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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. Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator

    SciTech Connect

    Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

    2009-05-15

    In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+{alpha}xx+{beta}x{sup 3}+{gamma}x=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+{alpha}x{sup q}x+{beta}x{sup 2q+1}=0, where {alpha}, {beta}, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.

  3. 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.

  4. Invariant metrics for Hamiltonian systems

    SciTech Connect

    Rangarajan, G. ); Dragt, A.J. ); Neri, F. )

    1991-05-01

    In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs.

  5. Fourier series expansion for nonlinear Hamiltonian oscillators.

    PubMed

    Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac

    2010-06-01

    The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate. PMID:20866495

  6. Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Tsallis, Constantino; Rapisarda, Andrea; Latora, Vito; Baldovin, Fulvio

    We present a brief pedagogical guided tour of the most recent applications of non-extensive statistical mechanics to well defined nonlinear dynamical systems, ranging from one-dimensional dissipative maps to many-body Hamiltonian systems.

  7. Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems.

    PubMed

    Custódio, M S; Manchein, C; Beims, M W

    2012-06-01

    The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions (ICs) and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and four particles globally coupled on a discrete lattice, we show that in these models, the transition from integrable motion to weak chaos emerges via chaotic stripes as the nonlinear parameter is increased. The stripes represent intervals of initial conditions which generate chaotic trajectories and increase with the nonlinear parameter of the system. In the billiard case, the initial conditions are the injection angles. For higher-dimensional systems and small nonlinearities, the chaotic stripes are the initial condition inside which Arnold diffusion occurs.

  8. 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.

  9. Persistence of hyperbolic tori in Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Li, Yong; Yi, Yingfei

    We generalize the well-known result of Graff and Zehnder on the persistence of hyperbolic invariant tori in Hamiltonian systems by considering non-Floquet, frequency varying normal forms and allowing the degeneracy of the unperturbed frequencies. The preservation of part or full frequency components associated to the degree of non-degeneracy is considered. As applications, we consider the persistence problem of hyperbolic tori on a submanifold of a nearly integrable Hamiltonian system and the persistence problem of a fixed invariant hyperbolic torus in a non-integrable Hamiltonian system.

  10. 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

  11. 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.

  12. 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

  13. 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.

  14. 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).

  15. 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.

  16. 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.

  17. 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.

  18. Hyperbolic tori in Hamiltonian systems with slowly varying parameter

    SciTech Connect

    Medvedev, Anton G

    2013-05-31

    This paper looks at a Hamiltonian system which depends periodically on a parameter. For each value of the parameter the system is assumed to have a hyperbolic periodic solution. Using the methods in KAM-theory it is proved that if the Hamiltonian is perturbed so that the value of the parameter varies with constant small frequency, then the nonautonomous system will have hyperbolic 2-tori in the extended phase space. Bibliography: 12 titles.

  19. 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.

  20. 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.

  1. Nonlinear Systems.

    ERIC Educational Resources Information Center

    Seider, Warren D.; Ungar, Lyle H.

    1987-01-01

    Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…

  2. Discrete Dirac Structures and Implicit Discrete Lagrangian and Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Leok, Melvin; Ohsawa, Tomoki

    2010-07-01

    We present discrete analogues of Dirac structures and the Tulczyjew's triple by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete analogues of implicit Lagrangian and Hamiltonian systems. In particular, this yields implicit nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. In addition to providing a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of Dirac mechanics, it provides a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators.

  3. Acoustic ray chaos and billiard system in Hamiltonian formalism (L)

    NASA Astrophysics Data System (ADS)

    Kawabe, Tetsuji; Aono, Keisuke; Shin-Ya, Masakazu

    2003-02-01

    The acoustic ray model with a strong connection to the billiard problem is presented within the framework of the Hamiltonian form. Introducing the background function into the sound-speed profile to confine all rays in a closed space, we obtain the ray trajectories consistent with a billiard picture. The ray chaos is observed when the perturbation due to inhomogeneity of the medium is taken into account. Based on the Poincaré surface of section and the Lyapunov exponents, we confirm that the chaos is characterized by almost the same structure as one observed in many Hamiltonian systems with two degrees of freedom.

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. Finite-time thermodynamics of port-Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Delvenne, Jean-Charles; Sandberg, Henrik

    2014-01-01

    In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second Laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell’s demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.

  12. 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.

  13. RG-Whitham dynamics and complex Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Gorsky, A.; Milekhin, A.

    2015-06-01

    Inspired by the Seiberg-Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG)-like Whitham behavior. We show that at the Argyres-Douglas (AD) point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne-Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.

  14. 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

  15. Path-integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems

    NASA Astrophysics Data System (ADS)

    Barth, A. M.; Vagov, A.; Axt, V. M.

    2016-09-01

    We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.

  16. Fluctuation theorem for Hamiltonian systems: Le Chatelier's principle.

    PubMed

    Evans, D J; Searles, D J; Mittag, E

    2001-05-01

    For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields. PMID:11414885

  17. Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

    NASA Astrophysics Data System (ADS)

    Evans, Denis J.; Searles, Debra J.; Mittag, Emil

    2001-05-01

    For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. The falling cat as a port-controlled Hamiltonian system

    NASA Astrophysics Data System (ADS)

    Iwai, Toshihiro; Matsunaka, Hiroki

    2012-02-01

    In this article, the falling cat is modeled as two jointed axial symmetric cylinders with arbitrary twist under the constraint of the vanishing total angular momentum. As a control system with the constraint taken into account, this model is formulated as a port-controlled Hamiltonian system defined on the cotangent bundle of the shape space for the jointed cylinders. A control is then designed as a function on the cotangent bundle, according to a standard procedure. Thus, the equations of motion are determined on the cotangent bundle together with the control. The whole motion as a vibrational motion of the falling cat is obtained after integrating the constraint equation of the vanishing total angular momentum. An example of the falling cat is given in which the model turns a somersault to approach a target state in equilibrium with an expected rotation after finishing a vibrational motion.

  3. 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

  4. 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.

  5. Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree - 3

    NASA Astrophysics Data System (ADS)

    Llibre, Jaume; Mahdi, Adam; Valls, Claudia

    2011-12-01

    In this paper, we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k=-2,-1,…,3,4, their polynomial integrability has been characterized. Here, we have two main results. First, we characterize the polynomial integrability of those Hamiltonian systems with homogeneous potential of degree -3. Second, we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian systems with homogeneous polynomial potentials. Finally, we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential.

  6. Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

    SciTech Connect

    Kaneko, Yuta; Yoshida, Zensho

    2014-03-15

    Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term −ΔQ, just representing the current density (Q is a Clebsch variable, and Δ is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the action variable P that is conjugate to Q. By numerical simulation, the predicted behavior of the canonical variables, yielding exponential growth of current sheets, has been demonstrated.

  7. 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.

  8. Phase Mixing in Unperturbed and Perturbed Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Kandrup, Henry E.; Novotny, Steven J.

    2004-01-01

    This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic driving, friction, and/or white and coloured noise. The evolution of initially localised ensembles of orbits was probed through lower order moments and coarse-grained distribution functions. In the absence of time-dependent perturbations, regular ensembles disperse initially as a power law in time and only exhibit a coarse-grained approach towards an invariant equilibrium over comparatively long times. Chaotic ensembles generally diverge exponentially fast on a time scale related to a typical finite time Lyapunov exponent, but can exhibit complex behaviour if they are impacted by the effects of cantori or the Arnold web. Viewed over somewhat longer times, chaotic ensembles typical converge exponentially towards an invariant or near-invariant equilibrium. This, however, need not correspond to a true equilibrium, which may only be approached over very long time scales. Time-dependent perturbations can dramatically increase the efficiency of phase mixing, both by accelerating the approach towards a near-equilibrium and by facilitating diffusion through cantori or along the Arnold web so as to accelerate the approach towards a true equilibrium. The efficacy of such perturbations typically scales logarithmically in amplitude, but is comparatively insensitive to most other details, a conclusion which reinforces the interpretation that the perturbations act via a resonant coupling.

  9. 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.

  10. 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.

  11. On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Giles, W.; Lamb, J. S. W.; Turaev, D.

    2016-10-01

    We consider a Hamiltonian system which has an elliptic-hyperbolic equilibrium with a homoclinic loop. We identify the set of orbits which are homoclinic to the center manifold of the equilibrium via a Lyapunov-Schmidt reduction procedure. This leads to the study of a singularity which inherits a certain structure from the Hamiltonian nature of the system. Under non-degeneracy assumptions, we classify the possible Morse indices of this singularity, permitting a local description of the set of homoclinic orbits. We also consider the case of time-reversible Hamiltonian systems.

  12. 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.

  13. 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.

  14. Generalized coherent states for time-dependent and nonlinear Hamiltonian operators via complex Riccati equations

    NASA Astrophysics Data System (ADS)

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

    2013-02-01

    Based on the Gaussian wave packet solution for the harmonic oscillator and the corresponding creation and annihilation operators, a generalization is presented that also applies for wave packets with time-dependent width as they occur for systems with different initial conditions, time-dependent frequency or in contact with a dissipative environment. In all these cases, the corresponding coherent states, position and momentum uncertainties and quantum mechanical energy contributions can be obtained in the same form if the creation and annihilation operators are expressed in terms of a complex variable that fulfils a nonlinear Riccati equation which determines the time-evolution of the wave packet width. The solutions of this Riccati equation depend on the physical system under consideration and on the (complex) initial conditions and have close formal similarities with general superpotentials leading to isospectral potentials in supersymmetric quantum mechanics. The definition of the generalized creation and annihilation operator is also in agreement with a factorization of the operator corresponding to the Ermakov invariant that exists in all cases considered.

  15. Non-integrable character of Hamiltonian systems with global and symmetric coupling

    NASA Astrophysics Data System (ADS)

    Umeno, Ken

    A new sufficient condition to prove non-integrability of Hamiltonian systems with symmetric variational equations is proposed. Though the present condition is taken as an extension of Ziglin and Yoshida's “non-resonant condition”, the algorithmic bottle-neck proving non-integrability in high dimensional cases can be removed here. As a result, the non-existence of additional integrals of various symmetric Hamiltonian systems with an arbitrary number of degrees of freedom is proven.

  16. 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.

  17. Hamiltonian purification

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

    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 {h1, …, hm} operating on a d-dimensional quantum system ℋd, the problem consists in identifying a set of commuting Hamiltonians {H1, …, Hm} operating on a larger dE-dimensional system ℋdE which embeds ℋd as a proper subspace, such that hj = PHjP with P being the projection which allows one to recover ℋd from ℋdE. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for 𝔲(d) are provided.

  18. 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.

  19. 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 → ∞.

  20. 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.

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

    PubMed

    Okuyama, Manaka; Takahashi, Kazutaka

    2016-08-12

    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 XY spin chains from the Toda equations are studied in detail.

  2. 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.

  3. Lie algebraic similarity transformed Hamiltonians for lattice model systems

    NASA Astrophysics Data System (ADS)

    Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.

    2015-01-01

    We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.

  4. 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.

  5. 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.

  6. Guidance of Nonlinear Systems

    NASA Technical Reports Server (NTRS)

    Meyer, George; Null, Cynthia H. (Technical Monitor)

    1996-01-01

    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 coordination, 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

    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.

  8. 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.

  9. Hamiltonian dynamics of spatially-homogeneous Vlasov-Einstein systems

    NASA Astrophysics Data System (ADS)

    Okabe, Takahide; Morrison, P. J.; Friedrichsen, J. E., III; Shepley, L. C.

    2011-07-01

    We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in general relativity. The Bianchi models are spatially-homogeneous solutions to the Einstein field equations, classified by the three-dimensional Lie algebra that describes the symmetry group of the model. The Einstein equations for these models reduce to a set of coupled ordinary differential equations. The class A Bianchi models admit a Hamiltonian formulation in which the components of the metric tensor and their time derivatives yield the canonical coordinates. The evolution of anisotropy in the vacuum Bianchi models is determined by a potential due to the curvature of the model, according to its symmetry. For illustrative purposes, we examine the evolution of anisotropy in models with Vlasov matter. The Vlasov content is further simplified by the assumption of cold, counter-streaming matter, a kind of matter that is far from thermal equilibrium and is not describable by an ordinary fluid model nor other more simplistic matter models. Qualitative differences and similarities are found in the dynamics of certain vacuum class A Bianchi models and Bianchi type I models with cold, counter-streaming Vlasov-matter potentials analogous to the curvature potentials of corresponding vacuum models.

  10. Error bounds via a new variational principle for classical Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Djukic, Dj. S.; Atanackovic, T. M.

    An extremum variational principle for clasical Hamiltonian systems (Djukic and Atanackovic, 1984) is used to estimate the error of the approximate solution for a mechanical system with one degree of freedom. The procedure is developed separately for two-point boundary-value problems and for Cauchy problems. Finally, the theory is illustrated by two concrete problems.

  11. Scaling and Locality properties of the Entanglement Hamiltonian in Critical Fermionic systems

    NASA Astrophysics Data System (ADS)

    Lanata, Nicola; Yao, Yong-Xin; Deng, Xiaoyu; Pouranvari, Mohammad

    We study the entanglement Hamiltonian of several gapless Fermionic systems. In particular, we consider an infinite metallic one dimensional chain of free Fermions, and show that the corresponding entanglement Hamiltonian F (L) for a subsystem of length L is local. Furthermore, we show that F (L) displays a well defined continuum limit, which is related with the so called logarithmically enhanced area law of the entanglement entropy, S (L) ~ log (L) . Finally, using the ``Gutzwiller renormalization group'' [arXiv:1509.05441], we discuss these concepts in relation with the physics of the Anderson impurity model.

  12. 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.

  13. Non-integrability of a class of Painlevé IV equations as Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Shi, Shaoyun; Li, Wenlei

    2013-10-01

    In this paper, we will prove the rational non-integrability of a class of Hamiltonian systems associated with Painlevé IV equation by using Morales-Ramis theory and Kovacic's algorithm, which, to some extent, also implies the non-integrability of the fourth Painlevé equation itself.

  14. 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.

  15. 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.

  16. Topological classification of integrable Hamiltonian systems in a potential field on surfaces of revolution

    NASA Astrophysics Data System (ADS)

    Kantonistova, E. O.

    2016-03-01

    A topological classification, up to Liouville (leafwise) equivalence of integrable Hamiltonian systems given by flows with a smooth potential on two-dimensional surfaces of revolution is presented. It is shown that the restrictions of such systems to three-dimensional isoenergy surfaces can be modelled by the geodesic flows (without potential) of certain surfaces of revolution. It is also shown that in many important cases the systems under consideration are equivalent to other well-known mechanical systems. Bibliography: 29 titles.

  17. Forward Period Analysis Method of the Periodic Hamiltonian System

    PubMed Central

    Wang, Pengfei

    2016-01-01

    Using the forward period analysis (FPA), we obtain the period of a Morse oscillator and mathematical pendulum system, with the accuracy of 100 significant digits. From these results, the long-term [0, 1060] (time unit) solutions, ranging from the Planck time to the age of the universe, are computed reliably and quickly with a parallel multiple-precision Taylor series (PMT) scheme. The application of FPA to periodic systems can greatly reduce the computation time of long-term reliable simulations. This scheme provides an efficient way to generate reference solutions, against which long-term simulations using other schemes can be tested. PMID:27727295

  18. 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.

  19. Inhibition of chaos in Hamiltonian systems by periodic pulses

    NASA Astrophysics Data System (ADS)

    Chacón, Ricardo

    1994-08-01

    It is shown that, depending on their amplitude, period, shape, and initial phase, a time-dependent periodic string of external driving pulses can suppress classical deterministic stochasticity. The analysis is based on a coupled pendulum-harmonic-oscillator system. Similar results are obtained by studying the behavior of the Lyapunov exponent from a simple recursion relation which models an unstable limit cycle affected by a periodic string of pulses.

  20. Macroscopic diffusive transport in a microscopically integrable Hamiltonian system.

    PubMed

    Prosen, Tomaž; Zunkovič, Bojan

    2013-07-26

    We demonstrate that a completely integrable classical mechanical model, namely the lattice Landau-Lifshitz classical spin chain, supports diffusive spin transport with a finite diffusion constant in the easy-axis regime, while in the easy-plane regime, it displays ballistic transport in the absence of any known relevant local or quasilocal constant of motion in the symmetry sector of the spin current. This surprising finding should open the way towards analytical computation of diffusion constants for integrable interacting systems and hints on the existence of new quasilocal classical conservation laws beyond the standard soliton theory.

  1. 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.

  2. Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

    PubMed

    Miller, Michael I; Trouvé, Alain; Younes, Laurent

    2015-01-01

    The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

  3. Kolmogorov-Sinai entropy of many-body Hamiltonian systems.

    PubMed

    Lakshminarayan, Arul; Tomsovic, Steven

    2011-07-01

    The Kolmogorov-Sinai (KS) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering N-dimensional symplectic maps and deriving a transfer matrix formalism for the stability problem. This approach makes explicit a duality relation that is exactly analogous to one found in a generalized Anderson tight-binding model and leads to a formally exact expression for the finite-time KS entropy. Within this formalism there is a hierarchy of approximations, the final one being a diagonal approximation that only makes use of instantaneous Hessians of the potential to find the KS entropy. By way of a nontrivial illustration, the KS entropy of N identically coupled kicked rotors (standard maps) is investigated. The validity of the various approximations with kicking strength, particle number, and time are elucidated. An analytic formula for the KS entropy within the diagonal approximation is derived and its range of validity is also explored.

