WorldWideScience

Sample records for nonlinear vortex dynamics

  1. Nonlinear dynamics of Airy-Vortex 3D wave packets: Emission of vortex light waves

    CERN Document Server

    Driben, Rodislav

    2014-01-01

    The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Due to the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and non-zero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse, especially those having small width.

  2. Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves.

    Science.gov (United States)

    Driben, Rodislav; Meier, Torsten

    2014-10-01

    The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse.

  3. Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

    Science.gov (United States)

    Matsuoka, C.; Nishihara, K.; Sano, T.

    2016-10-01

    A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

  4. Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

    Science.gov (United States)

    Matsuoka, C.; Nishihara, K.; Sano, T.

    2017-04-01

    A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

  5. Pattern dynamics of vortex ripples in sand: Nonlinear modeling and experimental validation

    DEFF Research Database (Denmark)

    Andersen, Ken Haste; Abel, M.; Krug, J.;

    2002-01-01

    Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for homogeneous patterns. The interaction function describing the mass...

  6. Generation of nonlinear vortex precursors

    CERN Document Server

    Chen, Yue-Yue; Liu, Chengpu

    2016-01-01

    We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex har- monics are generated in the transmitted field due to ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provide a straightforward way of measuring precursors. By the virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical informa- tion and communication fields where controllable loss, large information-carrying capacity and high speed communication are required.

  7. Nonlinear Dynamics of Multi-Component Bose-Einstein Condensates ---Anti-Gravity Transport and Vortex Chaos---

    Science.gov (United States)

    Nakamura, K.

    Bose-Einstein condensate(BEC) provides a nice stage when the nonlinearSchrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom. The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass. Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance r_{ij} on short scale and logarithmic in r_{ij} on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore ``the chaos in the three-body problem" in the context of vortices with inertia.

  8. Study of vortex ring dynamics in the nonlinear Schrodinger equation utilizing GPU-accelerated high-order compact numerical integrators

    Science.gov (United States)

    Caplan, Ronald Meyer

    We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrodinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles. Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics. Due to the inherent lack of a close form solution for vortex rings and the dimensionality where they live, efficient numerical methods to integrate the NLSE have to be developed in order to perform the extensive number of required simulations. To facilitate this, compact high-order numerical schemes for the spatial derivatives are developed which include a new semi-compact modulus-squared Dirichlet boundary condition. The schemes are combined with a fourth-order Runge-Kutta time-stepping scheme in order to keep the overall method fully explicit. To ensure efficient use of the schemes, a stability analysis is performed to find bounds on the largest usable time step-size as a function of the spatial step-size. The numerical methods are implemented into codes which are run on NVIDIA graphic processing unit (GPU) parallel architectures. The codes running on the GPU are shown to be many times faster than their serial counterparts. The codes are developed with future usability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with a MEX-compiler interface. Reproducibility of results is achieved by combining the codes into a code package called NLSEmagic which is freely distributed on a dedicated website.

  9. Ring vortex solitons in nonlocal nonlinear media

    DEFF Research Database (Denmark)

    Briedis, D.; Petersen, D.E.; Edmundson, D.;

    2005-01-01

    or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....

  10. Einstein observations and the internal dynamics of compact stars: further evidence against non-linear regimes of vortex creep

    Energy Technology Data Exchange (ETDEWEB)

    Horvath, J.E. (Sao Paulo Univ., SP (Brazil). Inst. Astronomico e Geofisico); Benvenuto, O.G. (La Plata Univ. Nacional (Argentina))

    1991-08-15

    We present structural constraints on the Crab and Vela pulsars imposed by the simultaneous assumptions of (a) surface temperatures close to those observed by the Einstein Observatory satellite, and (b) validity of the vortex creep theory in the non-linear regime for interpreting glitch observations and internal features predicted by it. The disagreement between both studies is quantified, thus pointing strongly to the need for linear regimes of creep, as recently suggested, or some alternative picture. (author).

  11. Nonlinear ion acoustic waves scattered by vortexes

    Science.gov (United States)

    Ohno, Yuji; Yoshida, Zensho

    2016-09-01

    The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.

  12. Vortex Dynamics in Anisotropic Superconductors

    Science.gov (United States)

    Steel, David Gordon

    Measurements of the ac screening response and resistance of superconducting Bi_2Sr _2CaCu_2O _8 (BSCCO) crystals have been used to probe the dynamics of the magnetic flux lines within the mixed state as a function of frequency, temperature, and applied dc field. For the particular range of temperature and magnetic field in which measurements were made, the systematic behavior of the observed dissipation peak in the screening response is consistent with electromagnetic skin size effects rather than a phase transition. According to microscopic theories of the interaction between the flux lines and a driving ac field, such a skin size effect is expected for the case when the vortex motion is diffusive in nature. However, diffusive motion is inconsistent with simple activation models that use a single value for the pinning energy (derived from direct measurement of the dc resistance). This contradiction suggests a distribution of pinning energies within the sample. Interlayer vortex decoupling has been directly observed as a function of temperature and applied magnetic field using electronic transport perpendicular to the layers in synthetic amorphous MoGe/Ge multilayer samples. Perpendicular transport has been shown to be a far more sensitive measure of the phase coupling between layers than in-plane properties. Below the decoupling temperature T_{D} the resistivity anisotropy collapses and striking nonlinearities appear in the perpendicular current-voltage behavior, which are not observed in parallel transport. A crossover in behavior is also observed at a field H _{x}, in accordance with theory. The data suggest the presence of a phase transition into a state with finite in-plane resistivity. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

  13. Nonlinear ion acoustic waves scattered by vortexes

    CERN Document Server

    Ohno, Yuji

    2015-01-01

    The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes `scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are `ambient' because they do not receive reciprocal reactions from the waves (i.e.,...

