATMS will utilize a rule-based Clips expert system to supervise a hierarchy of diagnostic signature analysis techniques in the Advanced Signal Analysis Library (ASAL). ASAL will perform automatic signal processing, archiving, and anomaly detection/identification tasks in order to provide an intelligent and fully automated engine diagnostic capability. The ATMS has been successfully developed under this contract. In summary, the program objectives to design, develop, test and conduct performance evaluation for an automated engine diagnostic system have been successfully achieved. Software implementation of the entire ATMS system on MSFC's OISPS computer has been completed. The significance of the ATMS developed under this program is attributed to the fully automated coherence analysis capability for anomaly detection and identification which can greatly enhance the power and reliability of engine diagnostic evaluation. The results have demonstrated that ATMS can significantly save time and man-hours in performing engine test/flight data analysis and performance evaluation of large volumes of dynamic test data.

  13. Multiscale Analysis of Nonlinear Systems Using Computational Topology

    SciTech Connect

    Schatz, Michael F.; Mischaikow, Konstantin; Kalies, William; Wanner, Thomas

    2010-08-31

    Computational Homology in Fluids: M. Schatz, K. Mischaikow. This effort focused on characterizing both the structure and dynamics of complex spatio-temporal flows that arise in thermal convection. Microstructure Characterization: T. Wanner, K. Mischaikow. We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. Probabilistic Homology Validation: W. Kalies, T. Wanner, K. Mischaikow. Our above mentioned work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. Computational Homology and Dynamics: W. Kalies, T. Wanner, K. Mischaikow. Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. Stress Networks in Polycrystals: T. Wanner. Together with E. Fuller (NIST) and D. Saylor (FDA) we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. Microstructure-Controlled Drug Release: K. Mischaikow, T. Wanner. This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. Microstructure of Fuel Cells: W. Kalies, K. Mischaikow. In collaboration with P. Voorhees (Northwestern Univ.) and M. Gameiro (Rutgers) we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid

  14. Advanced data assimilation in strongly nonlinear dynamical systems

    NASA Technical Reports Server (NTRS)

    Miller, Robert N.; Ghil, Michael; Gauthiez, Francois

    1994-01-01

    Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

  15. Quantum Hamiltonian identification from measurement time traces.

    PubMed

    Zhang, Jun; Sarovar, Mohan

    2014-08-22

    Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings. PMID:25192077

  16. Hamiltonian approach to frame dragging

    NASA Astrophysics Data System (ADS)

    Epstein, Kenneth J.

    2008-07-01

    A Hamiltonian approach makes the phenomenon of frame dragging apparent “up front” from the appearance of the drag velocity in the Hamiltonian of a test particle in an arbitrary metric. Hamiltonian (1) uses the inhomogeneous force equation (4), which applies to non-geodesic motion as well as to geodesics. The Hamiltonian is not in manifestly covariant form, but is covariant because it is derived from Hamilton’s manifestly covariant scalar action principle. A distinction is made between manifest frame dragging such as that in the Kerr metric, and hidden frame dragging that can be made manifest by a coordinate transformation such as that applied to the Robertson-Walker metric in Sect. 2. In Sect. 3 a zone of repulsive gravity is found in the extreme Kerr metric. Section 4 treats frame dragging in special relativity as a manifestation of the equivalence principle in accelerated frames. It answers a question posed by Bell about how the Lorentz contraction can break a thread connecting two uniformly accelerated rocket ships. In Sect. 5 the form of the Hamiltonian facilitates the definition of gravitomagnetic and gravitoelectric potentials.

  17. Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

    NASA Technical Reports Server (NTRS)

    Murthy, V. R.; Shultz, Louis A.

    1994-01-01

    The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

  18. Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD

    SciTech Connect

    Morrison, P.J.; Greene, J.M.

    1980-04-01

    A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables.

  19. Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data

    NASA Technical Reports Server (NTRS)

    Kukreja, Sunil L.