  4. Charge transfer in strongly correlated systems: An exact diagonalization approach to model Hamiltonians

    SciTech Connect

    Schöppach, Andreas; Gnandt, David; Koslowski, Thorsten

    2014-04-07

    We study charge transfer in bridged di- and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific Mott-Hubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the Hartree-Fock mean field theory overestimates both the activation barrier and the magnitude of charge-transfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths.

  5. 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.

  6. 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.

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

    PubMed

    Okuyama, Manaka; Takahashi, Kazutaka

    2016-08-12

    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 XY spin chains from the Toda equations are studied in detail. PMID:27563938

  8. 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.

  9. Weak Ergodicity Breaking and Aging of Chaotic Transport in Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Albers, Tony; Radons, Günter

    2014-10-01

    Momentum diffusion is a widespread phenomenon in generic Hamiltonian systems. We show for the prototypical standard map that this implies weak ergodicity breaking for the superdiffusive transport in coordinate direction with an averaging-dependent quadratic and cubic increase of the mean-squared displacement (MSD), respectively. This is explained via integrated Brownian motion, for which we derive aging time dependent expressions for the ensemble-averaged MSD, the distribution of time-averaged MSDs, and the ergodicity breaking parameter. Generalizations to other systems showing momentum diffusion are pointed out.

  10. 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. __________________________________________________

  11. 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

  12. Hamiltonian systems with detuned 1:1:2 resonance: Manifestation of bidromy

    SciTech Connect

    Sadovskii, D.A.; Zhilinskii, B.I. . E-mail: zhilin@univ-littoral.fr

    2007-01-15

    We consider a generalization of the 1:1:2 resonant swing-spring [see H. Dullin, A. Giacobbe, R.H. Cushman, Physica D 190 (2004) 15] which is suggested both by the symmetries of this system and by its physical and in particular molecular realizations [see R.H. Cushman, H.R. Dullin, A. Giacobbe, D.D. Holm, M. Joyeux, P. Lynch, D.A. Sadovskii, B.I. Zhilinskii, Phys. Rev. Lett. 93 (2004) 024302-1-024302-4]. Our generic integrable system is detuned off the exact Fermi resonance 1:2. The three-dimensional (3D) image of its energy-momentum map EM consists either of two or three qualitatively different non-intersecting 3D regions: a regular region at low vibrational excitation, a region with monodromy similar to that studied for the exact resonance, and in some cases-an intermediate region in which the 3D set of regular values of EM is partially self-overlapping while remaining connected. In the presence of this latter region, the system has an interesting property which we called bidromy. We analyze monodromy and bidromy for a concrete integrable classical Hamiltonian system of three coupled oscillators and for its quantum analog. We also show that the bifurcation involved in the transition from the regular region to the region with monodromy can be regarded as a special resonant equivariant analog of the Hamiltonian Hopf bifurcation.

  13. Topics in complex nonlinear systems

    NASA Astrophysics Data System (ADS)

    Ying, Linghang

    In the dissertation, I include two topics of my research in nonlinear dynamic systems. In the first topic, we use numerical optimization techniques to investigate the behavior of the success rates for two- and three-qubit entangling gates, first for perfect fidelity, and then extended to imperfect gates. We find that as the perfect fidelity condition is relaxed, the maximum attainable success rates increase in a predictable fashion depending on the size of the system, and we compare that rate of increase for several gates. Finally, we propose an experiment to test our imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing. In the second topic, we quantitatively study nonlinear effects on the evolution of surface gravity waves on the ocean, to explore systematically the effects of various input parameters on the probability of rogue wave formation. The fourth-order current-modified nonlinear Schrodinger equation (CNLS4) is employed to describe the wave evolution. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single "freak index" parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Then, we obtain quantitative predictions for the wave height distribution as a

  14. 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.

  15. Linear-optical simulation of the cooling of a cluster-state Hamiltonian system.

    PubMed

    Aguilar, G H; Kolb, T; Cavalcanti, D; Aolita, L; Chaves, R; Walborn, S P; Souto Ribeiro, P H

    2014-04-25

    A measurement-based quantum computer could consist of a local-gapped Hamiltonian system, whose thermal states-at sufficiently low temperature-are universal resources for the computation. Initialization of the computer would correspond to cooling the system. We perform an experimental quantum simulation of such a cooling process with entangled photons. We prepare three-qubit thermal cluster states exploiting the equivalence between local dephasing and thermalization for these states. This allows us to tune the system's temperature by changing the dephasing strength. We monitor the entanglement as the system cools down and observe the transitions from separability to bound entanglement, and then to free entanglement. We also analyze the performance of the system for measurement-based single-qubit state preparation. These studies constitute a basic characterization of experimental cluster-state computation under imperfect conditions.

  16. 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.

  17. 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).

  18. 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.

  19. 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.

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

    PubMed

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

  1. Peeling the onion of order and chaos in a high-dimensional Hamiltonian system

    NASA Astrophysics Data System (ADS)

    Kaneko, Kunihiko; Konishi, Tetsuro

    1994-02-01

    Coexistence of various ordered chaotic states in a Hamiltonian system is studied with the use of a symplectic coupled map lattice. Besides the clustered states for the attractive interaction, a novel chaotic ordered state is found for a system with repulsive interaction, characterized by a dispersed state of particles. The dispersed and clustered states form an onion-like structure in phase space. The degree of order increases towards the center of the onion, while chaos is enhanced at the edge between ordered and random chaotic states. For a longer time scale, orbits itinerate over ordered and random states. The existence of these ordered states leads to anomalous long-time correlation for many quantifiers such as the global diffusion.

  2. 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.

  3. 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.

  4. Hamiltonian Structure of the Schrödinger Classical Dynamical System

    NASA Astrophysics Data System (ADS)

    Tessarotto, Massimo; Mond, Michael; Batic, Davide

    2016-09-01

    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.

  5. 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.

  6. Numerical verification of the steepness of three and four degrees of freedom Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Schirinzi, Gabriella; Guzzo, Massimiliano

    2015-01-01

    We describe a new algorithm for the numerical verification of steepness, a necessary property for the application of Nekhoroshev's theorem, of functions of three and four variables. Specifically, by analyzing the Taylor expansion of order four, the algorithm analyzes the steepness of functions whose Taylor expansion of order three is not steep. In this way, we provide numerical evidence of steepness of the Birkhoff normal form around the Lagrangian equilibrium points L4-L5 of the spatial restricted three-body problem (for the only value of the reduced mass for which the Nekhoroshev stability was still unknown), and of the four-degrees-of-freedom Hamiltonian system obtained from the Fermi-Pasta-Ulam problem by setting the number of particles equal to four.

  7. 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.

  8. Tagged Particle Diffusion in One-Dimensional Systems with Hamiltonian Dynamics-II

    NASA Astrophysics Data System (ADS)

    Roy, Anjan; Dhar, Abhishek; Narayan, Onuttom; Sabhapandit, Sanjib

    2015-07-01

    We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal distribution. The correlation functions are studied in finite systems, and their forms examined at short and long times. Various one-dimensional systems are studied. Results of numerical simulations for the Fermi-Pasta-Ulam chain are qualitatively similar to results for the harmonic chain, and agree unexpectedly well with a simple description in terms of linearized equations for damped fluctuating sound waves. Simulation results for the alternate mass hard particle gas reveal that—in contradiction to our earlier results (Roy et al. in J Stat Phys 150(5):851-866, 2013) with smaller system sizes—the diffusion constant slowly converges to a constant value, in a manner consistent with mode coupling theories. Our simulations also show that the behaviour of the Lennard-Jones gas depends on its density. At low densities, it behaves like a hard-particle gas, and at high densities like an anharmonic chain. In all the systems studied, the tagged particle was found to show normal diffusion asymptotically, with convergence times depending on the system under study. Finite size effects show up at time scales larger than sound traversal times, their nature being system-specific.

  9. Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances

    SciTech Connect

    Miroshnichenko, Andrey E.; Kivshar, Yuri S.; Malomed, Boris A.

    2011-07-15

    We consider a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (in other words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear PT-symmetric dimer generates previously unexplored types of nonlinear Fano resonances, with completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically induced transparency. The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

    PubMed Central

    Du, Jiajia

    2014-01-01

    The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results. PMID:24592160

  15. 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.

  16. Stochastic surrogate Hamiltonian

    SciTech Connect

    Katz, Gil; Kosloff, Ronnie; Gelman, David; Ratner, Mark A.

    2008-07-21

    The surrogate Hamiltonian is a general scheme to simulate the many body quantum dynamics composed of a primary system coupled to a bath. The method has been based on a representative bath Hamiltonian composed of two-level systems that is able to mimic the true system-bath dynamics up to a prespecified time. The original surrogate Hamiltonian method is limited to short time dynamics since the size of the Hilbert space required to obtain convergence grows exponentially with time. By randomly swapping bath modes with a secondary thermal reservoir, the method can simulate quantum dynamics of the primary system from short times to thermal equilibrium. By averaging a small number of realizations converged values of the system observables are obtained avoiding the exponential increase in resources. The method is demonstrated for the equilibration of a molecular oscillator with a thermal bath.

  17. On an application of the intermediate Hamiltonian method for molecular systems

    SciTech Connect

    Seto, R.; Stankevich, I.V.

    1999-04-01

    An application of the intermediate Hamiltonian method is reported in estimation of the lower bounds to the potential energy curve of the hydrogen molecule ion. An improvement of the method and its limitation are also discussed.

  18. Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space.

    PubMed

    Altmann, Eduardo G; Motter, Adilson E; Kantz, Holger

    2006-02-01

    We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with nonhierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one-parameter families of marginally unstable periodic orbits and is characterized by an exponent gamma=2 for the asymptotic power-law decay of the distribution of recurrence times. Generic perturbations lead to systems with hierarchical phase space, where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and Cantori. In this case, we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power laws, depending on the relative contribution of the primary and secondary structures of the hierarchy. Numerical verification of our main results are provided for area-preserving maps, mushroom billiards, and the newly defined magnetic mushroom billiards. PMID:16605429

  19. 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.

  20. Dynamical and Hamiltonian Formulation of General Relativity

    NASA Astrophysics Data System (ADS)

    Giulini, Domenico

    Einstein's theory of General Relativity describes spacetime as a solution of a set of non-linear partial differential equations. These equations are initially not in the form of evolution equations and it is hence not clear how to formulate and solve initial-value problems, as would be physically highly desirable. In this contribution it will be shown how to cast Einstein's equations into the form of a constrained Hamiltonian system. This will allow to formulate and solve initial-value problems, integrate Einstein's equations by numerical codes, characterize dynamical degrees of freedom, and characterize isolated systems and their conserved quantities, like energy, momentum, and angular momentum. Moreover, this reformulation of General Relativity is also the starting point for various attempts to subject the gravitational field to the program of canonical quantization. The exposition given here is, to some degree, self contained. It attempts to comprehensively account for all the relevant geometric constructions, including the relevant symplectic geometry of constrained Hamiltonian systems.

  1. 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.

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

    PubMed

    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 ε0=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. PMID:26382486

  3. 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)

  4. Nonlinear Mode-Coupling in Nanomechanical Systems

    PubMed Central

    Matheny, M. H.; Villanueva, L. G.; Karabalin, R. B.; Sader, J. E.; Roukes, M. L.

    2013-01-01

    Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced nanomechanical devices; it has important implications for applications ranging from quantitative sensing to fundamental research. However, achieving accurate experimental characterization of nonlinearities in nanomechanical systems (NEMS) is problematic. Currently employed detection and actuation schemes themselves tend to be highly nonlinear, and this unrelated nonlinear response has been inadvertently convolved into many previous measurements. In this Letter we describe an experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities. By comparing predictions from Euler–Bernoulli theory for the intra- and intermodal nonlinearities of a doubly clamped beam, we assess the validity of our approach and find excellent agreement. PMID:23496001

  5. Nonlinear Dynamics of Parametrically Excited Gyroscopic Systems

    SciTech Connect

    Namachchivaya. N.S.

    2001-06-01

    The primary objective of this project is to determine how some of the powerful geometric methods of dynamical systems can be applied to study nonlinear gyroscopic systems. We proposed to develop techniques to predict local and global behavior and instability mechanisms and to analyze the interactions between noise, stability, and nonlinearities inherent in gyroscopic systems. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools.

  6. 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.

  7. On controllability of nonlinear stochastic systems

    NASA Astrophysics Data System (ADS)

    Sakthivel, R.; Kim, J.-H.; Mahmudov, N. I.

    2006-12-01

    In this paper, complete controllability for nonlinear stochastic systems is studied. First this paper addresses the problem of complete controllability of nonlinear stochastic systems with standard Brownian motion. Then this result is extended to establish complete controllability criterion for stochastic systems with fractional Brownian motion. A fixed point approach is employed for achieving the required result. The solutions are given by a variation of constants formula which allows us to study the complete controllability for nonlinear stochastic systems. In this paper, we prove the complete controllability of nonlinear stochastic system under the natural assumption that the associated linear control system is completely controllable. Finally, an illustrative example is provided to show the usefulness of the proposed technique.

  8. 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.

  9. Unitary quantum evolution for time-dependent quasi-Hermitian systems with nonobservable Hamiltonians

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Moussa, Miled H. Y.

    2016-04-01

    It has been argued that it is incompatible to maintain unitary time evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time dependent. We demonstrate here that the time-dependent Dyson equation and the time-dependent quasi-Hermiticity relation can be solved consistently in such a scenario for a time-dependent Dyson map and time-dependent metric operator, respectively. These solutions are obtained at the cost of rendering the non-Hermitian Hamiltonian to be a nonobservable operator as it ceases to be quasi-Hermitian when the metric becomes time dependent.

  10. 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.

  11. Darboux points and integrability analysis of Hamiltonian systems with homogeneous rational potentials

    NASA Astrophysics Data System (ADS)

    Studziński, Michał; Przybylska, Maria

    2013-04-01

    We study integrability in the Liouville sense for natural Hamiltonian systems with a homogeneous rational potential V(q). Strong necessary conditions for the integrability of such systems were obtained by analysis of differential Galois groups of variational equations along certain particular solutions. These conditions have the form of arithmetic restrictions on eigenvalues of the Hessians V″(d) calculated at non-zero solutions d of the equation gradV(d)=d. Such solutions are called proper Darboux points. It was recently proved that for generic polynomial homogeneous potentials, there exist universal relations between eigenvalues of Hessians of the potential taken at all proper Darboux points. The existence of such relations for rational potentials seems to be a difficult question. One of the reasons is the presence of points of indeterminacy of the potential and its gradient. Nevertheless, for two degrees of freedom we prove that such a relation exists. This result is important because it allows us to show that the set of admissible values for Hessian eigenvalues at a proper Darboux point for potentials satisfying the necessary conditions for integrability is finite. In turn, this provides a tool for classification of integrable rational potentials. It was also recently shown that for polynomial homogeneous potentials, additional necessary conditions for integrability can be deduced from the existence of improper Darboux points, that is, points d that are non-zero solutions of gradV(d)=0. These new conditions also take the form of arithmetic restrictions imposed on eigenvalues of V″(d). In this paper we prove that for rational potentials, improper Darboux points give the same necessary conditions for integrability.

  12. Nonlinear dynamics enabled systems design and control

    NASA Astrophysics Data System (ADS)

    Lacarbonara, Walter

    2012-08-01

    There is a growing interest towards design of high-performance structures and devices by seeking ways to exploit advantageously different nonlinearities at different scales rather than constraining operations to avoid nonlinear phenomena. Tools of robust nonlinear modeling and analysis are shown to be turned into design tools for achieving high levels of vibration control authority and synthesis of engineered systems and materials. A brief overview of methods and results on active resonance cancellation and passive nonlinear hysteretic vibration absorbers is illustrated. Recent results on the diffused hysteresis exhibited at the nano-microscale in nanocomposites due to the powerful nonlinear stick-slip mechanism exhibited by carbon nanotubes dispersed in a hosting matrix are discussed. The optimization of the main microstructural parameters is shown to lead to unprecedented levels of damping capacity in next-generation nanostructured materials tailored for wide-band vibrational energy dissipation.

  13. 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.

  14. Families of third and fourth algebraic order trigonometrically fitted symplectic methods for the numerical integration of Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.

    2007-11-01

    The numerical integration of Hamiltonian systems by symplectic and trigonometrically fitted (TF) symplectic method is considered in this work. We construct new trigonometrically fitted symplectic methods of third and fourth order. We apply our new methods as well as other existing methods to the numerical integration of the harmonic oscillator, the 2D harmonic oscillator with an integer frequency ratio and an orbit problem studied by Stiefel and Bettis.

  15. 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.

  16. Nonlinear resonance: Performance report, August 1, 1989--November 30, 1991

    SciTech Connect

    Kevorkian, J.

    1991-01-01

    This report discusses research concentrated on slowly varying nonlinear oscillatory systems. Some of the topics discussed are; adiabatic invariants and transient resonance in very slowly varying hamiltonians systems; sustained resonance in very slowly varying hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators. (LSP)

  17. Nonlinear resonance: Performance report, August 1, 1989--November 30, 1991

    SciTech Connect

    Kevorkian, J.

    1991-12-31

    This report discusses research concentrated on slowly varying nonlinear oscillatory systems. Some of the topics discussed are; adiabatic invariants and transient resonance in very slowly varying hamiltonians systems; sustained resonance in very slowly varying hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators. (LSP)

  18. Quantization of Inequivalent Classical Hamiltonians.

    ERIC Educational Resources Information Center

    Edwards, Ian K.

    1979-01-01

    Shows how the quantization of a Hamiltonian which is not canonically related to the energy is ambiguous and thereby results in conflicting physical interpretations. Concludes that only the Hamiltonian corresponding to the total energy of a classical system or one canonically related to it is suitable for consistent quantization. (GA)

  19. Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M. A.