  14. Dynamics of Vortex Cavitation

    NARCIS (Netherlands)

    Pennings, P.C.

    2016-01-01

    This thesis describes the mechanisms with which tip vortex cavitation is responsible for broadband pressure fluctuations on ship propellers. Hypotheses for these are described in detail by Bosschers (2009). Validation is provided by three main cavitation-tunnel experiments, one on a model propeller

  15. Nonlinear dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)

    1989-01-01

    Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.

  16. 150 Years of vortex dynamics

    DEFF Research Database (Denmark)

    Aref, Hassan

    2010-01-01

    An IUTAM symposium with the title of this paper was held on October 12-16, 2008, in Lyngby and Copenhagen, Denmark, to mark the sesquicentennial of publication of Helmholtz's seminal paper on vortex dynamics. This volume contains the proceedings of the Symposium. The present paper provides...

  17. Dynamic signatures of driven vortex motion.

    Energy Technology Data Exchange (ETDEWEB)

    Crabtree, G. W.; Kwok, W. K.; Lopez, D.; Olsson, R. J.; Paulius, L. M.; Petrean, A. M.; Safar, H.

    1999-09-16

    We probe the dynamic nature of driven vortex motion in superconductors with a new type of transport experiment. An inhomogeneous Lorentz driving force is applied to the sample, inducing vortex velocity gradients that distinguish the hydrodynamic motion of the vortex liquid from the elastic and-plastic motion of the vortex solid. We observe elastic depinning of the vortex lattice at the critical current, and shear induced plastic slip of the lattice at high Lorentz force gradients.

  18. Vortex dynamics in $R^4$

    CERN Document Server

    Shashikanth, Banavara N

    2011-01-01

    The vortex dynamics of Euler's equations for a constant density fluid flow in $R^4$ is studied. Most of the paper focuses on singular Dirac delta distributions of the vorticity two-form $\\omega$ in $R^4$. These distributions are supported on two-dimensional surfaces termed {\\it membranes} and are the analogs of vortex filaments in $R^3$ and point vortices in $R^2$. The self-induced velocity field of a membrane is shown to be unbounded and is regularized using a local induction approximation (LIA). The regularized self-induced velocity field is then shown to be proportional to the mean curvature vector field of the membrane but rotated by 90 degrees in the plane of normals. Next, the Hamiltonian membrane model is presented. The symplectic structure for this model is derived from a general formula for vorticity distributions due to Marsden and Weinstein (1983). Finally, the dynamics of the four-form $\\omega \\wedge \\omega$ is examined. It is shown that Ertel's vorticity theorem in $R^3$, for the constant density...

  19. Vortex dynamics in nonrelativistic Abelian Higgs model

    Directory of Open Access Journals (Sweden)

    A.A. Kozhevnikov

    2015-11-01

    Full Text Available The dynamics of the gauge vortex with arbitrary form of a contour is considered in the framework of the nonrelativistic Abelian Higgs model, including the possibility of the gauge field interaction with the fermion asymmetric background. The equations for the time derivatives of the curvature and the torsion of the vortex contour generalizing the Betchov–Da Rios equations in hydrodynamics, are obtained. They are applied to study the conservation of helicity of the gauge field forming the vortex, twist, and writhe numbers of the vortex contour. It is shown that the conservation of helicity is broken when both terms in the equation of the vortex motion are present, the first due to the exchange of excitations of the phase and modulus of the scalar field and the second one due to the coupling of the gauge field forming the vortex, with the fermion asymmetric background.

  20. Nonlinear Dynamics

    Institute of Scientific and Technical Information of China (English)

    1996-01-01

    3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.

  1. Vortex-based spatiotemporal characterization of nonlinear flows

    Science.gov (United States)

    Byrne, Gregory A.