    2008-01-01

    Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

  20. Toward a nonlinear ensemble filter for high-dimensional systems

    NASA Astrophysics Data System (ADS)

    Bengtsson, Thomas; Snyder, Chris; Nychka, Doug

    2003-12-01

    Many geophysical problems are characterized by high-dimensional, nonlinear systems and pose difficult challenges for real-time data assimilation (updating) and forecasting. The present work builds on the ensemble Kalman filter (EnsKF), with the goal of producing ensemble filtering techniques applicable to non-Gaussian densities and high-dimensional systems. Three filtering algorithms, based on representing the prior density as a Gaussian mixture, are presented. The first, referred to as a mixture ensemble Kalman filter (XEnsF), models local covariance structures adaptively using nearest neighbors. The XEnsF is effective in a three-dimensional system, but the required ensemble grows rapidly with the dimension and, even in a 40-dimensional system, we find the XEnsF to be unstable and inferior to the EnsKF for all computationally feasible ensemble sizes. A second algorithm, the local-local ensemble filter (LLEnsF), combines localizations in physical as well as phase space, allowing the update step in high-dimensional systems to be decomposed into a sequence of lower-dimensional updates tractable by the XEnsF. Given the same prior forecasts in a 40-dimensional system, the LLEnsF update produces more accurate state estimates than the EnsKF if the forecast distributions are sufficiently non-Gaussian. Cycling the LLEnsF for long times, however, produces results inferior to the EnsKF because the LLEnsF ignores spatial continuity or smoothness between local state estimates. To address this weakness of the LLEnsF, we consider ways of enforcing spatial smoothness by conditioning the local updates on the prior estimates outside the localization in physical space. These considerations yield a third algorithm, which is a hybrid of the LLEnsF and the EnsKF. The hybrid uses information from the EnsKF to ensure spatial continuity of local updates and outperforms the EnsKF by 5.7% in RMS error in the 40-dimensional system.

  1. Variational identities and Hamiltonian structures

    SciTech Connect

    Ma Wenxiu

    2010-03-08

    This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.

  2. First principles of Hamiltonian medicine

    PubMed Central

    Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

    2014-01-01

    We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease. PMID:24686937

  3. Cost-Effective Treatment of Scalar Relativistic Effects for Multireference Systems: A CASSCF Implementation Based on the Spin-free Dirac-Coulomb Hamiltonian.

    PubMed

    Lipparini, Filippo; Gauss, Jürgen

    2016-09-13

    We present an implementation of the complete active space-self-consistent field (CASSCF) method specifically designed to be used in four-component scalar relativistic calculations based on the spin-free Dirac-Coulomb (SFDC) Hamiltonian. Our implementation takes full advantage of the properties of the SFDC Hamiltonian that allow us to use real algebra and to exploit point-group and spin symmetry to their full extent while including in a rigorous way scalar relativistic effects in the treatment. The SFDC-CASSCF treatment is more expensive than its non-relativistic counterpart only in the orbital optimization step, while exhibiting the same computational cost for the rate-determining full configuration interaction part. The numerical aspects are discussed, and the capabilities of the SFDC-CASSCF methodology are demonstrated through a pilot application. PMID:27464026

  4. Nonlinearity management in fiber transmission systems with hybrid amplification

    NASA Astrophysics Data System (ADS)

    Ania-Castañón, J. D.; Nasieva, I. O.; Kurukitkoson, N.; Turitsyn, S. K.; Borsier, C.; Pincemin, E.

    2004-04-01

    Nonlinearity management in transmission lines with periodic dispersion compensation and hybrid Raman-Erbium doped fiber amplification is studied both analytically and numerically. Different transmission/compensating fiber pairs are considered, with particular focus on the SMF/DCF case.

  5. Exact traveling wave solutions for system of nonlinear evolution equations.

    PubMed

    Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

    2016-01-01

    In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis. PMID:27347461

  6. Some Thoughts on Stability in Nonlinear Periodic Focusing Systems [Addendum

    DOE R&D Accomplishments Database

    McMillan, Edwin M.

    1968-03-29

    Addendum to September 5, 1967 report with the same title and with the abstract: A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.

  7. Programmable quantum simulation by dynamic Hamiltonian engineering

    NASA Astrophysics Data System (ADS)

    Hayes, David; Flammia, Steven T.; Biercuk, Michael J.