    2012-06-01

    This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes-Dirac structure and demonstrate that it provides a natural framework for deriving finite-dimensional port-Hamiltonian systems that emulate their infinite-dimensional counterparts. The spatial domain, in the continuous theory represented by a finite-dimensional smooth manifold with boundary, is replaced by a homological manifold-like simplicial complex and its augmented circumcentric dual. The smooth differential forms, in discrete setting, are mirrored by cochains on the primal and dual complexes, while the discrete exterior derivative is defined to be the coboundary operator. This approach of discrete differential geometry, rather than discretizing the partial differential equations, allows to first discretize the underlying Stokes-Dirac structure and then to impose the corresponding finite-dimensional port-Hamiltonian dynamics. In this manner, a number of important intrinsically topological and geometrical properties of the system are preserved.

  20. Hamiltonian approach to internal geophysical waves

    NASA Astrophysics Data System (ADS)

    Constantin, Adrian; Ivanov, Rossen; Iulian Martin, Calin

    2015-04-01

    We study the interaction between two-dimensional surface water waves and internal waves in a flow consisting of a lower layer with an impermeable flat bed and an overlying layer with a free surface. Both layers have constant density and in each the flow is of constant vorticity, driven by gravity and the Coriolis force. This system arises as a simplified model of the coupling of surface and internal geophysical waves. By examining the governing equations of the system we provide a Hamiltonian formulation. This allows for linear and nonlinear approximations.

  1. Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

    SciTech Connect

    Richardson, W.H. . E-mail: whr@stanford.edu

    2006-06-15

    A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.

  2. Noise-induced phase space transport in two-dimensional Hamiltonian systems

    SciTech Connect

    Pogorelov, I.V.; Kandrup, H.E.

    1999-08-01

    First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of periodic driving. The objective was to quantify and understand the manner in which {open_quotes}sticky{close_quotes} chaotic orbits that, in the absence of perturbations, are confined near regular islands for very long times, can become {open_quotes}unstuck{close_quotes} much more quickly when subjected to even very weak perturbations. For both noise and periodic driving, the typical escape time scales logarithmically with the amplitude of the perturbation. For white noise, the details seem unimportant: Additive and multiplicative noise typically have very similar effects, and the presence or absence of a friction related to the noise by a fluctuation-dissipation theorem is also largely irrelevant. Allowing for colored noise {ital can} significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that there is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. Similarly, periodic driving is relatively inefficient when the driving frequency is not comparable to these natural frequencies. This suggests that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. The logarithmic dependence of the escape time on amplitude reflects the fact that the time required for perturbed and unperturbed orbits to diverge a given distance scales logarithmically in the amplitude of the perturbation. {copyright} {ital 1999} {ital The American Physical Society}

  3. 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.

  4. An eight-dimensional quantum mechanical Hamiltonian for X + YCZ3 system and its applications to H + CH4 reaction

    NASA Astrophysics Data System (ADS)

    Liu, Rui; Xiong, Hongwei; Yang, Minghui

    2012-11-01

    An eight-dimensional quantum mechanical Hamiltonian has been proposed based on Palma and Clary's model in which the non-reacting CZ3 group keeps a C3v symmetry in the X + YCZ3 ↔ XY + CZ3 reaction J. Palma and D. C. Clary [J. Chem. Phys. 112, 1859 (2000), 10.1063/1.480749]. By transforming the original Cartesian coordinate system (x, s) into a scaled polar coordinate system (q, γ), the vibrational Hamiltonian of CZ3 group is expressed in a simple form with a clear physical picture. This Hamiltonian is used to investigate the H + CH4 → H2 + CH3 reaction on the Jordan-Gilbert potential energy surface. The total reaction probabilities are calculated for the initial ground state, and umbrella, bending, symmetric, and asymmetric stretching excited states of CH4 with total angular momentum J = 0. The integral cross sections for the reaction are also studied for these initial vibrational states with a centrifugal-sudden approximation. The total integral cross sections for the asymmetric stretching vibrational excited state are in good agreement with the experimental observations. The results also showed the difference of dynamical behavior between reactions from symmetric and asymmetric stretching excited states. The thermal rate constants are calculated for the temperature range T = 250-2000 K and compared with the experimental and other theoretical results.

  5. Canonical perturbation theory; stability and diffusion in Hamiltonian systems: applications in dynamical astronomy

    NASA Astrophysics Data System (ADS)

    Efthymiopoulos, C.

    We present some basic methods and techniques of canonical perturbation theory, as well as some of its applications in problems of stability and/or dif- fusion in dynamical astronomy. The methods presented are: i) the Birkhoff normal form, ii) the Kolmogorov normal form, iii) the resonant normal form, and iv) the hyperbolic normal form used in the computation of in- variant manifolds of unstable periodic orbits in the chaotic regime. For each method we give concrete examples presented in some detail in order to facilitate study. In particular, we discuss a step by step implementation of a so-called `book-keeping' algorithm by which all quantities (i.e. Hamil- tonian, generating functions etc.) can be split in groups of terms of similar order of smallness. We explain why the book-keeping schemes presently suggested are particularly suitable in computer-algebraic implementations of normal forms. Also, for each method we explain the pattern by which small divisors are accumulated in the series terms at successive normaliza- tion steps, outlining why such accumulation leads to a divergent normal- ization process in the case of the Birkhoff normal form (both non-resonant or resonant), while it leads to a convergent normalization process in the case of the Kolmogorov normal form or the hyperbolic normal form. After these formal aspects, we present applications of canonical perturbation the- ory in concrete Hamiltonian dynamical systems appearing in problems of dynamical astronomy. In particular, we explain how resonant normal form theory is connected to the phenomenon of Arnold diffusion, as well as to estimates of the diffusion rate in the action space in systems of three (or more) degrees of freedom. We discuss how is `book-keeping' implemented in paradigmatic cases, like the treatment of mean motion resonances in so- lar system dynamics, and the study of orbits in axisymmetric galaxies or in barred-spiral rotating galaxies. Finally, we give an example of implemen

  6. Nonlinear identification of ionic polymer actuator systems

    NASA Astrophysics Data System (ADS)

    Kothera, Curt S.; Lacy, Seth L.; Erwin, R. Scott; Leo, Donald J.

    2004-07-01

    Ionic polymers are a class of electromechanically coupled materials that can be used as flexible transducers. When set up in the cantilever configuration, the actuators exhibit a large bending deflection when an electric field is applied across their thickness. Being a relatively new research topic, the governing physical and chemical mechanisms are not yet fully understood. Experimental results have demonstrated nonlinear dynamic behavior. The nonlinear dynamics can be seen in the response of current, displacement, and velocity of the actuator. This work presents results for the nonlinear identification of ionic polymer actuator systems driven at a specific frequency. Identification results using a 5th-degree Volterra expansion show that the nonlinear distortion can be accurately modeled. Using such a high power in the series expansion is necessary to capture the most dominant harmonics, as evidenced when examining the power spectral density of the response. An investigation of how nonlinearities enter into the response is also performed. By analyzing both the actuation current and tip velocity, results show that both the voltage to current and current to velocity stages influence the nonlinear response, but the voltage to current stage is more dominantly nonlinear.

  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. 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.

  10. Orbit structure of Hamiltonian systems arising from Lie transformation group actions

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

    This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.

  11. Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

    PubMed

    Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

    2012-03-01

    We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

  12. 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.

  13. Nonlinear Control of Delay and PDE Systems

    NASA Astrophysics Data System (ADS)

    Bekiaris-Liberis, Nikolaos

    In this dissertation we develop systematic procedures for the control and analysis of general nonlinear systems with delays and of nonlinear PDE systems. We design predictor feedback laws (i.e., feedback laws that use the future, rather than the current state of the system) for the compensation of delays (i.e., after the control signal reaches the system for the first time, the system behaves as there were no delay at all) that can be time-varying or state-dependent, on the input and on the state of nonlinear systems. We also provide designs of predic- tor feedback laws for linear systems with constant distributed delays and known or unknown plant parameters, and for linear systems with simultaneous known or unknown constant delays on the input and the state. Moreover, we intro- duce infinite-dimensional backstepping transformations for each particular prob-lem, which enables us to construct Lyapunov-Krasovskii functionals. With the available Lyapunov-Krasovskii functionals we study stability, as well as, robust- ness of our control laws to plant uncertainties. We deal with coupled PDE-ODE systems. We consider nonlinear systems with wave actuator dynamics, for which we design a predictor inspired feedback law. We study stability of the closed-loop system either by constructing Lyapunov functionals, or using arguments of explicit solutions. We also consider linear sys- tems with distributed actuator and sensor dynamics governed by diffusion or wave PDEs, for which we design stabilizing feedback laws. We study stability of the closed-loop systems using Lyapunov functionals that we construct with the intro- duction of infinite-dimensional transformations of forwarding type. Finally, we develop a control design methodology for coupled nonlinear first-order hyperbolic PDEs through an application to automotive catalysts.

  14. System interaction with linear and nonlinear characteristics

    SciTech Connect

    Lin, C.W. ); Tseng, W.S. )

    1991-01-01

    This book is covered under some of the following topics: seismic margins in piping systems, vibrational power flow in a cylindrical shell, inelastic pipework dynamics and aseismic design, an efficient method for dynamic analysis of a linearly elastic piping system with nonlinear supports.

  15. Nonlinear coupling in the human motor system

    PubMed Central

    Chen, C.C.; Kilner, J.M.; Friston, K.J.; Kiebel, S. J.; Jolly, R.K.; Ward, N. S.

    2010-01-01

    The synchronous discharge of neuronal assemblies is thought to facilitate communication between areas within distributed networks in the human brain. This oscillatory activity is especially interesting, given the pathological modulation of specific frequencies in diseases affecting the motor system. Many studies investigating oscillatory activity have focussed on same frequency, or linear, coupling between areas of a network. In this study, our aim was to establish a functional architecture in the human motor system responsible for induced responses as measured in normal subjects with magnetoencephalography. Specifically, we looked for evidence for additional nonlinear (between-frequency) coupling among neuronal sources and, in particular, whether nonlinearities were found predominantly in connections within areas (intrinsic), between areas (extrinsic) or both. We modelled the event-related modulation of spectral responses during a simple hand-grip using dynamic casual modelling. We compared models with and without nonlinear connections under conditions of symmetric and asymmetric interhemispheric connectivity. Bayesian model comparison suggested that the task-dependent motor network was asymmetric during right hand movements. Furthermore, it revealed very strong evidence for nonlinear coupling between sources in this distributed network, but interactions among frequencies within a source appeared linear in nature. Our results provide empirical evidence for nonlinear coupling among distributed neuronal sources in the motor system and that these play an important role in modulating spectral responses under normal conditions. PMID:20573886

  16. System characterization in nonlinear random vibration

    SciTech Connect

    Paez, T.L.; Gregory, D.L.

    1986-01-01

    Linear structural models are frequently used for structural system characterization and analysis. In most situations they can provide satisfactory results, but under some circumstances they are insufficient for system definition. The present investigation proposes a model for nonlinear structure characterization, and demonstrates how the functions describing the model can be identified using a random vibration experiment. Further, it is shown that the model is sufficient to completely characterize the stationary random vibration response of a structure that has a harmonic frequency generating form of nonlinearity. An analytical example is presented to demonstrate the plausibility of the model.

  17. 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.

  18. 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.

  19. Optimal control of open quantum systems: a combined surrogate hamiltonian optimal control theory approach applied to photochemistry on surfaces.

    PubMed

    Asplund, Erik; Klüner, 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., ℏ = m(e) = e = a(0) = 1, have been used unless otherwise stated. PMID:22462846

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

    NASA Astrophysics Data System (ADS)

    Asplund, Erik; Klüner, Thorsten

    2012-03-01

    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)], 10.1063/1.473950. 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), 10.1063/1.475576; Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)], 10.1063/1.1650297. 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., ℏ = me = e = a0 = 1, have been used unless otherwise stated.

  1. Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors.

    SciTech Connect

    Wang, C.-x.; Accelerator Systems Division

    2006-01-01

    A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.

  2. Quantum manifestations of classical stochasticity. I. Energetics of some nonlinear systems

    NASA Astrophysics Data System (ADS)

    Weissman, Yitzhak; Jortner, Joshua

    1982-08-01

    In this paper we present the results of a semiclassical investigation and a quantum mechanical study of the bound energy spectrum of the Henon-Heiles Hamiltonian (HHH) and of the Barbanis Hamiltonian (BH). We have derived a simple semiclassical formula for the energy levels E, and for their sensitivity dE/dɛ with respect to the strength ɛ of the nonlinear coupling for the HHH, and established general relations between E and its derivatives dnE/dɛn (n⩾1). Numerical quantum mechanical computations of the energy levels were conducted for the HHH and for the BH. The nonlinear coupling constant was adjusted so that for the HHH there will be ˜150 states up to the classical critical energy Ec and ˜300 states up to the dissociation energy ED. The E values were obtained by direct diagonalization using a basis containing 760 states, while the values of dE/dɛ were computed utilizing the Hellmann-Feynman theorem. Good agreement between the semiclassical and the quantum mechanical spectra was observerd well above Ec. These results raise the distict possibility that the semiclassical approxmation for these nonlinear systems does not break down in the vicinity of Ec and that the bound level structure does not provide a manifestation of the classical transition from quasiperiodic to chaotic motion.

  3. Optimized spectral estimation for nonlinear synchronizing systems

    NASA Astrophysics Data System (ADS)

    Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn

    2014-03-01

    In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.

  4. 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.

  5. 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.

  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. Spectral decomposition of nonlinear systems with memory.

    PubMed

    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.

  8. Connectance and stability of nonlinear symplectic systems

    NASA Astrophysics Data System (ADS)

    Laveder, D.; Cosentino, M.; Lega, Elena; Froeschlé, C.

    2008-09-01

    We have revisited the problem of the transition from ordered to chaotic motion for increasing number of degrees of freedom in nonlinear symplectic maps. Following the pioneer work of Froeschlé (Phys. Rev. A 18, 277 281, 1978) we investigate such systems as a function of the number of couplings among the equations of motion, i.e. as a function of a parameter called connectance since the seminal paper of Gardner and Ashby (Nature 228, 784, 1970) about linear systems. We compare two different models showing that in the nonlinear case the connectance has to be intended as the fraction of explicit dynamical couplings among degrees of freedom, rather than the fraction of non-zero elements in a given matrix. The chaoticity increases then with the connectance until the system is fully coupled.

  9. Accidental degeneracies in nonlinear quantum deformed systems

    NASA Astrophysics Data System (ADS)

    Aleixo, A. N. F.; Balantekin, A. B.

    2011-09-01

    We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.

  10. 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.

  11. 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.

  12. Low level monitoring and control of nonlinear systems

    SciTech Connect

    Cover, A.; Reneke, J.; Lenhart, S.; Protopopescu, V.

    1994-12-31

    In this paper, we propose a nonparametric method for monitoring and controlling nonlinear systems whose dynamics is, in general, unknown or only partially known. Our nonparametric method is based on the stochastic linearization of the underlying (unknown) nonlinear system.

  13. 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.

  14. 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.

  15. Identification of Nonlinear Cascade Systems with Noninvertible Piecewise Linear Input and Backlash Output Nonlinearities

    NASA Astrophysics Data System (ADS)

    Vörös, Jozef

    2016-07-01

    The paper deals with the parameter identification of cascade nonlinear dynamic systems with noninvertible piecewise linear input nonlinearities and backlash output nonlinearities. Application of the key term separation principle provides special expressions for the corresponding nonlinear model description that are linear in parameters. A least squares based iterative technique allows estimation of all the model parameters based on measured input/output data. Simulation studies illustrate the feasibility of proposed identification method.

  16. Approximations of nonlinear systems having outputs

    NASA Technical Reports Server (NTRS)

    Hunt, L. R.; Su, R.

    1985-01-01

    For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced.

  17. 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.

  18. Hamiltonian formulation of general relativity.

    NASA Astrophysics Data System (ADS)

    Teitelboim, Claudio

    The following sections are included: * INTRODUCTION * HAMILTONIAN FORMULATION OF GAUGE THEORIES (PRE-BRST) * BRST HAMILTONIAN FORMULATION OF GAUGE THEORIES * DYNAMICS OF GRAVITATIONAL FIELD * DOES THE HAMILTONIAN VANISH? GENERAL COVARIANCE AS AN "ORDINARY" GAUGE INVARIANCE * GENERALLY COVARIANT SYSTEMS * TIME AS A CANONICAL VARIABLE. ZERO HAMILTONIAN * Parametrized Systems * Zero Hamiltonian * Parametrization and Explicit Time Dependence * TIME REPARAMETRIZATION INVARIANCE * Form of Gauge Transformations * Must the Hamiltonian be Zero for a Generally Covariant System? * Simple Example of a Generally Covariant System with a Nonzero Hamiltonian * "TRUE DYNAMICS" VERSUS GAUGE TRANSFORMATIONS * Interpretation of the Formalism * Reduced Phase Space * MUST TIME FLOW? * GAUGE INDEPENDENCE OF PATH INTEGRAL FOR A PARAMETRIZED SYSTEM ILLUSTRATED. EQUIVALENCE OF THE GAUGES t = τ AND t = 0 * Reduced Phase Space Transition Amplitude as a Reduced Phase Space Path Integral * Canonical Gauge Conditions * Gauge t = 0 * Gauge t α τ * BRST CHARGE OF GRAVITATIONAL FIELD * ELEMENTS OF BRST THEORY * THE GHOST, YOU'VE COME A LONG WAY BABY * Introduction * Quantum mechanics, the art of finding and combining simple elementary processes * Ghosts necessary to keep elementary processes simple * BRST symmetry: ghosts and matter become different components of single geometrical object * BRST SYMMETRY IN CLASSICAL MECHANICS * Ghosts have role in classical mechanics * Gauge invariance and constraints * Classical mechanics over Grassmann algebra necessary * Higher order structure functions * Rank defined. Open algebras * Ghosts. Ghost number. BRST generator as generating function for structure functions * A belianization of constraints. Existence of Ω * Uniqueness of Ω * Classical BRST cohomology * QUANTUM BRST THEORY * States and operators * Ghost number * BRST invariant states * Quantum BRST cohomology * Equivalence of the BRST physical subspace with the conventional gauge

  19. 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.