    Although the ubiquity of vortices in nature has been recognized by artists for over seven centuries, it was the work of artist and scientist Leonardo da Vinci that provided the monumental transition from an aesthetic form to a scientific tool. DaVinci used vortices to describe the motions he observed in air currents, flowing water and blood flow in the human heart. Five centuries later, the Navier-Stokes equations allow us to recreate the swirling motions of fluid observed in nature. Computational fluid dynamic (CFD) simulations have provided a lens through which to study the role of vortices in a wide variety of modern day applications. The research summarized below represents an effort to look through this lens and bring into focus the practical use of vortices in describing nonlinear flows. Vortex-based spatiotemporal characterizations are obtained using two specific mathematical tools: vortex core lines (VCL) and proper orthogonal decomposition (POD). By applying these tools, we find that vortices continue to provide new insights in the realm of biofluids, urban flows and the phase space of dynamical systems. The insights we have gained are described in this thesis. Our primary focus is on biofluids. Specifically, we seek to gain new insights into the connection between vortices and vascular diseases in order to provide more effective methods for clinical diagnosis and treatment. We highlight several applications in which VCL and POD are used to characterize the flow conditions in a heart pump, identify stenosis in carotid arteries and validate numerical models against PIV-based experimental data. Next, we quantify the spatial complexity and temporal stability of hemodynamics generated by a database of 210 patient-specific aneurysm geometries. Visual classifications of the hemodynamics are compared to the automated, quantitative classifications. The quantities characterizing the hemodynamics are then compared to clinical data to determine conditions that are

  2. Stabilization of vortex beams in Kerr media by nonlinear absorption

    Science.gov (United States)

    Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.

    2016-11-01

    We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.

  3. Stabilization of vortex beams in Kerr media by nonlinear absorption

    CERN Document Server

    Porras, Miguel A; Leblond, Hervé; Malomed, Boris A

    2016-01-01

    We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.

  4. Dynamic Optimization for Vortex Shedding Suppression

    Directory of Open Access Journals (Sweden)

    Bonis Ioannis

    2016-01-01

    Full Text Available Flows around structures exhibiting vortex shedding induce vibrations that can potentially damage the structure. A way to avoid it is to suppress vortex shedding by controlling the wake. Wake control of laminar flow behind a rotating cylinder is formulated herein as a dynamic optimization problem. Angular cylinder speed is the manipulated variable that is adjusted to suppress vortex shedding by minimizing lift coefficient variation. The optimal angular speed is assumed to be periodic like wake formation. The control problem is solved for different time horizons tH. The impact of tH to control is evaluated and the need for feedback is assessed.

  5. Vortex dynamics in ferromagnetic/superconducting bilayers

    Energy Technology Data Exchange (ETDEWEB)

    Cieplak, M.Z.; Adamus, Z. [Polish Acad Sci, Inst Phys, PL-02668 Warsaw, (Poland); Konczykowski, M. [CEA, DSM, DRECAM, Lab Solides Irradies, Ecole Polytechnique, CNRS-UMR 7642, F-91128 Palaiseau (France); Zhu, L.Y.; Chien, C.L. [Johns Hopkins Univ, Dept Phys and Astron, Baltimore, MD 21218 (United States)

    2008-07-01

    The dependence of vortex dynamics on the geometry of magnetic domain pattern is studied in the superconducting/ferromagnetic bilayers, in which niobium is a superconductor, and Co/Pt multilayer with perpendicular magnetic anisotropy serves as a ferromagnetic layer. Magnetic domain patterns with different density of domains per surface area and different domain size, w, are obtained for Co/Pt with different thickness of Pt. The dense patterns of domains with the size comparable to the magnetic penetration depth (w {>=} {lambda}) produce large vortex pinning and smooth vortex penetration, while less dense patterns with larger domains (w {>=}{>=} {lambda}) enhance pinning less effectively and result in flux jumps during flux motion. (authors)

  6. Applications of 2D helical vortex dynamics

    DEFF Research Database (Denmark)

    Okulov, Valery; Sørensen, Jens Nørkær

    2010-01-01

    In the paper, we show how the assumption of helical symmetry in the context of 2D helical vortices can be exploited to analyse and to model various cases of rotating flows. From theory, examples of three basic applications of 2D dynamics of helical vortices embedded in flows with helical symmetry...... of the vorticity field are addressed. These included some of the problems related to vortex breakdown, instability of far wakes behind rotors and vortex theory of ideal rotors....

  7. Nonlinear dynamics and complexity

    CERN Document Server

    Luo, Albert; Fu, Xilin

    2014-01-01

    This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

  8. Wave–vortex interactions in the nonlinear Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Yuan, E-mail: yuanguo@cims.nyu.edu; Bühler, Oliver [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)

    2014-02-15

    This is a theoretical study of wave–vortex interaction effects in the two-dimensional nonlinear Schrödinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave–vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave–vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.

  9. Dynamics of vortex dipoles in confined Bose-Einstein condensates

    Energy Technology Data Exchange (ETDEWEB)

    Torres, P.J. [Departamento de Matematica Aplicada, Universidad de Granada, 18071 Granada (Spain); Kevrekidis, P.G., E-mail: kevrekid@gmail.com [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D.J. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece); Carretero-Gonzalez, R. [Nonlinear Dynamical System Group, Computational Science Research Center, and Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Schmelcher, P. [Zentrum fuer Optische Quantentechnologien, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); Hall, D.S. [Department of Physics, Amherst College, Amherst, MA 01002-5000 (United States)

    2011-08-01

    We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria. -- Highlights: → A model describing the motion of a vortex dipole in a quasi two-dimensional trapped Bose-Einstein condensate is considered. → The model is integrable and the generic motion of the dipole is quasi-periodic. → Stationary and periodic (guiding-center) equilibria are identified. → Both equilibria are found to be dynamically stable.