    2014-08-01

    Quantum simulation is a promising near term application for quantum information processors with the potential to solve computationally intractable problems using just a few dozen interacting qubits. A range of experimental platforms have recently demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions and relativistic quantum mechanics. However, in all cases, the physics of the underlying hardware restricts the achievable inter-particle interactions and forms a serious constraint on the versatility of the simulators. To broaden the scope of these analog devices, we develop a suite of pulse sequences that permit a user to efficiently realize average Hamiltonians that are beyond the native interactions of the system. Specifically, this approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin-1/2 XYZ chains, but generalized to include long-range couplings. Our work builds on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries. We show that determining the appropriate ‘program’ of unitary pulse sequences which implements an arbitrary Hamiltonian transformation can be formulated as a linear program over functions defined by those pulse sequences, running in polynomial time and scaling efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, representing an important and broad-based success in applying functional analysis to the field of quantum information.

  8. Redesign of the DFT/MRCI Hamiltonian

    NASA Astrophysics Data System (ADS)

    Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M.

    2016-01-01

    The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.

  9. Redesign of the DFT/MRCI Hamiltonian.

    PubMed

    Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M

    2016-01-21

    The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion. PMID:26801017

  10. Fractional Hamiltonian monodromy from a Gauss-Manin monodromy

    NASA Astrophysics Data System (ADS)

    Sugny, D.; Mardešić, P.; Pelletier, M.; Jebrane, A.; Jauslin, H. R.

    2008-04-01

    Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskií, and Zhilinskií, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); Nekhoroshev, Sadovskií, and Zhilinskií, Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m :-n resonant systems.

  11. Quasilocal Hamiltonians in general relativity

    SciTech Connect

    Anderson, Michael T.

    2010-10-15

    We analyze the definition of quasilocal energy in general relativity based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular, the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consistent definition of quasilocal energy in general relativity requires, at a minimum, a framework based on the (currently unknown) geometric well-posedness of the initial boundary value problem for the Einstein equations.

  12. Nonlocal Hamiltonian gauge theories and their connection with lattice Hamiltonians

    SciTech Connect

    Ktorides, C.N.; Mavromatos, N.E.

    1985-06-15

    We introduce the concept of primitive Hamiltonian density for nonlocal Abelian gauge theories. We subsequently study the local limit both with respect to the continuum and with respect to a lattice structure introduced via hypercubic cells. The non-Abelian case is also discussed.

  13. Frequency domain analysis and synthesis of lumped parameter systems using nonlinear least squares techniques

    NASA Technical Reports Server (NTRS)

    Hays, J. R.

    1969-01-01

    Lumped parametric system models are simplified and computationally advantageous in the frequency domain of linear systems. Nonlinear least squares computer program finds the least square best estimate for any number of parameters in an arbitrarily complicated model.

  14. State analysis of nonlinear systems using local canonical variate analysis

    SciTech Connect

    Hunter, N.F.

    1997-01-01

    There are many instances in which time series measurements are used to derive an empirical model of a dynamical system. State space reconstruction from time series measurement has applications in many scientific and engineering disciplines including structural engineering, biology, chemistry, climatology, control theory, and physics. Prediction of future time series values from empirical models was attempted as early as 1927 by Yule, who applied linear prediction methods to the sunspot values. More recently, efforts in this area have centered on two related aspects of time series analysis, namely prediction and modeling. In prediction future time series values are estimated from past values, in modeling, fundamental characteristics of the state model underlying the measurements are estimated, such as dimension and eigenvalues. In either approach a measured time series, [{bold y}(t{sub i})], i= 1,... N is assumed to derive from the action of a smooth dynamical system, s(t+{bold {tau}})=a(s(t)), where the bold notation indicates the (potentially ) multivariate nature of the time series. The time series is assumed to derive from the state evolution via a measurement function c. {bold y}(t)=c(s(t)) In general the states s(t), the state evolution function a and the measurement function c are In unknown, and must be inferred from the time series measurements. We approach this problem from the standpoint of time series analysis. We review the principles of state space reconstruction. The specific model formulation used in the local canonical variate analysis algorithm and a detailed description of the state space reconstruction algorithm are included. The application of the algorithm to a single-degree-of- freedom Duffing-like Oscillator and the difficulties involved in reconstruction of an unmeasured degree of freedom in a four degree of freedom nonlinear oscillator are presented. The advantages and current limitations of state space reconstruction are summarized.