  20. 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

  1. Effect of the Hamiltonian parameters on Blume-Capel Ising ferromagnet system with single-ion anisotropy

    NASA Astrophysics Data System (ADS)

    Batı, Mehmet; Ertaş, Mehmet

    2016-10-01

    The dynamic mean-field approach have been utilized to investigate effect of the Hamiltonian parameters on the dynamic magnetic properties of a Blume-Capel Ising ferromagnet system in two dimensions, comprising a ferromagnetic spins S = ±3/2, ±1/2. The effect of the single-ion anisotropy (d) and the frequency (w) of the external oscillating magnetic field on the dynamic hysteresis cycle (DHC) are explored in detail. It is found that the DHC increases as the d increases and at a certain d, the DHC decreases with increasing the d. Furthermore, the DHC is very sensitive to changes in the w. We also examine the effect of the w on the dynamic phase diagrams and observe the dynamic phase diagrams illustrate richer dynamic critical behavior for higher values of w than for lower values.

  2. The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications

    NASA Astrophysics Data System (ADS)

    Mei, Lijie; Wu, Xinyuan

    2016-10-01

    In general, extended Runge-Kutta-Nyström (ERKN) methods are more effective than traditional Runge-Kutta-Nyström (RKN) methods in dealing with oscillatory Hamiltonian systems. However, the theoretical analysis for ERKN methods, such as the order conditions, the symplectic conditions and the symmetric conditions, becomes much more complicated than that for RKN methods. Therefore, it is a bottleneck to construct high-order ERKN methods efficiently. In this paper, we first establish the ERKN group Ω for ERKN methods and the RKN group G for RKN methods, respectively. We then rigorously show that ERKN methods are a natural extension of RKN methods, that is, there exists an epimorphism η of the ERKN group Ω onto the RKN group G. This epimorphism gives a global insight into the structure of the ERKN group by the analysis of its kernel and the corresponding RKN group G. Meanwhile, we establish a particular mapping φ of G into Ω so that each image element is an ideal representative element of the congruence class in Ω. Furthermore, an elementary theoretical analysis shows that this map φ can preserve many structure-preserving properties, such as the order, the symmetry and the symplecticity. From the epimorphism η together with its section φ, we may gain knowledge about the structure of the ERKN group Ω via the RKN group G. In light of the theoretical analysis of this paper, we obtain high-order structure-preserving ERKN methods in an effective way for solving oscillatory Hamiltonian systems. Numerical experiments are carried out and the results are very promising, which strongly support our theoretical analysis presented in this paper.

  3. 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

  4. The geometric phase in nonlinear dissipative systems

    SciTech Connect

    Ning, C.Z.; Haken, H. )

    1992-10-30

    In this paper, the authors review the recent progress made in generalizing the concept of the geometric phase to nonlinear dissipative systems. The authors first illustrate the usual form of the parallel transport law with an elementary example of the parallel shift of a line on the complex plane. Important results about the non-adiabatical geometric (Aharonov and Anandan or AA) phase [sup 18] for the Schrodinger equations are reviewed in order to make a comparison with results for dissipative systems. The authors show that a geometric phase can be defined for dissipative systems with the cyclic attractors. Systems undergoing the Hopf bifurcation with a continuous symmetry are shown to possess such cyclic attractors. Examples from laser physics are discussed to exhibit the applicability of our formalism and the widespread existence of the geometric phase in dissipative systems.

  5. Hamiltonian formulation of the extended Green-Naghdi equations

    NASA Astrophysics Data System (ADS)

    Matsuno, Yoshimasa

    2015-05-01

    A novel method is developed for extending the Green-Naghdi (GN) shallow-water model equation to the general system which incorporates the arbitrary higher-order dispersive effects. As an illustrative example, we derive a model equation which is accurate to the fourth power of the shallowness parameter while preserving the full nonlinearity of the GN equation, and obtain its solitary wave solutions by means of a singular perturbation analysis. We show that the extended GN equations have the same Hamiltonian structure as that of the GN equation. We also demonstrate that Zakharov's Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.

  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. 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.

  8. Approximate controllability of nonlinear impulsive differential systems

    NASA Astrophysics Data System (ADS)

    Sakthivel, R.; Mahmudov, N. I.; Kim, J. H.

    2007-08-01

    Many practical systems in physical and biological sciences have impulsive dynamical be- haviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability issue for nonlinear impulsive differential and neutral functional differential equations in Hilbert spaces. Based on the semigroup theory and fixed point approach, sufficient conditions for approximate controllability of impulsive differential and neutral functional differential equations are established. Finally, two examples are presented to illustrate the utility of the proposed result. The results improve some recent results.

  9. 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.

  10. 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.

  11. Nonlinear gain-scheduling output-feedback control for polynomial nonlinear systems subject to actuator saturation

    NASA Astrophysics Data System (ADS)

    Wu, Fen; Hays, Scott

    2013-09-01

    This paper investigates nonlinear gain-scheduling control approaches for a class of polynomial nonlinear systems, containing an output-dependent vector field with input saturation. Using the polytopic differential inclusion and norm-bounded differential inclusion (NDI) of saturation and dead-zone functions, the nonlinear plants are transformed into systems with measurable parameters. For the polytopic differential inclusion description, a quasi-linear parameter varying (quasi-LPV) output-feedback controller will be sought for saturation control. On the other hand, the NDI model leads to a nonlinear fractional transformation (NFT) output-feedback controller for saturated nonlinear systems. The quasi-LPV and NFT output-feedback control synthesis conditions are derived in the forms of output-dependent matrix inequalities. They can be reformulated as sum-of-squares (SOS) optimisations and solved efficiently using SOS programming. The proposed nonlinear gain-scheduling saturation control approaches will be demonstrated using the Van der Pol equation.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. Boosted X waves in nonlinear optical systems.

    PubMed

    Arévalo, 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.

  18. 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.

  19. Double nonlinear resonance in ferromagnets and other dynamic systems

    NASA Astrophysics Data System (ADS)

    Bakai, A. S.

    2010-08-01

    The phenomenon of double nonlinear resonances in nonlinear oscillators of general type is described. The results are used to describe a double nonlinear ferromagnetic resonance in a uniaxial ferromagnet. The possibility of a similar resonance in the system of brain biocurrents is considered.

  20. Quantum dynamics of nonlinear cavity systems

    NASA Astrophysics Data System (ADS)

    Nation, Paul David

    In this work we investigate the quantum dynamics of three different configurations of nonlinear cavity systems. We begin by carrying out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprising a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing an external flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal and noise response where it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state. Next, we consider the use of a superconducting transmission line formed from an array of dc-SQUIDs for investigating analogue Hawking radiation. We will show that biasing the array with a space-time varying flux modifies the propagation velocity of the transmission line, leading to an effective metric with a horizon. As a fundamentally quantum mechanical device, this setup allows for investigations of quantum effects such as backreaction and analogue space-time fluctuations on the Hawking process. Finally, we investigate a quantum parametric amplifier with dynamical pump mode, viewed as a zero-dimensional model of Hawking radiation from an evaporating black hole. The conditions are derived under which the spectrum of particles generated from vacuum fluctuations deviates from the thermal spectrum predicted for the conventional parametric amplifier. We find that significant deviation occurs once the pump mode (black hole) has released nearly half of its initial energy in the signal (Hawking radiation) and idler (in-falling particle) modes. As a model of black hole dynamics, this finding lends support to the view that late-time Hawking radiation contains information about the quantum state of the black hole and is entangled with the black hole's quantum

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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)).

  7. 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.

  8. Bohr Hamiltonian with time-dependent potential

    NASA Astrophysics Data System (ADS)

    Naderi, L.; Hassanabadi, H.; Sobhani, H.

    2016-04-01

    In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.

  9. 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

  10. 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

  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. Extended Hamiltonian approach to continuous tempering

    NASA Astrophysics Data System (ADS)

    Gobbo, Gianpaolo; Leimkuhler, Benedict J.

    2015-06-01

    We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.

  13. 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.

  14. Nonstationary regimes of homogeneous Hamiltonian systems in the state of sonic vacuum

    NASA Astrophysics Data System (ADS)

    Starosvetsky, Y.; Ben-Meir, Y.

    2013-06-01

    In the present paper we study the mechanism that leads to the formation of regular patterns of energy localization and complete recurrent energy transport in the homogeneous systems of anharmonic oscillators and oscillatory chains subjected to a state of sonic vacuum. The basic model under investigation comprises a system of purely anharmonic oscillators as well as oscillatory chains given to a localized excitation where the initial energy is imported to one of the oscillators or oscillatory chains. The results of numerical simulations reveal the existence of a strong classical beating phenomenon, characterized by complete, recurrent, resonant energy exchanges between the oscillators and oscillatory chain and this in the state of sonic vacuum where no regular resonant frequencies can be defined. In this study we show that formation of the recurrent energy exchanges in this highly degenerate model is strictly stipulated by the system parameters. Thus, for instance, choosing the parameter of coupling below a certain threshold leads to significant energy localization on one of the oscillators or oscillatory chains. However, increasing the strength of coupling above the threshold leads to the formation of a strong beating response. The analytical study pursued in this paper predicts the origin of formation of a strong beating phenomenon and provides the necessary conditions on the system parameter for its excitation. Moreover, careful analysis of the beating phenomenon reveals the qualitatively different global bifurcation undergone by this type of highly nonstationary regime. The theoretical study is further extended to the system of coupled purely anharmonic lattices. Thus we show analytically and numerically that excitation of some particular solutions (e.g., spatially periodic standing waves and standing breathers) on one of the lattices results in the formation of similar patterns of energy (wave) localization as well as the regime of complete recurrent interchain

  15. Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Bambusi, Dario; Giorgilli, Antonio

    1993-05-01

    We develop canonical perturbation theory for a physically interesting class of infinite-dimensional systems. We prove stability up to exponentially large times for dynamical situations characterized by a finite number of frequencies. An application to two model problems is also made. For an arbitrarily large FPU-like system with alternate light and heavy masses we prove that the exchange of energy between the optical and the acoustical modes is frozen up to exponentially large times, provided the total energy is small enough. For an infinite chain of weakly coupled rotators we prove exponential stability for two kinds of initial data: (a) states with a finite number of excited rotators, and (b) states with the left part of the chain uniformly excited and the right part at rest.

  16. 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.

  17. A Simple Iterative Solution of Nonlinear Algebraic Systems

    NASA Astrophysics Data System (ADS)

    Gousidou, Maria; Koutitas, Christopher

    2009-09-01

    A simple, robust, easily programmable and efficient method for the iterative solution of nonlinear algebraic systems, commonly appearing in nonlinear mechanics, based on Newton-Raphson method (without repeatedly solving linear algebraic systems), is proposed, synoptically described and experimentally investigated. Fast convergence and easy programming are its main qualifications.

  18. 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.

  19. 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.

  20. 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.

  1. Robust nonlinear variable selective control for networked systems

    NASA Astrophysics Data System (ADS)

    Rahmani, Behrooz

    2016-10-01

    This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.

  2. Nonlinear Control of Dynamical Systems from Time Series

    NASA Astrophysics Data System (ADS)

    Petrov, Valery; Showalter, Kenneth

    1996-04-01

    Feedback control of multidimensional, nonlinear single-input single-output systems is formulated in terms of an invariant hypersurface in the delayed state space of a system observable and a control parameter. The surface is created directly from the response of the system to random perturbations, providing a model-independent nonlinear control algorithm. The algorithm can be used to stabilize unstable states or to drive a system to any particular objective state in a minimum number of steps.

  3. Breather compactons in nonlinear Klein-Gordon systems.

    PubMed

    Dinda, P T; Remoissenet, M

    1999-11-01

    We demonstrate the existence of a localized breathing mode with a compact support, i.e., a stationary breather compacton, in a nonlinear Klein-Gordon system. This breather compacton results from a delicate balance between the harmonicity of the substrate potential and the total nonlinearity induced by the substrate potential and the coupling forces between adjacent lattice sites.

  4. Efficient solution procedures for systems with local non-linearities

    NASA Astrophysics Data System (ADS)

    Ibrahimbegovic, Adnan; Wilson, Edward L.

    1992-06-01

    This paper presents several methods for enhancing computational efficiency in both static and dynamic analysis of structural systems with localized nonlinear behavior. A significant reduction of computational effort with respect to brute-force nonlinear analysis is achieved in all cases at the insignificant (or no) loss of accuracy. The presented methodologies are easily incorporated into a standard computer program for linear analysis.

  5. On the benefit of DMT modulation in nonlinear VLC systems.

    PubMed

    Qian, Hua; Cai, Sunzeng; Yao, Saijie; Zhou, Ting; Yang, Yang; Wang, Xudong

    2015-02-01

    In a visible light communication (VLC) system, the nonlinear characteristic of the light emitting diode (LED) in transmitter is a limiting factor of system performance. Modern modulation signals with large peak-to-power-ratio (PAPR) suffers uneven distortion. The nonlinear response directly impacts the intensity modulation and direct detection VLC system with pulse-amplitude modulation (PAM). The amplitude of the PAM signal is distorted unevenly and large signal is vulnerable to noise. Orthogonal linear transformations, such as discrete multi-tone (DMT) modulation, can spread the nonlinear effects evenly to each data symbol, thus perform better than PAM signals. In this paper, we provide theoretical analysis on the benefit of DMT modulation in nonlinear VLC system. We show that the DMT modulation is a better choice than the PAM modulation for the VLC system as the DMT modulation is more robust against nonlinearity. We also show that the post-distortion nonlinear elimination method, which is applied at the receiver, can be a reliable solution to the nonlinear VLC system. Simulation results show that the post-distortion greatly improves the system performance for the DMT modulation.

  6. Thermodynamics from a scaling Hamiltonian

    NASA Astrophysics Data System (ADS)

    Del Pino, L. A.; Troncoso, P.; Curilef, S.

    2007-11-01

    There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both extensive and nonextensive thermodynamic perspectives. We use a model, whose Hamiltonian takes into account spins ferromagnetically coupled in a chain via a power law that decays at large interparticle distance r as 1/rα for α⩾0 . Here, we review old nonextensive scaling. In addition, we propose a Hamiltonian scaled by 2((N/2)1-α-1)/(1-α) that explicitly includes symmetry of the lattice and dependence on the size N of the system. The approach enabled us to improve upon previous results. A numerical test is conducted through Monte Carlo simulations. In the model, periodic boundary conditions are adopted to eliminate surface effects.

  7. 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)

  8. 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.

  9. Control design for a class of nonlinear parameter varying systems

    NASA Astrophysics Data System (ADS)

    Cai, Xiushan; Liu, Yang; Zhang, Wei

    2015-07-01

    Stabilisation for a class of one-sided Lipschitz nonlinear parameter varying systems is dealt with in this paper. First, the nonlinear parameter varying system is represented as a subsystem of a differential inclusion. Sufficient conditions for exponential stabilisation for the differential inclusion are given by solving linear matrix inequalities. Then a continuous control law is designed to stabilise the differential inclusion. It leads to stabilising the nonlinear parameter varying system. Finally, a simulation example is presented to show the validity and advantages of the proposed method.

  10. 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.

  11. An experimental study of nonlinear dynamic system identification

    NASA Astrophysics Data System (ADS)

    Stry, Greselda I.; Mook, D. Joseph

    1990-12-01

    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.

  12. 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.

  13. Output feedback fuzzy controller design with local nonlinear feedback laws for discrete-time nonlinear systems.

    PubMed

    Dong, Jiuxiang; Wang, Youyi; Yang, Guang-Hong

    2010-12-01

    This paper considers the output feedback control problem for nonlinear discrete-time systems, which are represented by a type of fuzzy systems with local nonlinear models. By using the estimations of the states and nonlinear functions in local models, sufficient conditions for designing observer-based controllers are given for discrete-time nonlinear systems. First, a separation property, i.e., the controller and the observer can be independently designed, is proved for the class of fuzzy systems. Second, a two-step procedure with cone complementarity linearization algorithms is also developed for solving the H( ∞) dynamic output feedback (DOF) control problem. Moreover, for the case where the nonlinear functions in local submodels are measurable, a convex condition for designing H(∞) controllers is given by a new DOF control scheme. In contrast to the existing methods, the new methods can design output feedback controllers with fewer fuzzy rules as well as less computational burden, which is helpful for controller designs and implementations. Lastly, numerical examples are given to illustrate the effectiveness of the proposed methods.

  14. 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.

  15. Optimal second order sliding mode control for nonlinear uncertain systems.

    PubMed

    Das, Madhulika; Mahanta, Chitralekha

    2014-07-01

    In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.

  16. 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.

  17. New stability conditions for nonlinear time varying delay systems

    NASA Astrophysics Data System (ADS)

    Elmadssia, S.; Saadaoui, K.; Benrejeb, M.

    2016-07-01

    In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie-Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.