  10. Untangling knots via reaction-diffusion dynamics of vortex strings

    CERN Document Server

    Maucher, Fabian

    2016-01-01

    We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.

  11. Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings

    Science.gov (United States)

    Maucher, Fabian; Sutcliffe, Paul

    2016-04-01

    We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.

  12. A Nonlinear Vortex Induced Vibration Model of Marine Risers

    Institute of Scientific and Technical Information of China (English)

    LIU Juan; HUANG Weiping

    2013-01-01

    With the exploitation of oil and gas in deep water,the traditional vortex induced vibration (VIV) theory is challenged by the unprecedented flexibility of risers.A nonlinear time-dependent VIV model is developed in this paper based on a VIV lift force model and the Morison equation.Both the inline vibration induced by the flow due to vortex shedding and the fluid-structure interaction in the transverse direction are included in the model.One of the characteristics of the model is the response-dependent lift force with nonlinear damping,which is different from other VIV models.The calculations show that the model can well describe the VIV of deepwater risers with the results agreeing with those calculated by other models.

  13. Nonlinear effects in the bounded dust-vortex flow in plasma

    Science.gov (United States)

    Laishram, Modhuchandra; Sharma, Devendra; Chattopdhyay, Prabal K.; Kaw, Predhiman K.

    2017-03-01

    The vortex structures in a cloud of electrically suspended dust in a streaming plasma constitutes a driven system with a rich nonlinear flow regime. Experimentally recovered toroidal formations of this system have motivated study of its volumetrically driven-dissipative vortex flow dynamics using two-dimensional hydrodynamics in the incompressible Navier-Stokes regime. Nonlinear equilibrium solutions are obtained for this system where a nonuniformly driven two-dimensional dust flow exhibits distinct regions of localized accelerations and strong friction caused by stationary fluids at the confining boundaries resisting the dust flow. In agreement with observations in experiments, it is demonstrated that the nonlinear effects appear in the limit of small viscosity, where the primary vortices form scaling with the most dominant spatial scales of the domain topology and develop separated virtual boundaries along their periphery. This separation is triggered beyond a critical dust viscosity that signifies a structural bifurcation. Emergence of uniform vorticity core and secondary vortices with a newer level of identical dynamics highlights the applicability of the studied dynamics to gigantic vortex flows, such as the Jovian great red spot, to microscopic biophysical intracellular activity.

  14. Intramolecular and nonlinear dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Davis, M.J. [Argonne National Laboratory, IL (United States)

    1993-12-01

    Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.

  15. Pattern formation due to non-linear vortex diffusion

    Science.gov (United States)

    Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.

    Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.

  16. Vortex-Surface Interactions: Vortex Dynamics and Instabilities

    Science.gov (United States)

    2015-10-16

    a) Main vortex structures developing on a typical submarine hull; (b) Schematic illustrating a horseshoe vortex at a wing-body junction of a " Rood ...secondary vortices. Firstly, looking at Figure 7, showing only the secondary vortices being visualized by our technique , we see that a tongue of secondary

  17. Nonlinear dynamics of structures

    CERN Document Server

    Oller, Sergio

    2014-01-01

    This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics.   This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects.   Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution  are studied, and the theoretical concepts and its programming algorithms are presented.  

  18. Dynamic Evolution Equations for Isolated Smoke Vortexes in Rational Mechanics

    CERN Document Server

    Jianhua, Xiao

    2011-01-01

    Smoke circle vortexes are a typical dynamic phenomenon in nature. The similar circle vortexes phenomenon appears in hurricane, turbulence, and many others. A semi-empirical method is constructed to get some intrinsic understanding about such circle vortex structures. Firstly, the geometrical motion equations for smoke circle is formulated based on empirical observations. Based on them, the mechanic dynamic motion equations are established. Finally, the general dynamic evolution equations for smoke vortex are formulated. They are dynamic evolution equations for exact stress field and dynamic evolution equations for average stress field. For industrial application and experimental data processing, their corresponding approximation equations for viscous fluid are given. Some simple discussions are made.

  19. Dynamic Evolution Equations for Isolated Smoke Vortexes in Rational Mechanics

    OpenAIRE

    2011-01-01

    Smoke circle vortexes are a typical dynamic phenomenon in nature. The similar circle vortexes phenomenon appears in hurricane, turbulence, and many others. A semi-empirical method is constructed to get some intrinsic understanding about such circle vortex structures. Firstly, the geometrical motion equations for smoke circle is formulated based on empirical observations. Based on them, the mechanic dynamic motion equations are established. Finally, the general dynamic evolution equations for ...