  15. A method for zooming of nonlinear models of biochemical systems

    PubMed Central

    2011-01-01

    Background Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model. Results In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved. Conclusions We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to

  16. A nonlinear lumped model for ultrasound systems using CMUT arrays.

    PubMed

    Satir, Sarp; Degertekin, F Levent

    2015-10-01

    We present a nonlinear lumped model that predicts the electrical input-output behavior of an ultrasonic system using CMUTs with arbitrary array/membrane/electrode geometry in different transmit-receive configurations and drive signals. The receive-only operation, where the electrical output signal of the CMUT array in response to incident pressure field is calculated, is included by modifying the boundary elementbased vibroacoustic formulation for a CMUT array in rigid baffle. Along with the accurate large signal transmit model, this formulation covers pitch-catch and pulse-echo operation when transmit and receive signals can be separated in time. In cases when this separation is not valid, such as CMUTs used in continuous wave transmit-receive mode, pulse-echo mode with a nearby hard or soft wall or in a bounded space such as in a microfluidic channel, an efficient formulation based on the method of images is used. Some of these particular applications and the overall modeling approach have been validated through comparison with finite element analysis on specific examples including CMUTs with multiple electrodes. To further demonstrate the capability of the model for imaging applications, the two-way response of a partial dual-ring intravascular ultrasound array is simulated using a parallel computing cluster, where the output currents of individual array elements are calculated for given input pulse and compared with experimental results. With its versatility, the presented model can be a useful tool for rapid iterative CMUT-based system design and simulation for a broad range of ultrasonic applications. PMID:26470049

  17. Ground states of nonlinear Schrödinger systems with saturable nonlinearity in R{sup 2} for two counterpropagating beams

    SciTech Connect

    Lin, Tai-Chia; Belić, Milivoj R.; Petrović, Milan S.; Chen, Goong

    2014-01-15

    Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.

  18. A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input.

    PubMed

    Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip

    2016-01-01

    In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example. PMID:26353383

  19. Solution of the problem of uniqueness and Hermiticity of Hamiltonians for Dirac particles in gravitational fields

    SciTech Connect

    Gorbatenko, M. V.; Neznamov, V. P.

    2010-11-15

    The authors prove that the dynamics of spin 1/2 particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin 1/2 particles in the gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are nonunique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian. The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors. For description of the dynamics of spin 1/2 particles in stationary gravitational fields can be used not only the formalism of pseudo-Hermitian Hamiltonians but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.

  20. Asymptotic investigation of the nonlinear boundary value dynamic problem for the systems with finite sizes

    SciTech Connect

    Andrianov, I.V.; Danishevsky, V.V.

    1994-12-31

    Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions.

  1. Robust control of nonlinear flexible multibody systems using quaternion feedback and dissipative compensation

    NASA Technical Reports Server (NTRS)

    Kelkar, Atul G.; Joshi, Suresh M.

    1994-01-01

    Global asymptotic stability of a class of nonlinear multibody flexible space-stnuctures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore for the second case the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems including flexible space-structures with articulated flexible appendages.

  2. Robust control of nonlinear flexible multibody systems using quaternion feedback and dissipative compensation

    NASA Technical Reports Server (NTRS)

    Kelkar, Atul G.; Joshi, Suresh M.

    1994-01-01

    Global asymptotic stability of a class of nonlinear multibody flexible space structures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore, for the second case, the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems, including flexible space structures with articulated flexible appendages.