  18. Preparing topologically ordered states by Hamiltonian interpolation

    NASA Astrophysics Data System (ADS)

    Ni, Xiaotong; Pastawski, Fernando; Yoshida, Beni; König, Robert

    2016-09-01

    We study the preparation of topologically ordered states by interpolating between an initial Hamiltonian with a unique product ground state and a Hamiltonian with a topologically degenerate ground state space. By simulating the dynamics for small systems, we numerically observe a certain stability of the prepared state as a function of the initial Hamiltonian. For small systems or long interpolation times, we argue that the resulting state can be identified by computing suitable effective Hamiltonians. For effective anyon models, this analysis singles out the relevant physical processes and extends the study of the splitting of the topological degeneracy by Bonderson (2009 Phys. Rev. Lett. 103 110403). We illustrate our findings using Kitaev’s Majorana chain, effective anyon chains, the toric code and Levin-Wen string-net models.

  19. 3-D Mesh Generation Nonlinear Systems

    SciTech Connect

    Christon, M. A.; Dovey, D.; Stillman, D. W.; Hallquist, J. O.; Rainsberger, R. B

    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 surface 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.

  20. 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

  1. 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.

  2. 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

  3. Parameter and Structure Inference for Nonlinear Dynamical Systems

    NASA Technical Reports Server (NTRS)

    Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

    2006-01-01

    A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

  4. 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.

  5. Nonlinear time reversal in a wave chaotic system.

    PubMed

    Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M

    2013-02-01

    Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.

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

    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.

  7. 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.

  8. Adaptive control of nonlinear systems with actuator failures and uncertainties

    NASA Astrophysics Data System (ADS)

    Tang, Xidong

    2005-11-01

    Actuator failures have damaging effect on the performance of control systems, leading to undesired system behavior or even instability. Actuator failures are unknown in terms of failure time instants, failure patterns, and failure parameters. For system safety and reliability, the compensation of actuator failures is of both theoretical and practical significance. This dissertation is to further the study of adaptive designs for actuator failure compensation to nonlinear systems. In this dissertation a theoretical framework for adaptive control of nonlinear systems with actuator failures and system uncertainties is established. The contributions are the development of new adaptive nonlinear control schemes to handle unknown actuator failures for convergent tracking performance, the specification of conditions as a guideline for applications and system designs, and the extension of the adaptive nonlinear control theory. In the dissertation, adaptive actuator failure compensation is studied for several classes of nonlinear systems. In particular, adaptive state feedback schemes are developed for feedback linearizable systems and parametric strict-feedback systems. Adaptive output feedback schemes are deigned for output-feedback systems and a class of systems with unknown state-dependent nonlinearities. Furthermore, adaptive designs are addressed for MIMO systems with actuator failures, based on two grouping techniques: fixed grouping and virtual grouping. Theoretical issues such as controller structures, actuation schemes, zero dynamics, observation, grouping conditions, closed-loop stability, and tracking performance are extensively investigated. For each scheme, design conditions are clarified, and detailed stability and performance analysis is presented. A variety of applications including a wing-rock model, twin otter aircraft, hypersonic aircraft, and cooperative multiple manipulators are addressed with simulation results showing the effectiveness of the

  9. Identification of nonlinear optical systems using adaptive kernel methods

    NASA Astrophysics Data System (ADS)

    Wang, Xiaodong; Zhang, Changjiang; Zhang, Haoran; Feng, Genliang; Xu, Xiuling

    2005-12-01

    An identification approach of nonlinear optical dynamic systems, based on adaptive kernel methods which are modified version of least squares support vector machine (LS-SVM), is presented in order to obtain the reference dynamic model for solving real time applications such as adaptive signal processing of the optical systems. The feasibility of this approach is demonstrated with the computer simulation through identifying a Bragg acoustic-optical bistable system. Unlike artificial neural networks, the adaptive kernel methods possess prominent advantages: over fitting is unlikely to occur by employing structural risk minimization criterion, the global optimal solution can be uniquely obtained owing to that its training is performed through the solution of a set of linear equations. Also, the adaptive kernel methods are still effective for the nonlinear optical systems with a variation of the system parameter. This method is robust with respect to noise, and it constitutes another powerful tool for the identification of nonlinear optical systems.

  10. 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.

  11. Relations between static and dynamic exponents in nonlinear dynamical systems

    NASA Astrophysics Data System (ADS)

    Badii, R.; Broggi, G.

    1990-01-01

    The rules governing the evolution of nonlinear dynamical systems are systematically detected by constructing a hierarchical tree of symbol sequences. Relations between local partial dimensions and Lyapunov exponents are obtained from equations for the probabilities of symbol sequences on the logic tree. These relations are nonlinear and involve an open hierarchy of equations, which shows that the dimension spectrum f(α) cannot be obtained in closed form from the sole knowledge of the local Lyapunov exponents.

  12. 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.

  13. 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.

  14. 3-D Mesh Generation Nonlinear Systems

    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

  15. 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

  16. 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.

  17. Variational principle for nonlinear wave propagation in dissipative systems

    NASA Astrophysics Data System (ADS)

    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.

  18. Modeling a Nonlinear Liquid Level System by Cellular Neural Networks

    NASA Astrophysics Data System (ADS)

    Hernandez-Romero, Norberto; Seck-Tuoh-Mora, Juan Carlos; Gonzalez-Hernandez, Manuel; Medina-Marin, Joselito; Flores-Romero, Juan Jose

    This paper presents the analogue simulation of a nonlinear liquid level system composed by two tanks; the system is controlled using the methodology of exact linearization via state feedback by cellular neural networks (CNNs). The relevance of this manuscript is to show how a block diagram representing the analogue modeling and control of a nonlinear dynamical system, can be implemented and regulated by CNNs, whose cells may contain numerical values or arithmetic and control operations. In this way the dynamical system is modeled by a set of local-interacting elements without need of a central supervisor.

  19. Towards Port-Hamiltonian Approach for Modeling and Control of Two-wheeled Wheelchair

    NASA Astrophysics Data System (ADS)

    Aula, A.; Akmeliawati, R.; Ahmad, S.; Altalmas, T. M.; Sidek, S. N.

    2013-12-01

    This paper introduces the modeling and control design of a two-wheeled wheelchair (TWW) based on structure-preserving port-Hamiltonian concept. In this paper, a model of TWW with features, including space-saving, four to two-wheel transformation, and adjustable seat height is proposed to increased mobility and independence of the user. Then, the mathematical model of a TWW in its balanced mode is derived. The model is based on the total energy in the system. The system is divided into subsystems whereby the interconnections which exist are utilized. The nonlinearity of the model is preserved using port-controlled Hamiltonian (PCH) system and made to advantage. The proposed controlled is designed based on the idea of PCH such that the energy balance in the system can be achieved while stabilizing the system.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. Convex aggregative modelling of infinite memory nonlinear systems

    NASA Astrophysics Data System (ADS)

    Wachel, Paweł

    2016-08-01

    The convex aggregation technique is applied for modelling general class of nonlinear systems with unknown structure and infinite memory. The finite sample size properties of the algorithm are formally established and compared to the standard least-squares counterpart of the method. The proposed algorithm demonstrates its advantages when the a-priori knowledge and the measurement data are both scarce, that is, when the information about the actual system structure is unknown or uncertain and the measurement set is small and disturbed by a noise. Numerical experiments illustrate application and practical benefits of the method for various nonlinear systems.

  7. Performance evaluation of nonlinear weighted T-system

    NASA Astrophysics Data System (ADS)

    Benfekir, A.; Hamaci, S.; Boimond, J.-L.; Labadi, K.

    2013-10-01

    This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min, +) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model.

  8. Squeezed states from a quantum deformed oscillator Hamiltonian

    NASA Astrophysics Data System (ADS)

    Ramírez, R.; Reboiro, M.

    2016-03-01

    The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions.

  9. 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.

  10. Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification

    NASA Astrophysics Data System (ADS)

    Kurt, Mehmet; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

    2014-03-01

    We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong

  11. 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.

  12. H∞ filtering for piecewise homogeneous Markovian jump nonlinear systems

    NASA Astrophysics Data System (ADS)

    Zhao, Feng; Zhang, Qingling; Wang, Guoliang

    2016-10-01

    This paper concerns the problem of H∞ filtering for piecewise homogeneous Markovian jump nonlinear systems. Different from the existing studies in the literatures, the existence of variations in transition rates for Markovian jump nonlinear systems is considered. The purpose of the paper is to design mode-dependent and mode-independent filters, such that the dynamics of the filtering errors are stochastic integral input-to-state stable with H∞ performance index. Using the linear matrix inequality method and the Lyapunov functional method, sufficient conditions for the solution to the H∞ filtering problem are derived. Finally, three examples are proposed to illustrate the effectiveness of the given theoretical results.

  13. Explicit symplectic approximation of nonseparable Hamiltonians: Algorithm and long time performance

    NASA Astrophysics Data System (ADS)

    Tao, Molei

    2016-10-01

    Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. This article proposes for arbitrary Hamiltonians similar integrators, which are explicit, of any even order, symplectic in an extended phase space, and with pleasant long time properties. They are based on a mechanical restraint that binds two copies of phase space together. Using backward error analysis, Kolmogorov-Arnold-Moser theory, and additional multiscale analysis, an error bound of O (T δlω ) is established for integrable systems, where T ,δ ,l , and ω are, respectively, the (long) simulation time, step size, integrator order, and some binding constant. For nonintegrable systems with positive Lyapunov exponents, such an error bound is generally impossible, but satisfactory statistical behaviors were observed in a numerical experiment with a nonlinear Schrödinger equation.

  14. Geometrically Induced Nonlinearity in Materials and Structural Systems

    NASA Astrophysics Data System (ADS)

    Ebrahimi, Hamid

    For structural analysis there are three sources of nonlinear behavior. The corresponding nonlinear effects are identified by material, geometry and boundary condition nonlinearities. Here in the present work we focused on nonlinear behavior of structural systems that arises from geometry and specifically tackled three problems: nonlinearity in shell structures, nonlinearity in scale-substrate systems and nonlinearity is cellular solids. Firstly, we present a new instability that is observed in the indentation of a highly ellipsoidal shell by a horizontal plate. Above a critical indentation depth, the plate loses contact with the shell in a series of well-defined `blisters' along the long axis of the ellipsoid. We characterize the onset of this instability and explain it using scaling arguments, numerical simulations and experiments. We also characterize the properties of the blistering pattern by showing how the number of blisters and their size depend on both the geometrical properties of the shell and the indentation but not on the shell's elastic modulus. This blistering instability may be used to determine the thickness of highly ellipsoidal shells simply by squashing them between two plates. For the second problem, we investigate the nonlinear mechanical effects of biomimetic scale like attachments on the behavior of an elastic substrate brought about by the contact interaction of scales in pure bending using qualitative experiments, analytical models and detailed finite element analysis. Our results reveal the existence of three distinct kinematic phases of operation spanning linear, nonlinear and rigid behavior driven by kinematic interactions of scales. The response of the modified elastic beam strongly depends on the size and spatial overlap of rigid scales. The nonlinearity is perceptible even in relatively small strain regime and without invoking material level complexities of either the scales or the substrate. And lastly, we develop a new class of two

  15. 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.

  16. Federated nonlinear predictive filtering for the gyroless attitude determination system

    NASA Astrophysics Data System (ADS)

    Zhang, Lijun; Qian, Shan; Zhang, Shifeng; Cai, Hong

    2016-11-01

    This paper presents a federated nonlinear predictive filter (NPF) for the gyroless attitude determination system with star sensor and Global Positioning System (GPS) sensor. This approach combines the good qualities of both the NPF and federated filter. In order to combine them, the equivalence relationship between the NPF and classical Kalman filter (KF) is demonstrated from algorithm structure and estimation criterion. The main features of this approach include a nonlinear predictive filtering algorithm to estimate uncertain model errors and determine the spacecraft attitude by using attitude kinematics and dynamics, and a federated filtering algorithm to process measurement data from multiple attitude sensors. Moreover, a fault detection and isolation algorithm is applied to the proposed federated NPF to improve the estimation accuracy even when one sensor fails. Numerical examples are given to verify the navigation performance and fault-tolerant performance of the proposed federated nonlinear predictive attitude determination algorithm.

  17. 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.

  18. Frequency bands of strongly nonlinear homogeneous granular systems.

    PubMed

    Lydon, Joseph; Jayaprakash, K R; Ngo, Duc; Starosvetsky, Yuli; Vakakis, Alexander F; Daraio, Chiara

    2013-07-01

    Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [Jayaprakash, Starosvetsky, Vakakis, Peeters, and Kerschen, Nonlinear Dyn. 63, 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in "sonic vacua." Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB. PMID:23944453

  19. 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.

  20. Dual variational principles for nonlinear traveling waves in multifluid plasmas

    SciTech Connect

    Webb, G. M.; McKenzie, J. F.; Mace, R. L.; Ko, C. M.; Zank, G. P.

    2007-08-15

    A Hamiltonian description of nonlinear, obliquely propagating traveling waves in a charge neutral, electron-proton, multifluid plasma is developed. The governing equations are written as a dual spatial Hamiltonian system. In the first formulation, the Hamiltonian is identified with the longitudinal, x-momentum flux integral P{sub x}=const, in which the energy integral {epsilon}={epsilon}{sub 0} acts as a constraint, and the Hamiltonian evolution operator is d/dx, where x is the position coordinate in the wave frame. In the second Hamiltonian formulation, the Hamiltonian is proportional to the conserved energy integral {epsilon}, in which the momentum integral P{sub x}=const acts as a constraint, and the Hamiltonian evolution operator d/d{tau}=u{sub x}d/dx is the Lagrangian time derivative where u{sub x} is the x component of the electron and proton fluids. The analysis is facilitated by using the de Hoffman-Teller frame of magnetohydrodynamic shock theory to simplify the transverse electron and proton momentum equations. The system is exactly integrable in cases in which the total transverse momentum fluxes of the system are zero in the de Hoffman-Teller frame. The implications of this constraint for the Alfven Mach number of the traveling wave are discussed. The physical conditions for the formation of whistler oscillitons based on the whistler dispersion equation are discussed.

  1. 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.

  2. 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.

  3. 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.

  4. Exciton-polaritons in lattices: A non-linear photonic simulator

    NASA Astrophysics Data System (ADS)

    Amo, Alberto; Bloch, Jacqueline

    2016-10-01

    Microcavity polaritons are mixed light-matter quasiparticles with extraordinary nonlinear properties, which can be easily accessed in photoluminescence experiments. Thanks to the possibility of designing the potential landscape of polaritons, this system provides a versatile photonic platform to emulate 1D and 2D Hamiltonians. Polaritons allow transposing to the photonic world some of the properties of electrons in solid-state systems, and to engineer Hamiltonians for photons with novel transport properties. Here we review some experimental implementations of polariton Hamiltonians using lattice geometries.

  5. 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.

  6. 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

  7. Turing instability in reaction-diffusion systems with nonlinear diffusion

    NASA Astrophysics Data System (ADS)

    Zemskov, E. P.

    2013-10-01

    The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

  8. Turing instability in reaction-diffusion systems with nonlinear diffusion

    SciTech Connect

    Zemskov, E. P.

    2013-10-15

    The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

  9. Nonlinear optical systems based on fullerene-containing media

    NASA Astrophysics Data System (ADS)

    Belousova, Inna M.; Belousov, Vlidilen P.; Bespalov, Victor G.; Grigorev, V. A.; Danilov, Oleg B.; Zevlakov, A. P.; Zgonnick, V. N.; Kalintsev, Alexander G.; Kris'ko, A. V.; Mironova, N. G.; Sosnov, Eugene N.; Ponomarev, Alexander N.

    2000-03-01

    We present the results of theoretical and experimental studies on creation of nonlinear optical systems on a base of fullerene-containing media: power radiation limiters, photorefractive media for dynamic hologram recording, and devices for controlling spatial and temporal parameters of radiation.

  10. 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.

  11. Non-linear Systems and Educational Development in Europe.

    ERIC Educational Resources Information Center

    Reilly, David H.

    1999-01-01

    European educational systems are under immense pressure to change, develop, improve, and satisfy many conflicting demands. Educational development and improvement in these countries is unlikely to progress in a neat, orderly, and linear fashion. Applying nonlinear (chaos) theory to development theory may aid understanding of educational…

  12. Identifying approximate linear models for simple nonlinear systems

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

    This paper addresses the identification (realization) of approximate linear models from response data for certain nonlinear dynamic systems. Response characteristics for several typical nonlinear joints are analyzed mathematically and represented by series expansions. The parameters of the series expansion are then compared with the modal parameters of a linear model identified by the Eigensystem Realization Algorithm. The agreement of the identified model and the analytically derived representation is excellent for the cases studied. Also laboratory data from a model which exhibited stiffening behavior was analyzed using the Eigensystem Realization algorithm and Fast Fourier Transform. The laboratory experiment demonstrated the ability of the technique to recover the model characteristics using real data.

  13. 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.

  14. 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.

  15. Robust Decentralized Nonlinear Control for a Twin Rotor MIMO System

    PubMed Central

    Belmonte, Lidia María; Morales, Rafael; Fernández-Caballero, Antonio; Somolinos, José Andrés

    2016-01-01

    This article presents the design of a novel decentralized nonlinear multivariate control scheme for an underactuated, nonlinear and multivariate laboratory helicopter denominated the twin rotor MIMO system (TRMS). The TRMS is characterized by a coupling effect between rotor dynamics and the body of the model, which is due to the action-reaction principle originated in the acceleration and deceleration of the motor-propeller groups. The proposed controller is composed of two nested loops that are utilized to achieve stabilization and precise trajectory tracking tasks for the controlled position of the generalized coordinates of the TRMS. The nonlinear internal loop is used to control the electrical dynamics of the platform, and the nonlinear external loop allows the platform to be perfectly stabilized and positioned in space. Finally, we illustrate the theoretical control developments with a set of experiments in order to verify the effectiveness of the proposed nonlinear decentralized feedback controller, in which a comparative study with other controllers is performed, illustrating the excellent performance of the proposed robust decentralized control scheme in both stabilization and trajectory tracking tasks. PMID:27472338

  16. Tracer experiment design for unique identification of nonlinear physiological systems.

    PubMed

    DiStefano, J J

    1976-02-01

    The design of tracer kinetic experiments, the purpose of which is to elucidate uniquely the internal couplings of a nonlinear dynamic system, is considered for a practical class of models of physiological systems. The extent of information about the real system contained in tracer kinetic data is a central issue. Criteria for determining whether nonlinear model parameters can be estimated from small-signal, "linearizing" tracer experiments are developed and illustrated by examples. The concept of "structural identifiability" is employed in this analysis to determine which model parameters can be and which cannot be determined "uniquely" from given input-output data; a step-by-step procedure based on an extension of this concept is presented for adapting the overall approach to the experimental design problem. Estimation of unmeasurable endogenous inputs and system state variables, problems that are intimately related to parameter estimation for physiological systems, are also considered. PMID:1259027

  17. 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.