  20. Evaluation of travelling vortex speed by means of vortex tracking and dynamic mode decomposition

    Science.gov (United States)

    Hyhlík, Tomáš

    2016-06-01

    The article deals with the analysis of unsteady periodic flow field related to synthetic jet creation. The analyses are based on the data obtained using ANSYS Fluent solver. Numerical results are validated by hot wire anemometry data measured along the jet centerline. The speed of travelling vortex ring is evaluated by using vortex tracking method and by using dynamic mode decomposition method. Vortex identification is based on residual vorticity which allows identifying regions in the flow field where fluid particles perform the rotational motion. The regime of the synthetic jet with Re = 329 and S = 19.7 is chosen. Both the vortex tracking and the dynamic mode decomposition based vortex speed evaluation indicate an increase in the vortex speed close to the orifice and then decrease with maximum reaching almost one and half of orifice centerline velocity. The article contains extended version the article presented at the conference AEaNMiFMaE 2016.

  1. Dynamically controlled energy dissipation for fast magnetic vortex switching

    Science.gov (United States)

    Badea, R.; Berezovsky, J.

    2017-09-01

    Manipulation of vortex states in magnetic media provides new routes towards information storage and processing technology. The typical slow relaxation times (˜100 ns) of magnetic vortex dynamics may present an obstacle to the realization of these applications. Here, we investigate how a vortex state in a ferromagnetic microdisk can be manipulated in a way that translates the vortex core while enhancing energy dissipation to rapidly damp the vortex dynamics. We use time-resolved differential magneto-optical Kerr effect microscopy to measure the motion of the vortex core in response to applied magnetic fields. We first map out how the vortex core becomes sequentially trapped by pinning sites as it translates across the disk. After applying a fast magnetic field step to translate the vortex from one pinning site to another, we observe long-lived dynamics of the vortex as it settles to the new equilibrium. We then demonstrate how the addition of a short (magnetic field pulse can induce additional energy dissipation, strongly damping the long-lived dynamics. A model of the vortex dynamics using the Thiele equation of motion explains the mechanism behind this effect.

  2. Nonlinear quantum piston for the controlled generation of vortex rings and soliton trains

    KAUST Repository

    Pinsker, Florian

    2013-05-29

    We propose a simple way to generate nonlinear excitations in a controllable way by managing interactions in Bose-Einstein condensates. Under the action of a quantum analog of a classical piston, the condensed atoms are pushed through the trap, generating vortex rings infully three-dimensional condensates or soliton trains in quasi-one-dimensional scenarios. The vortex rings form due to transverse instability of the shock-wave train, enhanced and supported by the energy transfer between waves. We elucidate in what sense the self-interactions within the atom cloud define the properties of the generated vortex rings and soliton trains. Based on the quantum-piston scheme we study the behavior of two-component Bose-Einstein condensates and analyze how the presence of an additional superfluid influences the generation of vortex rings or solitons in the other component, and vice versa. Finally, we show the dynamical emergence of skyrmions within two-component systems in the immiscible regime. © 2013 American Physical Society.

  3. Topics in Nonlinear Dynamics

    DEFF Research Database (Denmark)

    Mosekilde, Erik

    Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...

  4. Theory and application of nonlinear river dynamics

    Institute of Scientific and Technical Information of China (English)

    Yu-chuan BAI; Zhao-yin WANG

    2014-01-01

    A theoretical model for river evolution including riverbed formation and meandering pattern formation is presented in this paper. Based on nonlinear mathematic theory, the nonlinear river dynamic theory is set up for river dynamic process. Its core content includes the stability and tropism characteristics of flow motion in river and river selves’ evolution. The stability of river dynamic process depends on the response of river selves to the external disturbance, if the disturbance and the resulting response will eventually attenuate, and the river dynamics process can be restored to new equilibrium state, the river dynamic process is known as stable;otherwise, the river dynamic process is unstable. The river dynamic process tropism refers to that the evolution tendency of river morphology after the disturbance. As an application of this theory, the dynamical stability of the constant curvature river bend is calculated for its coherent vortex disturbance and response. In addition, this paper discusses the nonlinear evolution of the river peristaltic process under a large-scale disturbance, showing the nonlinear tendency of river dynamic processes, such as river filtering and butterfly effect.

  5. Vortex dynamics and shear layer instability in high intensity cyclotrons

    CERN Document Server

    Cerfon, Antoine J

    2016-01-01

    We show that the space charge dynamics of high intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam break up behavior observed in experiments and in simulations. In particular, we demonstrate that beam break up is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps.

  6. Nonlinear Dynamic Force Spectroscopy

    CERN Document Server

    Björnham, Oscar

    2016-01-01

    Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...

  7. On the Vortex Dynamics in Fractal Fourier Turbulence

    CERN Document Server

    Lanotte, Alessandra S; Biferale, Luca

    2016-01-01

    Incompressible, homogeneous and isotropic turbulence is studied by solving the Navier-Stokes equations on a reduced set of Fourier modes, belonging to a fractal set of dimension $D$. By tuning the fractal dimension parameter, we study the dynamical effects of Fourier decimation on the vortex stretching mechanism and on the statistics of the velocity and the velocity gradient tensor. In particular, we show that as we move from $D=3$ to $D \\sim 2.8$, the statistics gradually turns into a purely Gaussian one. This result suggests that even a mild fractal mode reduction strongly depletes the stretching properties of the non-linear term of the Navier-Stokes equations and suppresses anomalous fluctuations.