  3. Parametric and nonparametric nonlinear system identification of lung tissue strip mechanics.

    PubMed

    Yuan, H; Westwick, D T; Ingenito, E P; Lutchen, K R; Suki, B

    1999-01-01

    Lung parenchyma is a soft biological material composed of many interacting elements such as the interstitial cells, extracellular collagen-elastin fiber network, and proteoglycan ground substance. The mechanical behavior of this delicate structure is complex showing several mild but distinct types of nonlinearities and a fractal-like long memory stress relaxation characterized by a power-law function. To characterize tissue nonlinearity in the presence of such long memory, we investigated the robustness and predictive ability of several nonlinear system identification techniques on stress-strain data obtained from lung tissue strips with various input wave forms. We found that in general, for a mildly nonlinear system with long memory, a nonparametric nonlinear system identification in the frequency domain is preferred over time-domain techniques. More importantly, if a suitable parametric nonlinear model is available that captures the long memory of the system with only a few parameters, high predictive ability with substantially increased robustness can be achieved. The results provide evidence that the first-order kernel of the stress-strain relationship is consistent with a fractal-type long memory stress relaxation and the nonlinearity can be described as a Wiener-type nonlinear structure for displacements mimicking tidal breathing. PMID:10468239

  4. A nonlinear screen as an element for sound absorption and frequency conversion systems

    NASA Astrophysics Data System (ADS)

    Rudenko, O. V.

    2016-01-01

    The paper discusses a model for a screen with dissipative and nonlinear elastic properties that can be used in acoustic sound absorption and frequency conversion systems. Calculation and estimation schemes are explained that are necessary for understanding the functional capabilities of the device. Examples of the nonlinear elements in the screen and promising applications are described.

  5. On Schrödinger systems with cubic dissipative nonlinearities of derivative type

    NASA Astrophysics Data System (ADS)

    Li, Chunhua; Sunagawa, Hideaki

    2016-05-01

    Consider the initial value problem for systems of cubic derivative nonlinear Schrödinger equations in one space dimension with the masses satisfying a suitable resonance relation. We give structural conditions on the nonlinearity under which the small data solution gains an additional logarithmic decay as t\\to +∞ compared with the corresponding free evolution.

  6. Is DNA a nonlinear dynamical system where solitary conformational waves are possible?

    PubMed

    Yakushevich, L V

    2001-09-01

    DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA's nonlinear properties. PMID:11568475

  7. Implementation guide for MINPACK-1. [Package of Fortran subprograms for solution of systems of nonlinear equations

    SciTech Connect

    Garbow, B.S.; Hillstrom, K.E.; More, J.J.

    1980-07-01

    MINPACK-1 is a package of Fortran subprograms for the numerical solution of systems of nonlinear equations and nonlinear least-squares problems. This report describes how to implement the package from the tape on which it is transmitted. 3 tables.

  8. Extensive Adiabatic Invariants for Nonlinear Chains

    NASA Astrophysics Data System (ADS)

    Giorgilli, Antonio; Paleari, Simone; Penati, Tiziano

    2012-09-01

    We look for extensive adiabatic invariants in nonlinear chains in the thermodynamic limit. Considering the quadratic part of the Klein-Gordon Hamiltonian, by a linear change of variables we transform it into a sum of two parts in involution. At variance with the usual method of introducing normal modes, our constructive procedure allows us to exploit the complete resonance, while keeping the extensive nature of the system. Next we construct a nonlinear approximation of an extensive adiabatic invariant for a perturbation of the discrete nonlinear Schrödinger model. The fluctuations of this quantity are controlled via Gibbs measure estimates independent of the system size, for a large set of initial data at low specific energy. Finally, by numerical calculations we show that our adiabatic invariant is well conserved for times much longer than predicted by our first order theory, with fluctuation much smaller than expected according to standard statistical estimates.

  9. A Note on Hamiltonian Graphs

    ERIC Educational Resources Information Center

    Skurnick, Ronald; Davi, Charles; Skurnick, Mia

    2005-01-01

    Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

  10. Nonlinear gyrokinetic equations

    SciTech Connect

    Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.

    1983-03-01

    Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.