  18. Nonlinear dynamics and quantum entanglement in optomechanical systems.

    PubMed

    Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

    2014-03-21

    To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.

  19. 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.

  20. 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

  1. Nonlinear gyrokinetic equations for tokamak microturbulence

    SciTech Connect

    Hahm, T.S.

    1988-05-01

    A nonlinear electrostatic gyrokinetic Vlasov equation, as well as Poisson equation, has been derived in a form suitable for particle simulation studies of tokamak microturbulence and associated anomalous transport. This work differs from the existing nonlinear gyrokinetic theories in toroidal geometry, since the present equations conserve energy while retaining the crucial linear and nonlinear polarization physics. In the derivation, the action-variational Lie perturbation method is utilized in order to preserve the Hamiltonian structure of the original Vlasov-Poisson system. Emphasis is placed on the dominant physics of the collective fluctuations in toroidal geometry, rather than on details of particle orbits. 13 refs.

  2. 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.

  3. Covariant hamiltonian spin dynamics in curved space-time

    NASA Astrophysics Data System (ADS)

    d'Ambrosi, G.; Satish Kumar, S.; van Holten, J. W.

    2015-04-01

    The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.

  4. 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.

  5. Nonlinear system vibration---The appearance of chaos

    SciTech Connect

    Hunter, N.F. Jr.

    1990-01-01

    This paper begins with an examination of the differential equation for a single degree of freedom force excited oscillator and considers the state space behavior of linear, nonlinear, and chaotic single degree of freedom systems. The fundamental characteristics of classical chaos are reviewed: sensitivity to initial conditions, positive Lyapunov exponents, complex Poincare maps, fractal properties of motion in the state space, and broadening of the power spectrum of the system response. Illustrated examples of chaotic behavior include motion in a two well potential -- the chaos beam described in Moon and a hardening base excited Duffing system. Chaos-like phenomenon which occur with nonperiodic forcing are examined in the context of the two well potential and hardening Duffing systems. The paper concludes with some suggestions for detecting and modelling nonlinear or chaotic behavior. 19 refs., 19 figs.

  6. Stable Inversion for Nonlinear Nonminimum-Phase Time Varying Systems

    NASA Technical Reports Server (NTRS)

    Devasia, S.; Paden, B.

    1998-01-01

    In this paper, we extend stable inversion to nonlinear time-varying systems and study computational issues; the technique is applicable to minimum-phase as well as nonminimum-phase systems. The inversion technique is new, even in the linear time-varying case, and relies on partitioning (the dichotomic split of) the linearized system dynamics into time-varying, stable, and unstable, submanifolds. This dichotomic split is used to build time-varying filters which are, in turn, the basis of a contraction used to find a bounded inverse input-state trajectory. Finding the inverse input-state trajectory allows the development or exact-output tracking controllers. The method is local to the time-varying trajectory and requires that the internal dynamics vary slowly; however, the method represents a significant advance relative to presently available tracking controllers. Present techniques are restricted to time-invariant nonlinear systems and, in the general case, track only asymptotically.

  7. Robust nonlinear system identification using neural-network models.

    PubMed

    Lu, S; Basar, T

    1998-01-01

    We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the persistency of excitation condition inherent to the standard schemes in the neural identification literature. This difficulty is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained by Didinsky et al. We show how these algorithms can be exploited to successfully identify the nonlinearity in the system using neural-network models. By embedding the original problem in one with noise-perturbed state measurements, we present a class of identifiers (under L1 and L2 cost criteria) which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. In this respect, many available learning algorithms in the current neural-network literature, e.g., the backpropagation scheme and the genetic algorithms-based scheme, with slight modifications, can ensure the identification of the system nonlinearity. Subsequently, we address the same problem under a third, worst case L(infinity) criterion for an RBF modeling. We present a neural-network version of an H(infinity)-based identification algorithm from Didinsky et al and show how, along with an appropriate choice of control input to enhance excitation, under both full-state-derivative information (FSDI) and noise-perturbed full-state-information (NPFSI), it leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the nonlinearity. Results from several simulation studies have been included to demonstrate the effectiveness of these algorithms.

  8. Robust Stabilization of a Class of passive Nonlinear Systems

    NASA Technical Reports Server (NTRS)

    Joshi, Suresh M.; Kelkar, Atul G.

    1996-01-01

    The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.

  9. Diffusive limits of nonlinear hyperbolic systems with variable coefficients

    NASA Astrophysics Data System (ADS)

    Miyoshi, Hironari; Tsutsumi, Masayoshi

    2016-09-01

    We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.

  10. Reduced-size kernel models for nonlinear hybrid system identification.

    PubMed

    Le, Van Luong; Bloch, Grard; Lauer, Fabien

    2011-12-01

    This brief paper focuses on the identification of nonlinear hybrid dynamical systems, i.e., systems switching between multiple nonlinear dynamical behaviors. Thus the aim is to learn an ensemble of submodels from a single set of input-output data in a regression setting with no prior knowledge on the grouping of the data points into similar behaviors. To be able to approximate arbitrary nonlinearities, kernel submodels are considered. However, in order to maintain efficiency when applying the method to large data sets, a preprocessing step is required in order to fix the submodel sizes and limit the number of optimization variables. This brief paper proposes four approaches, respectively inspired by the fixed-size least-squares support vector machines, the feature vector selection method, the kernel principal component regression and a modification of the latter, in order to deal with this issue and build sparse kernel submodels. These are compared in numerical experiments, which show that the proposed approach achieves the simultaneous classification of data points and approximation of the nonlinear behaviors in an efficient and accurate manner.

  11. 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.

  12. 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).

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. 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.

  2. 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.

  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. 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.

  5. 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.

  6. Spatial nonlinearities: Cascading effects in the earth system

    USGS Publications Warehouse

    Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, S.; Havstad, K. M.

    2006-01-01

    Nonlinear interactions and feedbacks associated with thresholds through time and across space are common features of biological, physical and materials systems. These spatial nonlinearities generate surprising behavior where dynamics at one scale cannot be easily predicted based on information obtained at finer or broader scales. These cascading effects often result in severe consequences for the environment and human welfare (i.e., catastrophes) that are expected to be particularly important under conditions of changes in climate and land use. In this chapter, we illustrate the usefulness of a general conceptual and mathematical framework for understanding and forecasting spatially nonlinear responses to global change. This framework includes cross-scale interactions, threshold behavior and feedback mechanisms. We focus on spatial nonlinearities produced by fine-scale processes that cascade through time and across space to influence broad spatial extents. Here we describe the spread of catastrophic events in the context of our cross-disciplinary framework using examples from biology (wildfires, desertification, infectious diseases) and engineering (structural failures) and discuss the consequences of applying these ideas to forecasting future dynamics under a changing global environment.

  7. Non-linear HRV indices under autonomic nervous system blockade.

    PubMed

    Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel

    2014-01-01

    Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.

  8. 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.

  9. 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

  10. Blow-up of the solution of a nonlinear system of equations with positive energy

    NASA Astrophysics Data System (ADS)

    Korpusov, M. O.

    2012-06-01

    We consider the Dirichlet problem for a nonlinear system of equations, continuing our study of nonlinear hyperbolic equations and systems of equations with an arbitrarily large positive energy. We use a modified Levine method to prove the blow-up.

  11. 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.

  12. Modeling and identification of parallel and feedback nonlinear systems

    SciTech Connect

    Chen, Hai-Wen

    1994-10-01

    Structural classification and parameter estimation (SCPE) methods have been used for studying single-input single. output (SISO) parallel and feedback nonlinear system models from input-output (I-O) measurements. The uniqueness of the I-O mappings of different models and parameter uniqueness of the I-O mapping of a given structural model are evaluated. The former aids in defining the conditions under which different model structures may be differentiated from one another. The latter defines the conditions under which a given model parameter can be uniquely estimated from I-O measurements. SCPE methods presented in this paper can be further developed to study more complicated multi-input multi-output (MIMO) block-structured models which will provide useful techniques for modeling and identifying highly complex nonlinear systems.

  13. Nonlinear formulation for flexible multibody system with large deformation

    NASA Astrophysics Data System (ADS)

    Liu, Jinyang; Hong, Jiazhen

    2007-02-01

    In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.

  14. Diagnosis of nonlinear systems using kernel principal component analysis

    NASA Astrophysics Data System (ADS)

    Kallas, M.; Mourot, G.; Maquin, D.; Ragot, J.

    2014-12-01

    Technological advances in the process industries during the past decade have resulted in increasingly complicated processes, systems and products. Therefore, recent researches consider the challenges in their design and management for successful operation. While principal component analysis (PCA) technique is widely used for diagnosis, its structure cannot describe nonlinear related variables. Thus, an extension to the case of nonlinear systems is presented in a feature space for process monitoring. Working in a high-dimensional feature space, it is necessary to get back to the original space. Hence, an iterative pre-image technique is derived to provide a solution for fault diagnosis. The relevance of the proposed technique is illustrated on artificial and real dataset.

  15. On-line estimation of nonlinear physical systems

    USGS Publications Warehouse

    Christakos, G.

    1988-01-01

    Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm 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. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared. ?? 1988 International Association for Mathematical Geology.

  16. 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.

  17. 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.

  18. Nonlinear closed-loop control system for intracranial pressure regulation.

    PubMed

    Coté, G L; Durai, R; Zoghi, B

    1995-01-01

    A nonlinear closed-loop control system with flat pressure-versus-flow characteristics that is aimed at regulating intracranial pressure (ICP) by adjusting the volume of cerebral spinal fluid (CSF) was designed, built, and tested. The control system design allows both the pressure setpoint and hysteresis to be adjusted to overcome the difficulties inherent in differential pressure-activated, fixed resistance, open-loop shunts. A dynamic six-compartment bench-top fluid system, which mimics the cerebral spinal fluid system, was designed, built, and tested. A computer simulation was developed which included the nonlinear on-off controller with hysteresis and a sixth-order, linear, multicompartmental model of the CSF system. The computer model and in vitro system results showed the ability of the system to track and compensate for pressure variations above and below normal as well as for spurious outputs that mimic such in vivo problems as blood pressure changes, sneezing, or coughing. There was one discrepancy between the simulated and in vitro results. The in vitro system had a higher rate of increase in pressure due to the more rigid compliance of the materials used, whereas the computer model compliance, based on the basal in vivo compliance of the CSF system, was less rigid. Based on these findings, the controller was modified to account for short-duration, extremely elevated pressures. PMID:8572426

  19. 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.

  20. 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.

  1. Noise and nonlinearities in digital magnetic recording systems

    NASA Astrophysics Data System (ADS)

    Xing, Xinzhi

    1998-11-01

    Various types of noise and nonlinearities in digital magnetic recording systems are investigated in this dissertation. Measurement techniques and analyzing methods are developed to understand each phenomenon. The nonlinearities due to the replay process using MR sensors are studied in Chapter 4. The nonlinearities are determined by comparing the measured signal with that obtained from a linear analysis. A characterization method of transition noise is developed in Chapter 5. Approximating transition noise by several leading 'modes' allows the noise parameters to be determined experimentally. Chapter 6 covers the investigation of disk substrate texture induced noise. The noise mechanism and characteristics are systematically studied. An analytical noise correlation function that directly relates the noise with the fluctuations of the textured disk surface is also developed in this chapter. An error rate model including colored and nonstationary noise is developed to further understand the impact of noise on system performance in Chapter 7. Noise with different characteristics is shown to influence the system performance differently. In addition, the influence of texture noise is examined in term of each noise parameter based upon the noise model developed in Chapter 6. Finally, in Chapter 8, the effect of finite write field rise time on recording performance is studied. Recording performance predicted by a simplified analytical model is compared with the measurements. It is shown that a slow flux rise time causes a degraded field gradient during writing, which results in a broader written transition, a larger NLTS, and noisier transition boundaries.

  2. Multicomponent Nonlinear Systems of Bose-Fermi Fields: Exact Solutions

    SciTech Connect

    Kostov, Nikolay A.; Gerdjikov, Vladimir S.; Valchev, Tihomir I.

    2011-04-07

    We present families of stationary solutions for a multicomponent nonlinear system of two boson and N{sub f} fermion fields in terms of elliptic functions of modulus k. This system is an extention of models, describing Bose-Fermi mixtures in the mean field approximation. We also single out the particular cases when the quasiperiodic solutions become periodic ones. In the limit of sinusoidal external potential (k{yields}0) our solutions model periodic waves trapped in an optical lattice. The other limit k{yields}1 provides solutions expressed by hyperbolic functions (vector solitons). Thus we demonstrate that our system describes quasi-periodic and periodic waves, as well as solitons.

  3. Continuous decomposition of quantum measurements via Hamiltonian feedback

    NASA Astrophysics Data System (ADS)

    Florjanczyk, Jan; Brun, Todd A.

    2015-12-01

    We characterize the set of generalized quantum measurements that can be decomposed into a continuous measurement process using a stream of probe qubits and a tunable interaction Hamiltonian. Each probe in the stream interacts weakly with the target quantum system and then is measured projectively in a standard basis. This measurement result is used in a closed feedback loop to tune the interaction Hamiltonian for the next probe. The resulting evolution is a stochastic process with the structure of a one-dimensional random walk. To maintain this structure and require that at long times the measurement outcomes be independent of the path, the allowed interaction Hamiltonians must lie in a restricted set such that the Hamiltonian terms on the target system form a finite-dimensional Jordan algebra. This algebraic structure of the interaction Hamiltonians yields a large class of generalized measurements that can be continuously performed by our scheme and we fully describe this set.

  4. 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.

  5. Bifurcations and safe regions in open Hamiltonians

    NASA Astrophysics Data System (ADS)

    Barrio, R.; Blesa, F.; Serrano, S.

    2009-05-01

    By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.

  6. A Hamiltonian approach to Thermodynamics

    NASA Astrophysics Data System (ADS)

    Baldiotti, M. C.; Fresneda, R.; Molina, C.

    2016-10-01

    In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac's theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases.

  7. 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.

  8. Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.

    PubMed

    Nagarale, Ravindrakumar M; Patre, B M

    2014-05-01

    This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.

  9. Reinforcement learning to adaptive control of nonlinear systems.

    PubMed

    Hwang, Kao-Shing; Tan, S W; Tsai, Min-Cheng

    2003-01-01

    Based on the feedback linearization theory, this paper presents how a reinforcement learning scheme that is adopted to construct artificial neural networks (ANNs) can linearize a nonlinear system effectively. The proposed reinforcement linearization learning system (RLLS) consists of two sub-systems: The evaluation predictor (EP) is a long-term policy selector, and the other is a short-term action selector composed of linearizing control (LC) and reinforce predictor (RP) elements. In addition, a reference model plays the role of the environment, which provides the reinforcement signal to the linearizing process. The RLLS thus receives reinforcement signals to accomplish the linearizing behavior to control a nonlinear system such that it can behave similarly to the reference model. Eventually, the RLLS performs identification and linearization concurrently. Simulation results demonstrate that the proposed learning scheme, which is applied to linearizing a pendulum system, provides better control reliability and robustness than conventional ANN schemes. Furthermore, a PI controller is used to control the linearized plant where the affine system behaves like a linear system.

  10. Autonomous Navigation System Using a Fuzzy Adaptive Nonlinear H∞ Filter

    PubMed Central

    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 (δi) and adaptive disturbance attenuation (γ), 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

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

    PubMed

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

    2014-09-19

    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.

  12. 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.

  13. 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

  14. Digit replacement: A generic map for nonlinear dynamical systems

    NASA Astrophysics Data System (ADS)

    García-Morales, Vladimir

    2016-09-01

    A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.

  15. Nonlinear problems of complex natural systems: Sun and climate dynamics.

    PubMed

    Bershadskii, A

    2013-01-13

    The universal role of the nonlinear one-third subharmonic resonance mechanism in generation of strong fluctuations in complex natural dynamical systems related to global climate is discussed using wavelet regression detrended data. The role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Niño phenomenon have been discussed in detail. The large fluctuations in the reconstructed temperature on millennial time scales (Antarctic ice core data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to the Earth's precession effect on the energy that the intertropical regions receive from the Sun. The effects of galactic turbulence on the temperature fluctuations are also discussed. PMID:23185052

  16. General formalism for singly thermostated Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    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.

  17. 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.

  18. A minimum time control algorithm for linear and nonlinear systems

    NASA Technical Reports Server (NTRS)

    Wen, J.; Desrochers, A. A.

    1985-01-01

    The minimum time control problem with bounded control has long been of interest to control engineers. Much of the theoretical study of this problem has been limited to linear systems and the results are usually problem-specific. This paper presents a new computational method for solving the minimum-time control problem when the control action is assumed to be bang-bang. A gradient-based algorithm is developed where the switching times are updated to minimize the final state missed distance. The algorithm is applicable to linear and nonlinear problems, including multi-input systems.