  8. Quantum vortex dynamics in two-dimensional neutral superfluids

    NARCIS (Netherlands)

    Wang, C. -C J.; Duine, R.A.; MacDonald, A.H.

    2010-01-01

    We derive an effective action for the vortex-position degree of freedom in a superfluid by integrating out condensate phase- and density-fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and

  9. Device for separation of vortex gas-dynamic energy

    Science.gov (United States)

    Leontiev, A. I.; Burtsev, S. A.

    2015-10-01

    A device for separation of vortex gas-dynamic energy, which combines the mechanism of separation of vortex energy used in the Ranque-Hilsch tubes and the mechanism of separation of gas-dynamic energy, is proposed for supersonic flows. A method of calculation of this device is developed. A comparison is made that showed that, when working with natural gas, the cooling depth of half of the mass flow rate proves to be 1.3 times higher than that for the vortex tube and three times higher than that for the device for separation of the gas-dynamic energy.

  10. Nonlinear dynamics in psychology

    Directory of Open Access Journals (Sweden)

    Stephen J. Guastello

    2001-01-01

    Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.

  11. Global Analysis of Nonlinear Dynamics

    CERN Document Server

    Luo, Albert

    2012-01-01

    Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.  

  12. Dynamical coefficients for a Josephson vortex in an anisotropic junction

    Science.gov (United States)

    Coffey, Mark W.

    2000-05-01

    The mass per unit length μ and drag coefficient η for a Josephson vortex moving and aligned parallel to the plane of an anisotropic Josephson junction are calculated. The tilt angle between the vortex direction and the crystal uniaxial directions of the superconducting banks is allowed to vary, so that this type of misalignment of the banks is included. These low-field results are suitable for inclusion in the dynamic mobility of Josephson vortices. These dynamical coefficients should be applicable to the description of the intergrain motion of vortices in polycrystals of high-Tc superconductors. The extension of the approach for the regime of relativistic vortex motion is presented.

  13. Dynamics of vortex-antivortex pairs and rarefaction pulses in liquid light.

    Science.gov (United States)

    Feijoo, David; Paredes, Angel; Michinel, Humberto

    2017-03-01

    We present a numerical study of the cubic-quintic nonlinear Schrödinger equation in two transverse dimensions, relevant for the propagation of light in certain exotic media. A well-known feature of the model is the existence of flat-top bright solitons of fixed intensity, whose dynamics resembles the physics of a liquid. They support traveling wave solutions, consisting of rarefaction pulses and vortex-antivortex pairs. In this work, we demonstrate how the vortex-antivortex pairs can be generated in bright soliton collisions displaying destructive interference followed by a snake instability. We then discuss the collisional dynamics of the dark excitations for different initial conditions. We describe a number of distinct phenomena including vortex exchange modes, quasielastic flyby scattering, solitonlike crossing, fully inelastic collisions, and rarefaction pulse merging.

  14. Non-local dynamics governing the self-induced motion of a planar vortex filament

    Science.gov (United States)

    Van Gorder, Robert A.

    2015-06-01

    While the Hasimoto planar vortex filament is one of the few exact solutions to the local induction approximation (LIA) approximating the self-induced motion of a vortex filament, it is natural to wonder whether such a vortex filament solution would exist for the non-local Biot-Savart dynamics exactly governing the filament motion, and if so, whether the non-local effects would drastically modify the solution properties. Both helical vortex filaments and vortex rings are known to exist under both the LIA and non-local Biot-Savart dynamics; however, the planar filament is a bit more complicated. In the present paper, we demonstrate that a planar vortex filament solution does exist for the non-local Biot-Savart formulation, provided that a specific non-linear integral equation (governing the spatial structure of such a filament) has a non-trivial solution. By using the Poincaré-Lindstedt method, we are able to obtain an accurate analytical approximation to the solution of this integral equation under physically reasonable assumptions. To obtain these solutions, we approximate local effects near the singularity of the integral equation using the LIA and non-local effects using the Biot-Savart formulation. Mathematically, the results constitute an analytical solution to an interesting nonlinear singular integro-differential equation in space and time variables. Physically, these results show that planar vortex filaments exist and maintain their forms under the non-local Biot-Savart formulation, as one would hope. Due to the regularization approach utilized, we are able to compare the structure of the planar filaments obtained under both LIA and Biot-Savart formulations in a rather straightforward manner, in order to determine the role of the non-locality on the structure of the planar filament.

  15. Classical black holes: the nonlinear dynamics of curved spacetime.

    Science.gov (United States)

    Thorne, Kip S

    2012-08-03

    Numerical simulations have revealed two types of physical structures, made from curved spacetime, that are attached to black holes: tendexes, which stretch or squeeze anything they encounter, and vortexes, which twist adjacent inertial frames relative to each other. When black holes collide, their tendexes and vortexes interact and oscillate (a form of nonlinear dynamics of curved spacetime). These oscillations generate gravitational waves, which can give kicks up to 4000 kilometers per second to the merged black hole. The gravitational waves encode details of the spacetime dynamics and will soon be observed and studied by the Laser Interferometer Gravitational Wave Observatory and its international partners.