  11. MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD

    SciTech Connect

    K. HANSON

    2001-02-01

    The Markov Chain Monte Carlo technique provides a means for drawing random samples from a target probability density function (pdf). MCMC allows one to assess the uncertainties in a Bayesian analysis described by a numerically calculated posterior distribution. This paper describes the Hamiltonian MCMC technique in which a momentum variable is introduced for each parameter of the target pdf. In analogy to a physical system, a Hamiltonian H is defined as a kinetic energy involving the momenta plus a potential energy {var_phi}, where {var_phi} is minus the logarithm of the target pdf. Hamiltonian dynamics allows one to move along trajectories of constant H, taking large jumps in the parameter space with relatively few evaluations of {var_phi} and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. The efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs is shown to remain constant at around 7% for up to several hundred dimensions. The Hamiltonian method handles correlations among the variables much better than the standard Metropolis algorithm. A new test, based on the gradient of {var_phi}, is proposed to measure the convergence of the MCMC sequence.

  12. The peak response distributions of structure-DVA systems with nonlinear damping

    NASA Astrophysics Data System (ADS)

    Love, J. S.; Tait, M. J.

    2015-07-01

    Dynamic vibration absorbers (DVAs) with nonlinear damping are often modelled using a power-law equivalent viscous damping relationship. There is currently not a method available to predict the peak response of this type of nonlinear DVA without resorting to computationally expensive nonlinear simulations. Since the peak response of the DVA is required during the design process, it is advantageous to have a simplified method to estimate the peak response. In this study, statistical linearization is employed to represent the nonlinear damping as amplitude-dependent viscous damping and predict the rms response of the structure-DVA system. Subsequently, statistical nonlinearization is used to describe the probability density function of the DVA response amplitude. A probability density function is developed, which enables the peak response expected during an interval of time (e.g. 1-h) to be estimated from the rms response of the structure-DVA system. Higher power-law damping exponents are shown to result in smaller peak factors. Results of nonlinear simulations reveal that the model can estimate the peak structural and DVA responses with acceptable accuracy. A plot is developed to show the peak factors for nonlinear DVAs as a function of the number of system cycles for several power-law damping exponents. This plot can be used to estimate the peak response of a nonlinear DVA as a function of its rms response.

  13. Real time simulation of nonlinear generalized predictive control for wind energy conversion system with nonlinear observer.

    PubMed

    Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand

    2014-01-01

    In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller. PMID:24021543

  14. Discrete-time neural inverse optimal control for nonlinear systems via passivation.

    PubMed

    Ornelas-Tellez, Fernando; Sanchez, Edgar N; Loukianov, Alexander G

    2012-08-01

    This paper presents a discrete-time inverse optimal neural controller, which is constituted by combination of two techniques: 1) inverse optimal control to avoid solving the Hamilton-Jacobi-Bellman equation associated with nonlinear system optimal control and 2) on-line neural identification, using a recurrent neural network trained with an extended Kalman filter, in order to build a model of the assumed unknown nonlinear system. The inverse optimal controller is based on passivity theory. The applicability of the proposed approach is illustrated via simulations for an unstable nonlinear system and a planar robot. PMID:24807528

  15. Adaptive Neural Control of Nonaffine Systems With Unknown Control Coefficient and Nonsmooth Actuator Nonlinearities.

    PubMed

    Yang, Zaiyue; Yang, Qinmin; Sun, Youxian

    2015-08-01

    This brief considers the asymptotic tracking problem for a class of high-order nonaffine nonlinear dynamical systems with nonsmooth actuator nonlinearities. A novel transformation approach is proposed, which is able to systematically transfer the original nonaffine nonlinear system into an equivalent affine one. Then, to deal with the unknown dynamics and unknown control coefficient contained in the affine system, online approximator and Nussbaum gain techniques are utilized in the controller design. It is proven rigorously that asymptotic convergence of the tracking error and ultimate uniform boundedness of all the other signals can be guaranteed by the proposed control method. The control feasibility is further verified by numerical simulations. PMID:25265633

  16. Transitions to broad cells in a nonlinear thermal convection system

    NASA Astrophysics Data System (ADS)

    Fiedler, Brian H.

    This paper explores the properties of a two-dimensional, Boussinesq convection model with an ad hoc term in the buoyancy tendency equation that represents a positive external feedback process acting on the buoyancy fluctuations. Linear stability analyses and nonlinear integrations are presented for the case of constant heat flux boundary conditions. Although the large wavenumber modes grow the fastest from a state of rest, the nonlinear solutions progressively evolve to cells of small wavenumber. Applications to mesoscale cellular convection in the atmosphere are discussed.