  19. 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.

  20. 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.

  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. 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

  3. 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

  4. Hybrid fault diagnosis of nonlinear systems using neural parameter estimators.

    PubMed

    Sobhani-Tehrani, E; Talebi, H A; Khorasani, K

    2014-02-01

    This paper presents a novel integrated hybrid approach for fault diagnosis (FD) of nonlinear systems taking advantage of both the system's mathematical model and the adaptive nonlinear approximation capability of computational intelligence techniques. Unlike most FD techniques, the proposed solution simultaneously accomplishes fault detection, isolation, and identification (FDII) within a unified diagnostic module. At the core of this solution is a bank of adaptive neural parameter estimators (NPEs) associated with a set of single-parameter fault models. The NPEs continuously estimate unknown fault parameters (FPs) that are indicators of faults in the system. Two NPE structures, series-parallel and parallel, are developed with their exclusive set of desirable attributes. The parallel scheme is extremely robust to measurement noise and possesses a simpler, yet more solid, fault isolation logic. In contrast, the series-parallel scheme displays short FD delays and is robust to closed-loop system transients due to changes in control commands. Finally, a fault tolerant observer (FTO) is designed to extend the capability of the two NPEs that originally assumes full state measurements for systems that have only partial state measurements. The proposed FTO is a neural state estimator that can estimate unmeasured states even in the presence of faults. The estimated and the measured states then comprise the inputs to the two proposed FDII schemes. Simulation results for FDII of reaction wheels of a three-axis stabilized satellite in the presence of disturbances and noise demonstrate the effectiveness of the proposed FDII solutions under partial state measurements.

  5. Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems.

    PubMed

    Wang, Chi-Hsu; Lin, Tsung-Chih; Lee, Tsu-Tian; Liu, Han-Leih

    2002-01-01

    A new hybrid direct/indirect adaptive fuzzy neural network (FNN) controller with a state observer and supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which can be adjusted by the tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive FNN controller and direct adaptive FNN controller. Furthermore, a supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be deactivated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Two nonlinear systems, namely, inverted pendulum system and Chua's (1989) chaotic circuit, are fully illustrated to track sinusoidal signals. The resulting hybrid direct/indirect FNN control systems show better performances, i.e., tracking error and control effort can be made smaller and it is more flexible during the design process.

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

    PubMed

    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. PMID:24229267

  7. 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.

  8. Nonlinear Information Processing in a Model Sensory System

    PubMed Central

    Chacron, Maurice J.

    2016-01-01

    Understanding the mechanisms by which sensory neurons encode and decode information remains an important goal in neuroscience. We quantified the performance of optimal linear and nonlinear encoding models in a well-characterized sensory system: the electric sense of weakly electric fish. We show that linear encoding models generally perform better under spatially localized stimulation than under spatially diffuse stimulation. Through pharmacological blockade of feedback input and spatial saturation of the receptive field center, we show that there is significantly less synaptic noise under spatially diffuse stimuli as compared with spatially localized stimuli. Modeling results suggest that pyramidal cells nonlinearly encode sensory information through shunting in their dendrites and clarify the influence of synaptic noise on the performance of linear encoding models. Finally, we used information theory to quantify the performance of linear decoders. While the optimal linear decoder for spatially localized stimuli could capture 60% of the information in pyramidal cell spike trains, the optimal linear decoder for spatially diffuse stimuli could only capture 40% of the information. These results show that nonlinear decoders are necessary to fully access information in pyramidal cell spike trains, and we discuss potential mechanisms by which higher-order neurons could decode this information. PMID:16495358

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

    SciTech Connect

    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].

  10. 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.

  11. 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.

  12. Linear theory for filtering nonlinear multiscale systems with model error

    PubMed Central

    Berry, Tyrus; Harlim, John

    2014-01-01

    In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure

  13. Hamiltonian structure of propagation equations for ultrashort optical pulses

    SciTech Connect

    Amiranashvili, Sh.; Demircan, A.

    2010-07-15

    A Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium. To this end a second-order nonlinear wave equation for the electric field is transformed into a first-order propagation equation for a suitably defined complex electric field. The Hamiltonian formulation is then introduced in terms of normal variables, i.e., classical complex fields referring to the quantum creation and annihilation operators. The derived z-propagated Hamiltonian accounts for forward and backward waves, arbitrary medium dispersion, and four-wave mixing processes. As a simple application we obtain integrals of motion for the pulse propagation. The integrals reflect time-averaged fluxes of energy, momentum, and photons transferred by the pulse. Furthermore, pulses in the form of stationary nonlinear waves are considered. They yield extremal values of the momentum flux for a given energy flux. Simplified propagation equations are obtained by reduction of the Hamiltonian. In particular, the complex electric field reduces to an analytic signal for the unidirectional propagation. Solutions of the full bidirectional model are numerically compared to the predictions of the simplified equation for the analytic signal and to the so-called forward Maxwell equation. The numerics is effectively tested by examining the conservation laws.

  14. 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.

  15. Lotka-Volterra representation of general nonlinear systems.

    PubMed

    Hernández-Bermejo, B; Fairén, V

    1997-02-01

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

  16. Lessons from the quantum control landscape: Robust optimal control of quantum systems and optimal control of nonlinear Schrodinger equations

    NASA Astrophysics Data System (ADS)

    Hocker, David Lance

    The control of quantum systems occurs across a broad range of length and energy scales in modern science, and efforts have demonstrated that locating suitable controls to perform a range of objectives has been widely successful. The justification for this success arises from a favorable topology of a quantum control landscape, defined as a mapping of the controls to a cost function measuring the success of the operation. This is summarized in the landscape principle that no suboptimal extrema exist on the landscape for well-suited control problems, explaining a trend of successful optimizations in both theory and experiment. This dissertation explores what additional lessons may be gleaned from the quantum control landscape through numerical and theoretical studies. The first topic examines the experimentally relevant problem of assessing and reducing disturbances due to noise. The local curvature of the landscape is found to play an important role on noise effects in the control of targeted quantum unitary operations, and provides a conceptual framework for assessing robustness to noise. Software for assessing noise effects in quantum computing architectures was also developed and applied to survey the performance of current quantum control techniques for quantum computing. A lack of competition between robustness and perfect unitary control operation was discovered to fundamentally limit noise effects, and highlights a renewed focus upon system engineering for reducing noise. This convergent behavior generally arises for any secondary objective in the situation of high primary objective fidelity. The other dissertation topic examines the utility of quantum control for a class of nonlinear Hamiltonians not previously considered under the landscape principle. Nonlinear Schrodinger equations are commonly used to model the dynamics of Bose-Einstein condensates (BECs), one of the largest known quantum objects. Optimizations of BEC dynamics were performed in which the

  17. Directing nonlinear dynamic systems to any desired orbit

    SciTech Connect

    Zonghua, L. |; Shigang, C.

    1997-01-01

    A method of controlling arbitrary nonlinear dynamic systems, dx/dt=F(x,t) (x{element_of}R{sup n}), is presented. It is proved that the system can be entrained to any arbitrary {open_quotes}goal{close_quotes} dynamics g(t) by use of the open-loop action and adjusting the control parameter at the same time. Examples of some entrainment {open_quotes}goals{close_quotes} are given for the Lorenz and the R{umlt o}ssler systems. The basins of entrainment are also established for the Lorenz, R{umlt o}ssler, and Duffing systems. Numerical studies show that this method works as well as the closed-loop control method [Physica D {bold 85}, 1 (1995); Phys. Lett. A {bold 213}, 148 (1996)]. {copyright} {ital 1997} {ital The American Physical Society}

  18. 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.

  19. Sustained small oscillations in nonlinear control systems. [launch vehicle dynamics

    NASA Technical Reports Server (NTRS)

    George, J. H.; Gunderson, R. W.; Hahn, H.

    1975-01-01

    Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.

  20. 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.

  1. M-MRAC for Nonlinear Systems with Bounded Disturbances

    NASA Technical Reports Server (NTRS)

    Stepanyan, Vahram; Krishnakumar, Kalmanje

    2011-01-01

    This paper presents design and performance analysis of a modified reference model MRAC (M-MRAC) architecture for a class of multi-input multi-output uncertain nonlinear systems in the presence of bounded disturbances. M-MRAC incorporates an error feedback in the reference model definition, which allows for fast adaptation without generating high frequency oscillations in the control signal, which closely follows the certainty equivalent control signal. The benefits of the method are demonstrated via a simulation example of an aircraft's wing rock motion.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. Nonlinear natural engine: Model for thermodynamic processes in mesoscale systems

    PubMed Central

    Wheatley, John; Buchanan, D. S.; Swift, G. W.; Migliori, A.; Hofler, T.

    1985-01-01

    To develop intuition on the possible application of concepts from thermodynamic heat engines to mesoscale systems, we have constructed and studied a model thermoacoustic heat engine. The model consists of a chain of coupled nonlinear acoustic vibrators in which the primary thermodynamic medium is argon gas, the secondary thermodynamic medium is constituted by solids bounding the gas, and frequencies are ca. 3 × 102 Hz. The nonlinear elements are the necks, made flexible by means of an oil-loaded DuPont Kapton film, of Helmholtz resonators. When the primary medium is driven uniformly by an acoustic driver at a frequency somewhat below the low-amplitude resonant frequency and at a high enough driving amplitude, stationary localized or solitary states appear irreversibly on the chain. These are characterized by a higher vibrational amplitude than that in surrounding vibrators, where the amplitude can decrease; by the appearance of deep subharmonics of the drive frequency, corresponding to driven low-frequency vibrations of the Kapton film-oil systems; and by the pumping of heat toward the localized states. Possible implications of these results for mesoscale systems consisting of chains of molecular vibrators are then discussed. Images PMID:16593625

  9. 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.

  10. 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.

  11. Hamiltonian gadgets with reduced resource requirements

    NASA Astrophysics Data System (ADS)

    Cao, Yudong; Babbush, Ryan; Biamonte, Jacob; Kais, Sabre

    2015-01-01

    Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental systems are typically limited to restricted forms of two-body interactions. Therefore, universal adiabatic quantum computation requires a method for approximating quantum many-body Hamiltonians up to arbitrary spectral error using at most two-body interactions. Hamiltonian gadgets, introduced around a decade ago, offer the only current means to address this requirement. Although the applications of Hamiltonian gadgets have steadily grown since their introduction, little progress has been made in overcoming the limitations of the gadgets themselves. In this experimentally motivated theoretical study, we introduce several gadgets which require significantly more realistic control parameters than similar gadgets in the literature. We employ analytical techniques which result in a reduction of the resource scaling as a function of spectral error for the commonly used subdivision, three- to two-body and k -body gadgets. Accordingly, our improvements reduce the resource requirements of all proofs and experimental proposals making use of these common gadgets. Next, we numerically optimize these gadgets to illustrate the tightness of our analytical bounds. Finally, we introduce a gadget that simulates a Y Y interaction term using Hamiltonians containing only {X ,Z ,X X ,Z Z } terms. Apart from possible implications in a theoretical context, this work could also be useful for a first experimental implementation of these key building blocks by requiring less control precision without introducing extra ancillary qubits.

  12. Stabilizing model predictive control for constrained nonlinear distributed delay systems.

    PubMed

    Mahboobi Esfanjani, R; Nikravesh, S K Y

    2011-04-01

    In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.

  13. 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.

  14. 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.

  15. Nonlinear system modeling with random matrices: echo state networks revisited.

    PubMed

    Zhang, Bai; Miller, David J; Wang, Yue

    2012-01-01

    Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the "reservoir") are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.

  16. 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.

  17. 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.

  18. Time-optimal quantum control of nonlinear two-level systems

    NASA Astrophysics Data System (ADS)

    Chen, Xi; Ban, Yue; Hegerfeldt, Gerhard C.

    2016-08-01

    Nonlinear two-level Landau-Zener type equations for systems with relevance for Bose-Einstein condensates and nonlinear optics are considered and the minimal time Tmin to drive an initial state to a given target state is investigated. Surprisingly, the nonlinearity may be canceled by a time-optimal unconstrained driving and Tmin becomes independent of the nonlinearity. For constrained and unconstrained driving explicit expressions are derived for Tmin, the optimal driving, and the protocol.

  19. A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

    NASA Astrophysics Data System (ADS)

    Dasari, Nagamalleswararao; Mondal, Wasim Raja; Zhang, Peng; Moreno, Juana; Jarrell, Mark; Vidhyadhiraja, N. S.

    2016-09-01

    The dynamical mean field theory (DMFT) has emerged as one of the most important frameworks for theoretical investigations of strongly correlated lattice models and real material systems. Within DMFT, a lattice model can be mapped onto the problem of a magnetic impurity embedded in a self-consistently determined bath. The solution of this impurity problem is the most challenging step in this framework. The available numerically exact methods such as quantum Monte Carlo, numerical renormalization group or exact diagonalization are naturally unbiased and accurate, but are computationally expensive. Thus, approximate methods, based e.g. on diagrammatic perturbation theory have gained substantial importance. Although such methods are not always reliable in various parameter regimes such as in the proximity of phase transitions or for strong coupling, the advantages they offer, in terms of being computationally inexpensive, with real frequency output at zero and finite temperatures, compensate for their deficiencies and offer a quick, qualitative analysis of the system behavior. In this work, we have developed such a method, that can be classified as a multi-orbital iterated perturbation theory (MO-IPT) to study N-fold degenerate and non degenerate Anderson impurity models. As applications of the solver, we have embedded the MO-IPT within DMFT and explored lattice models like the single orbital Hubbard model, covalent band insulator and the multi-orbital Hubbard model for density-density type interactions in different parameter regimes. The Hund's coupling effects in case of multiple orbitals is also studied. The limitations and quality of results are gauged through extensive comparison with data from the numerically exact continuous time quantum Monte Carlo method (CTQMC). In the case of the single orbital Hubbard model, covalent band insulators and non degenerate multi-orbital Hubbard models, we obtained an excellent agreement between the Matsubara self-energies of MO

  20. 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.

  1. 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.

  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. Entangling capacities of noisy two-qubit Hamiltonians

    SciTech Connect

    Bandyopadhyay, Somshubhro; Lidar, Daniel A.

    2004-07-01

    We study the limits imposed by intrinsic fluctuations in system-control parameters on the ability of two-qubit (exchange) Hamiltonians to generate entanglement, starting from arbitrary initial states. We find three classes for Gaussian and Laplacian fluctuations. For the Ising and XYZ models there are qualitatively distinct, sharp entanglement-generation transitions, while the class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement for any finite noise level. Our findings imply that exchange Hamiltonians are surprisingly robust in their ability to generate entanglement in the presence of noise, thus potentially reducing the need for quantum error correction.

  4. Nonlinear wave propagation in discrete and continuous systems

    NASA Astrophysics Data System (ADS)

    Rothos, V. M.

    2016-09-01

    In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.

  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. 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.

  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. Evidence for nonlinear capacitance in biomembrane channel system.

    PubMed

    Ghosh, S; Bera, A K; Das, S

    1999-10-01

    The electrophysiological properties of voltage-dependent anion channels from mitochondrial membrane have been studied in a bilayer membrane system. It was observed that the probability of opening of the membrane channel depends on externally applied voltage and the plot is a bell-shaped curve symmetric around probability axis. A scheme of conformational energy levels under varying externally applied voltage was formulated. Assuming that the probability follows Boltzmann distribution, we arrive at an expression of change in energy containing a separate term identical to the energy of a capacitor. This fact indicates the possibility of existence of an added capacitance due to the channel protein. Further it was shown that the aforesaid channel capacitor could be a function of voltage leading to nonlinearity. We have offered a general method of calculating nonlinear capacitance from the experimental data on opening probability of a membrane channel. In case of voltage-dependent anion channel the voltage dependence of the capacitor has a power 0.786. The results have been interpreted in view of the structural organization of the channel protein in the membrane. Our hypothesis is that the phenomenon of capacitor behaviour is a general one for membrane channels.

  10. 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.

  11. 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.

  12. 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

  13. 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.

  14. 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.

  15. 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

  16. 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

    2016-04-14

    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.

  17. 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

  18. Robust prevention of limit cycle for nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity.

    PubMed

    Wang, Yuan-Jay

    2007-10-01

    A new method is proposed to compute all feasible robust stabilizing controllers for preventing the generation of limit cycle of nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity. The describing function analysis method is employed to approximate the behaviors of the nonlinearity. The Kharitonov theorem is utilized to characterize parametric uncertainties in the linear plant and nonlinearity. Necessary conditions for limit cycles are established. Boundaries for the generation of limit cycle and boundaries for asymptotic stability are portrayed exploiting the stability equation method. The region for prescribed limit cycle behavior and the region for asymptotic stability are located. An admissible specification-oriented Kharitonov region is found directly on the controller parameter plane. The region is non-conservative and constitutes all of the feasible controller gain sets to achieve robust prevention of limit cycle for the considered uncertain nonlinear control systems. The way to tune the controller gains is suggested. Finally, for comparison purpose, two illustrative examples proposed in the literature are given to show how the proposed algorithm can be effectively applied to tune a robust controller to achieve a prescribed limit cycle behavior and accomplish robust limit cycle amplitude suppression and prevention.

  19. 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

  20. Quantum mechanical Hamiltonian models of discrete processes

    SciTech Connect

    Benioff, P.

    1981-03-01

    Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.

  1. 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

  2. Linear homotopy solution of nonlinear systems of equations in geodesy

    NASA Astrophysics Data System (ADS)

    Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.

    2010-01-01

    A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.

  3. 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

  4. 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.

  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. 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.