  16. Proceedings of the NASA First Wake Vortex Dynamic Spacing Workshop

    Science.gov (United States)

    Creduer, Leonard (Editor); Perry, R. Brad (Editor)

    1997-01-01

    A Government and Industry workshop on wake vortex dynamic spacing systems was conducted on May 13-15, 1997, at the NASA Langley Research Center. The purpose of the workshop was to disclose the status of ongoing NASA wake vortex R&D to the international community and to seek feedback on the direction of future work to assure an optimized research approach. Workshop sessions examined wake vortex characterization and physics, wake sensor technologies, aircraft/wake encounters, terminal area weather characterization and prediction, and wake vortex systems integration and implementation. A final workshop session surveyed the Government and Industry perspectives on the NASA research underway and related international wake vortex activities. This document contains the proceedings of the workshop including the presenters' slides, the discussion following each presentation, the wrap-up panel discussion, and the attendees' evaluation feedback.

  17. IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence

    CERN Document Server

    Borisov, Alexey V; Mamaev, Ivan S; Sokolovskiy, Mikhail A; IUTAM BOOKSERIES : Volume 6

    2008-01-01

    This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important. The last few decades have shown that serious possibilities for progress in the research of real turbulent vortex motions are essentially related to the combined use of mathematical methods, computer simulation and laboratory experiments. These approaches have led to a series of interesting results which allow us to study these processes from new perspectives. Based on this principle, the papers collected in this proceedings volume present new results on theoretical and applied aspects of the processes of formation and evolution of various flows, wave a...

  18. Nonlinear dynamics in atom optics

    Energy Technology Data Exchange (ETDEWEB)

    Chen Wenyu; Dyrting, S.; Milburn, G.J. [Queensland Univ., St. Lucia, QLD (Australia). Dept. of Physics

    1996-12-31

    In this paper theoretical work on classical and quantum nonlinear dynamics of cold atoms is reported. The basic concepts in nonlinear dynamics are reviewed and then applied to the motion of atoms in time-dependent standing waves and to the atomic bouncer. The quantum dynamics for the cases of regular and chaotic classical dynamics is described. The effect of spontaneous emission and external noise is also discussed. 104 refs., 1 tab., 21 figs.

  19. Numerical investigation on nonlinear effect and vortex formation of oscillatory flow throughout a short tube in a thermoacoustic Stirling engine

    Science.gov (United States)

    Yang, Peng; Chen, Hui; Liu, Yingwen

    2017-06-01

    In this paper, a two-dimensional axisymmetric model of a thermoacoustic Stirling engine with a short tube where the cross section narrows has been developed. The transient streamlines and vortex formation through short tubes with different diameters in oscillatory flow have been investigated visually by computational fluid dynamics. Three dimensionless parameters, Reynolds number (Re), Keulegan-Carpenter number (KC), and Womersley number (Wo), are used to describe the flow regime and vortex characteristic throughout the short tube. High Re and Wo numbers indicate that the oscillatory flow develops into the turbulent flow through the short tube. The KC number has a direct effect on the transition of streamlines and the development of the vortex. For a small cross section where KC ≈ 1, streamlines rotate and the vortex forms at both sides of the short tube. The vortex stays in the main flow region, and intensity varies as streamlines are convected downstream. The velocity along the radius presents a Poiseuille profile within the influence of the vortex. For a large cross section where KC < 1, streamlines pass the short tube with little rotation and the vortex disappears in the main flow region and confines near the short tube. The velocity profile tends to be flat. The nonlinear effects including instantaneous pressure drop and power dissipation throughout the short tube are also discussed. It shows that the time averaged pressure drop is generated at the cost of power dissipation. Finally, the "effectiveness" is applied to evaluate the performance of the short tube. The results suggest that increasing the diameter of the short tube is in favor of reducing power dissipation, which is beneficial to improve "effectiveness."

  20. Nonlinear vortex-phonon interactions in a Bose-Einstein condensate

    Science.gov (United States)

    Mendonça, J. T.; Haas, F.; Gammal, A.

    2016-07-01

    We consider the nonlinear coupling between an exact vortex solution in a Bose-Einstein condensate and a spectrum of elementary excitations in the medium. These excitations, or Bogoliubov-de Gennes modes, are indeed a special kind of phonons. We treat the spectrum of elementary excitations in the medium as a gas of quantum particles, sometimes also called bogolons. An exact kinetic equation for the bogolon gas is derived, and an approximate form of this equation, valid in the quasi-classical limit, is also obtained. We study the energy transfer between the vortex and the bogolon gas, and establish conditions for vortex instability and damping.