  17. Correlation techniques to determine model form in robust nonlinear system realization/identification

    NASA Technical Reports Server (NTRS)

    Stry, Greselda I.; Mook, D. Joseph

    1991-01-01

    The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

  18. Analysis of start-up transient for a powertrain system with a nonlinear clutch damper

    NASA Astrophysics Data System (ADS)

    Li, Laihang; Singh, Rajendra

    2015-10-01

    The transient vibration phenomenon in a vehicle powertrain system during the start-up (or shut-down) process is studied with a focus on the nonlinear characteristics of a multi-staged clutch damper. First, a four-degree-of-freedom torsional model with multiple discontinuous nonlinearities under flywheel motion input is developed, and the powertrain transient event is validated with a vehicle start-up experiment. Second, the role of the nonlinear torsional path on the transient event is investigated in the time and time-frequency domains; interactions between the clutch damper and the transmission transients are estimated by using two metrics. Third, the harmonic balance method is applied to examine the nonlinear characteristics of clutch damper during a slowly varying non-stationary process in a simplified and validated single-degree-of-freedom powertrain system model. Finally, analytical formulas are successfully developed and verified to approximate the nonlinear amplification level for a rapidly varying process.

  19. Noise-induced transitions and resonant effects in nonlinear systems

    NASA Astrophysics Data System (ADS)

    Zaikin, Alexei

    2003-02-01

    Our every-day experience is connected with different acoustical noise or music. Usually noise plays the role of nuisance in any communication and destroys any order in a system. Similar optical effects are known: strong snowing or raining decreases quality of a vision. In contrast to these situations noisy stimuli can also play a positive constructive role, e.g. a driver can be more concentrated in a presence of quiet music. Transmission processes in neural systems are of especial interest from this point of view: excitation or information will be transmitted only in the case if a signal overcomes a threshold. Dr. Alexei Zaikin from the Potsdam University studies noise-induced phenomena in nonlinear systems from a theoretical point of view. Especially he is interested in the processes, in which noise influences the behaviour of a system twice: if the intensity of noise is over a threshold, it induces some regular structure that will be synchronized with the behaviour of neighbour elements. To obtain such a system with a threshold one needs one more noise source. Dr. Zaikin has analyzed further examples of such doubly stochastic effects and developed a concept of these new phenomena. These theoretical findings are important, because such processes can play a crucial role in neurophysics, technical communication devices and living sciences. Unsere alltägliche Erfahrung ist mit verschiedenen akustischen Einfluessen wie Lärm, aber auch Musik verbunden. Jeder weiss, wie Lärm stören kann und Kommunikation behindert oder gar unterbindet. Ähnliche optische Effekte sind bekannt: starkes Schneetreiben oder Regengüsse verschlechtern die Sicht und lassen uns Umrisse nur noch schemenhaft erkennen. Jedoch koennen ähnliche Stimuli auch sehr positive Auswirkungen haben: Autofahrer fahren bei leiser Musik konzentrierter -- die Behauptung von Schulkindern, nur bei dröhnenden Bässen die Mathehausaufgaben richtig rechnen zu können, ist allerdings nicht wissenschaftlich

  20. Teaching and Learning the Interplay Between Chance and Determinism in Nonlinear Systems

    NASA Astrophysics Data System (ADS)

    Stavrou, Dimitrios; Duit, Reinders

    2014-02-01

    That the interplay of random and deterministic processes may result in both the limited predictability of nonlinear systems and the formation of structures seems to be a most valuable general insight into the nature of science. This study investigates the possibility of teaching and learning the interplay of chance and determinism in nonlinear systems in school science instruction. An analysis of the relevant scientific literature and an explorative learning process study with 30 11th-grade students are included. Three experiments displaying the behaviour of nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment demonstrating the behaviour of linear systems were discussed using a teaching experiment design. The findings show that although the majority of students initially considered chance and determinism as contradictory conceptions, they finally developed sound explanations concerning the interplay of chance and determinism in the investigated nonlinear systems.