  7. Linear and Nonlinear Systems Analysis of the Visual System: Why does it seem so linear?

    PubMed Central

    Shapley, Robert

    2009-01-01

    Linear and nonlinear systems analysis are tools that can be used to study communication systems like the visual system. The first step of systems analysis often is to test whether or not the system is linear. Retinal pathways are surprisingly linear, and some neurons in the visual cortex also emulate linear sensory transducers. We conclude that the retinal linearity depends on specialized ribbon synapses while cortical linearity is the result of balanced excitatory and inhibitory synaptic interactions. PMID:18940193

  8. Nonlinear Silicon Waveguides for Integrated Fiber Laser Systems

    NASA Astrophysics Data System (ADS)

    Wong, Chi Yan

    Silicon-on-insulator (SOI) based photonic devices have attracted great interest from photonics community because of its compatibility with state-of-the-art CMOS fabrication processes and its potential of making energy efficient and low cost photonic integrated circuits (PICs) for high bandwidth optical interconnects and integrated optical sensors. Wavelength division multiplexing (WDM) is already widely used in optical communications and is also of interest for optical sensors, providing advantages of low cost, and high speed compared with single wavelength approach. However, the cost and the bulkiness of WDM systems increase proportionally with the number of wavelengths if conventional external laser source is used. Therefore, low cost and compact laser source with stable and high line quality is of great interest for integrated sensors. In this thesis, we investigate the incorporation of silicon photonic devices as intracavity elements in fiber lasers for various applications. Therefore, the high flexibly and rich functionalities of fiber lasers can be directly used in the PIC. Also, high-speed feedback control of the cavity becomes possible. The possibility of applying nonlinear SOI waveguides to fiber lasers is investigated. We propose and demonstrate a multiwavelength erbium-doped fiber laser stabilized by four-wave mixing (FWM) in a nonlinear SOI waveguide. Such multiwavelength lasers are potentially suitable for WDM sensing. The wavelength selectivity was achieved by an intracavity Fabry-Perot comb filter. Making use of the nonlinearity of the SOI waveguide, a multiwavelength laser with six output wavelengths at 0.8 nm spacing was achieved. We study a passive mode-locked erbium-doped fiber ring laser based on a nonlinear SOI microring resonator (MRR). By using the MRR as the comb filter and the nonlinear medium, a stable mode-locked pulse train at 100 GHz was produced by filter-driven four-wave mixing. Such lasers can act as high repetition rate optical

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. A nonlinear control method based on ANFIS and multiple models for a class of SISO nonlinear systems and its application.

    PubMed

    Zhang, Yajun; Chai, Tianyou; Wang, Hong

    2011-11-01

    This paper presents a novel nonlinear control strategy for a class of uncertain single-input and single-output discrete-time nonlinear systems with unstable zero-dynamics. The proposed method combines adaptive-network-based fuzzy inference system (ANFIS) with multiple models, where a linear robust controller, an ANFIS-based nonlinear controller and a switching mechanism are integrated using multiple models technique. It has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system. Moreover, it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance. As a result, the controller has the following three outstanding features compared with existing control strategies. First, this method relaxes the assumption of commonly-used uniform boundedness on the unmodeled dynamics and thus enhances its applicability. Second, since ANFIS is used to estimate and compensate the effect caused by the unmodeled dynamics, the convergence rate of neural network learning has been increased. Third, a "one-to-one mapping" technique is adapted to guarantee the universal approximation property of ANFIS. The proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system, respectively, where its effectiveness has been justified.

  14. 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…

  15. 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.

  16. 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...

  17. 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.

  18. Design of nonlinear observer by augmented linear system based on formal linearization using fourier expansion

    NASA Astrophysics Data System (ADS)

    Komatsu, Kazuo; Takata, Hitoshi

    2012-11-01

    In this paper, we consider an observer design by using a formal linearization based on Fourier expansion for nonlinear dynamic and measurement systems. A non-linear dynamic system is given by a nonlinear ordinary differential equation, and a measurement sysetm is done by a nonlinear equation. Defining a linearization function which consists of the trigonometric functions considered up to the higher-order, a nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function by using Fourier expansion. Introducing an augmented measurement vector which consists of polynomials of measurement data, a measurement equation is transformed into an augmented linear one with respect to the linearization function in the same way. To these augmented linearized systems, a linear estimation theory is applied to design a new non-linear observer.

  19. Robust nonlinear generalised predictive control for a class of uncertain nonlinear systems via an integral sliding mode approach

    NASA Astrophysics Data System (ADS)

    Errouissi, Rachid; Yang, Jun; Chen, Wen-Hua; Al-Durra, Ahmed

    2016-08-01

    In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.

  20. 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

  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

    Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

    2014-05-19

    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.

  3. 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

  4. 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

  5. Self-synchronization in an ensemble of nonlinear oscillators

    NASA Astrophysics Data System (ADS)

    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.

  6. 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.

  7. Neural Feedback Passivity of Unknown Nonlinear Systems via Sliding Mode Technique.

    PubMed

    Yu, Wen

    2015-07-01

    Passivity method is very effective to analyze large-scale nonlinear systems with strong nonlinearities. However, when most parts of the nonlinear system are unknown, the published neural passivity methods are not suitable for feedback stability. In this brief, we propose a novel sliding mode learning algorithm and sliding mode feedback passivity control. We prove that for a wide class of unknown nonlinear systems, this neural sliding mode control can passify and stabilize them. This passivity method is validated with a simulation and real experiment tests.

  8. Nonintegrability of the classical Zeeman Hamiltonian

    NASA Astrophysics Data System (ADS)

    Kummer, M.; Saenz, A. W.

    1994-05-01

    We prove that the Hamiltonian H of the three dimensional hydrogen atom in a uniform static magnetic field B does not have an integral which (i) is real analytic on the phase space ℳ of the system; (ii) is in involution with the component M 3 of the angular momentum along B; (iii) is functionally independent of H and M 3 and (iv) has a meromorphic (single-valued) extension to the complexification of ℳ in ℂ6;. This follows from the fact that the Hamiltonian K M of two degrees of freedom obtained by fixing M 3 at certain nonzero values M and reducing H w.r. to the rotational symmetry about the magnetic field, has a complexification which is nonintegrable in the Ziglin sense. We prove this nonintegrability by demonstrating that for each such M the monodromy group of the normal variational equation along a certain complexified phase curve of K M is not Ziglin, using Churchill and Rod's adaptation of Kovacic's algorithm to the Ziglin analysis. Analogous arguments prove that the Hamiltonian of the Størmer problem is nonintegrable in the same sense.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.

    ERIC Educational Resources Information Center

    Raw, Cecil J. G.; Stacey, Larry M.

    1989-01-01

    Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…

  19. Nonlinear behavior of coupled magnetostrictive material systems analytical/experimental

    NASA Astrophysics Data System (ADS)

    Roberts, Mark M.; Mitrovic, Milan; Carman, Gregory P.

    1995-05-01

    In this paper, we present a nonlinear constitutive relation for magnetostrictive materials that includes coupling between temperature/preload and magnetic field strengths. The nonlinear constitutive relations are also integrated into a 1-dimensional nonlinear finite element model for studying structural components or composite materials containing magnetostrictive materials. The accuracy of the nonlinear constitutive relation is evaluated by comparing experimental results obtained on a Terfenol-D rod operating under both magnetic field and stress biases with theoretical values present in the literature. Results indicate that the model adequately predicts the nonlinear strain/field relations in specific regimes. Experimental tests, conducted on monolithic samples of different geometry, suggests that size effects may be important. A manufacturing process and preliminary experimental tests are also presented for a 1 - 3 magnetostrictive composite sample.

  20. Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

    NASA Astrophysics Data System (ADS)

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

    2005-03-01

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

  1. 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.

  2. On classical mechanical systems with non-linear constraints

    NASA Astrophysics Data System (ADS)

    Terra, Gláucio; Kobayashi, Marcelo H.

    2004-03-01

    In the present work, we analyze classical mechanical systems with non-linear constraints in the velocities. We prove that the d'Alembert-Chetaev trajectories of a constrained mechanical system satisfy both Gauss' principle of least constraint and Hölder's principle. In the case of a free mechanics, they also satisfy Hertz's principle of least curvature if the constraint manifold is a cone. We show that the Gibbs-Maggi-Appell (GMA) vector field (i.e. the second-order vector field which defines the d'Alembert-Chetaev trajectories) conserves energy for any potential energy if, and only if, the constraint is homogeneous (i.e. if the Liouville vector field is tangent to the constraint manifold). We introduce the Jacobi-Carathéodory metric tensor and prove Jacobi-Carathéodory's theorem assuming that the constraint manifold is a cone. Finally, we present a version of Liouville's theorem on the conservation of volume for the flow of the GMA vector field.

  3. 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.

  4. A closed-loop identification protocol for nonlinear dynamical systems.

    PubMed

    Feng, Xiao-jiang; Rabitz, Herschel; Turinici, Gabriel; Le Bris, Claude

    2006-06-29

    A previous work introduced an optimal identification (OI) technique for reliably extracting model parameters of biochemical reaction systems from tailored laboratory experiments. The notion of optimality enters through seeking an external control in the laboratory producing data that leads to minimum uncertainties in the identified parameter distributions. A number of algorithmic and operational improvements are introduced in this paper to OI, aiming to build a more practical and efficient closed-loop identification protocol/procedure (CLIP) for nonlinear dynamical systems. The improvements in CLIP include (a) inversion cost function modification to preferably search for the upper and lower boundaries of the parameter distributions consistent with the observed data, (b) dynamic search range updating of the unknown parameters to better exploit the information from the prior iterative experiments, (c) replacing the control genetic algorithm by the simplex method to enable better balance between operational cost and inversion quality, and (d) utilizing virtual sensitivity optimization techniques to further reduce the laboratory costs. The workings of CLIP utilizing these new algorithms are illustrated in indentifying a simulated tRNA proofreading model, and the results demonstrate enhanced performance of CLIP in terms of algorithmic reliability and efficiency. PMID:16789759

  5. 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.

  6. 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.

  7. Applications to aeronautics of the theory of transformations of nonlinear systems

    NASA Technical Reports Server (NTRS)

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

    1982-01-01

    The development of the transformation theory is discussed. Results and applications concerning the use of this design technique for automatic flight control of aircraft are presented. The theory examines the transformation of nonlinear systems to linear systems. The tracking of linear models by nonlinear plants is discussed. Results of manned simulation are also presented.

  8. Global adaptive output feedback control for a class of nonlinear time-delay systems.

    PubMed

    Zhai, Jun-yong; Zha, Wen-ting

    2014-01-01

    This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.

  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. 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.

  11. 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.

  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. Model predictive control for a class of systems with isolated nonlinearity.

    PubMed

    Tao, Jili; Zhu, Yong; Fan, Qinru

    2014-07-01

    The paper is concerned with an overall convergent nonlinear model predictive control design for a kind of nonlinear mechatronic drive systems. The proposed nonlinear model predictive control results in the improvement of regulatory capacity for reference tracking and load disturbance rejection. The design of the nonlinear model predictive controller consists of two steps: the first step is to design a linear model predictive controller based on the linear part of the system at each sample instant, then an overall convergent nonlinear part is added to the linear model predictive controller to combine a nonlinear controller using error driven. The structure of the proposed controller is similar to that of classical PI optimal regulator but it also bears a set-point feed forward control loop, thus tracking ability and disturbance rejection are improved. The proposed method is compared with the results from recent literature, where control performance under both model match and mismatch cases are enlightened. PMID:24755053

  14. 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.

  15. Hamiltonian structure for two-dimensional extended Green-Naghdi equations

    NASA Astrophysics Data System (ADS)

    Matsuno, Yoshimasa

    2016-06-01

    The two-dimensional Green-Naghdi (GN) shallow-water model for surface gravity waves is extended to incorporate the arbitrary higher-order dispersive effects. This can be achieved by developing a novel asymptotic analysis applied to the basic nonlinear water wave problem. The linear dispersion relation for the extended GN system is then explored in detail. In particular, we use its characteristics to discuss the well-posedness of the linearized problem. As illustrative examples of approximate model equations, we derive a higher-order model that is accurate to the fourth power of the dispersion parameter in the case of a flat bottom topography, and address the related issues such as the linear dispersion relation, conservation laws and the pressure distribution at the fluid bottom on the basis of this model. The original Green-Naghdi (GN) model is then briefly described in the case of an uneven bottom topography. Subsequently, the extended GN system presented here is shown to have the same Hamiltonian structure as that of the original GN system. Last, we demonstrate that Zakharov's Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.

  16. 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.

  17. Hamiltonian methods for the study of polarized proton beam dynamics in accelerators and storage rings

    SciTech Connect

    Balandin, Vladimir; Golubeva, Nina

    1997-02-01

    The equations of classical spin-orbit motion can be extended to a Hamiltonian system in 9-dimensional phase space by introducing a coupled spin-orbit Poisson bracket and Hamiltonian function. After this extension it becomes possible to apply the methods of the theory of Hamiltonian systems to the study of polarized particles beam dynamics in circular accelerators and storage rings. Some of those methods have been implemented in the computer code FORGET-ME-NOT.

  18. Construction of the metric and equivalent Hermitian Hamiltonian via SUSY transformation operators

    SciTech Connect

    Shamshutdinova, V. V.

    2012-10-15

    The metric operator, which is the basic ingredient for studying a quantum system described by a pseudo-Hermitian Hamiltonian, provides the necessary means for obtaining an equivalent description of the system using a Hermitian Hamiltonian. In the framework of supersymmetric quantum mechanics, we propose a method of constructing the metric operator and to obtain the Hermitian Hamiltonian equivalent to the given pseudo-Hermitian.

  19. A modal capacity method for nonlinear dynamic analysis on transputer systems

    SciTech Connect

    Nordhues, H.W.; Woerner, J.D.

    1995-12-31

    A new method to calculate the response of nonlinear behaving systems is described. The two fundamentals of the modal capacity method are the principle of a modal capacity method are the principle of a modal reduction on the one hand and the capacity design method on the other hand. The nonlinear behavior of systems can be expressed by nonlinear modes in combination with a new superposition method. The procedure can be used either for the design of systems [Nor95] or to derive existing systems similar to the ultimate load method [WSK91]. Because of the modal reduction of the modal capacity method transputer systems can be used in a very efficient way.

  20. Intraband discrete breathers in disordered nonlinear systems. II. Localization

    NASA Astrophysics Data System (ADS)

    Kopidakis, G.; Aubry, S.

    2000-05-01

    We find spatially localized, time-periodic solutions (discrete breathers or DBs) in disordered nonlinear systems with frequency inside the linear phonon spectrum under conditions that strictly prohibit their existence in their periodic counterparts. For that purpose, we develop a new in situ method for the accurate calculation of these solutions which does not make use of any continuation from an anticontinuous limit. Using this method, we demonstrate that intraband localized modes (intraband discrete breathers or IDBs) at a given site with frequencies inside the discrete linear spectrum do exist, provided these frequencies do not belong to forbidden resonance gaps. Since there is a dense set of resonant frequencies, we illustrate numerically, in agreement with a theorem by Albanese and Fröhlich, that the localized DBs exist provided that their frequencies belong to fat Cantor sets (i.e., with finite measure). Such a set contains as accumulation points the linear frequency of the normal mode at the occupied site. We check that many of these solutions are linearly stable and conjecture that their frequency belongs to another smaller fat Cantor set. Our numerical methods provide a much wider set of exact solutions which are multisite breathers and suggest conjectures extending the existing theorems. The physical implications of the existence of IDBs and possible applications for glasses and the persistent spectral hole burning are discussed.

  1. 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.

  2. 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.

  3. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

    SciTech Connect

    Tronko, Natalia; Brizard, Alain J.

    2015-11-15

    A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.

  4. 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.

  5. Stability analysis and limit cycle in fractional system with Brusselator nonlinearities

    NASA Astrophysics Data System (ADS)

    Gafiychuk, V.; Datsko, B.

    2008-07-01

    The investigation of limit cycles in the fractional dynamical systems with Brusselator nonlinearities is considered. We present analysis of the stability domains as well as possible solutions realizing at different system parameters.

  6. Constructing Dense Graphs with Unique Hamiltonian Cycles

    ERIC Educational Resources Information Center

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  7. 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.

  8. 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

  9. A Nonlinear Lumped Model for Ultrasound Systems Using CMUT Arrays

    PubMed Central

    Satir, Sarp; Degertekin, F. Levent

    2015-01-01

    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 element based 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

  10. 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.

  11. 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

  12. Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection

    NASA Astrophysics Data System (ADS)

    Tassi, E.

    2014-11-01

    We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and drift- kinetic systems.

  13. Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

    PubMed Central

    Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

    2014-01-01

    In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293

  14. Numerical solutions of the nonlinear fractional-order brusselator system by Bernstein polynomials.

    PubMed

    Khan, Hasib; Jafari, Hossein; Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

    2014-01-01

    In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293

  15. 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.

  16. Nonabelian N = 2 superstrings: Hamiltonian structure

    NASA Astrophysics Data System (ADS)

    Isaev, A. P.; Ivanov, E. A.

    1991-04-01

    We examine the Hamiltonian structure of nonabelian N = 2 superstring models which are the supergroup manifold extensions of N = 2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type 2A Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d = 10) present a particular case of this general system corresponding to a special choice of the background.

  17. 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.

  18. 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.

  19. 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.

  20. On asymptotic completeness of scattering in the nonlinear Lamb system, II

    NASA Astrophysics Data System (ADS)

    Komech, A. I.; Merzon, A. E.

    2013-01-01

    We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ordinary differential equation) converging to a hyperbolic stationary point using the inverse function theorem in a Banach space. We give counterexamples which show nonexistence of such trajectories for nonhyperbolic stationary points.