  1. Nonlinear magnetization dynamics in nanosystems

    CERN Document Server

    Mayergoyz, Isaak D; Serpico, Claudio

    2014-01-01

    As data transfer rates increase within the magnetic recording industry, improvements in device performance and reliability crucially depend on the thorough understanding of nonlinear magnetization dynamics at a sub-nanoscale level. This book offers a modern, stimulating approach to the subject of nonlinear magnetization dynamics by discussing important aspects such as the Landau-Lifshitz-Gilbert (LLG) equation, analytical solutions, and the connection between the general topological and structural aspects of dynamics. An advanced reference for the study and understanding of non

  2. Near wake vortex dynamics of a hovering hawkmoth

    Institute of Scientific and Technical Information of China (English)

    Hikaru Aono; Wei Shyy; Hao Liu

    2009-01-01

    Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerody-namics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wing-based micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventu-ally break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and roll-ing torques are canceled out due to the symmetric wing kine-matics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time-varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle.

  3. Vortex pinning and dynamics in the neutron star crust

    CERN Document Server

    Wlazłowski, Gabriel; Magierski, Piotr; Bulgac, Aurel; Forbes, Michael McNeil

    2016-01-01

    The nature of the interaction between superfluid vortices and the neutron star crust, conjectured by Anderson and Itoh in 1975 to be at the heart vortex creep and the cause of glitches, has been a longstanding question in astrophysics. Previous estimates of the vortex-"nucleus" interaction have been error-prone, being either phenomenological or derived from tiny differences of large energies of stationary configurations. Using a qualitatively new approach, we follow the dynamics as superfluid vortices move in response to the presence of "nuclei" (nuclear defects in the crust). The resulting motion is perpendicular to the force, similar to the motion of a spinning top when pushed. We show that nuclei repel vortices in the neutron star crust, leading thus to interstitial vortex pinning, and characterize the force as a function of the vortex-nucleus separation.

  4. Neurodynamics: nonlinear dynamics and neurobiology.

    Science.gov (United States)

    Abarbanel, H D; Rabinovich, M I

    2001-08-01

    The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.

  5. Nonlinear Dynamic Phenomena in Mechanics

    CERN Document Server

    Warminski, Jerzy; Cartmell, Matthew P

    2012-01-01

    Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear

  6. Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates

    Energy Technology Data Exchange (ETDEWEB)

    Middelkamp, S.; Schmelcher, P. [Zentrum fuer Optische Quantentechnologien, Universitaet Hamburg, Luruper Chaussee 149, DE-22761 Hamburg (Germany); Torres, P. J. [Departamento de Matematica Aplicada, Universidad de Granada, ES-18071 Granada (Spain); Kevrekidis, P. G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515 (United States); Frantzeskakis, D. J. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece); Carretero-Gonzalez, R. [Nonlinear Dynamical System Group, Computational Science Research Center and Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720 (United States); Freilich, D. V.; Hall, D. S. [Department of Physics, Amherst College, Amherst, Massachusetts 01002-5000 (United States)

    2011-07-15

    A quantized vortex dipole is the simplest vortex molecule, comprising two countercirculating vortex lines in a superfluid. Although vortex dipoles are endemic in two-dimensional superfluids, the precise details of their dynamics have remained largely unexplored. We present here several striking observations of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a vortex-particle model that generates vortex line trajectories that are in good agreement with the experimental data. Interestingly, these diverse trajectories exhibit essentially identical quasiperiodic behavior, in which the vortex lines undergo stable epicyclic orbits.

  7. Nonlinear vortex structures with perpendicular shear flow, hot ions, and nonthermal distribution of electrons

    Energy Technology Data Exchange (ETDEWEB)

    Gul-e-Ali,; Mirza, Arshad M. [Theoretical Plasma Physics Group, Physics Department, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Masood, W. [COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000 (Pakistan); National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan)

    2016-02-15

    Coupling of drift vortex and the ion acoustic modes in the linear and nonlinear regimes are investigated with sheared ion flow perpendicular to the ambient magnetic field in a plasma comprising of hot ions and nonthermal population of electrons. In this regard, generation of nonlinear vortex structures in the presence of kappa, Cairns, and q-nonextensive electron distributions are investigated in detail, and comparison with the Maxwellian distribution is also made. The appositeness of the present investigation in the matter of auroral F-region is also pointed out.

  8. Electron vortex magnetic holes: A nonlinear coherent plasma structure

    NARCIS (Netherlands)

    Haynes, C.T.; Burgess, D.; Camporeale, E.; Sundberg, T.

    2015-01-01

    We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic

  9. Geometry and Dynamics of Vortex Loops at Superfluid Phase Transitions

    Science.gov (United States)

    Williams, Gary A.

    2004-03-01

    The geometrical properties of thermally-excited vortex loops near a superfluid phase transition can be deduced from the dynamics of the transition. The frictional force on a loop is proportional to the total length of the vortex core, and hence depends on the fractal Hausdorff dimension DH of the random-walking core. By comparing the results for the loop dynamics with the dynamic-scaling predictions of Halperin and Hohenberg for the relaxation time, we find DH = (D+2)/2 = 2.5 in D = 3 dimensions, if the dynamic exponent is z = D/2. Computing the frequency-dependence of the superfluid density and comparing with the dynamic scaling of Fisher, Fisher, and Huse gives just the same value. Since Shenoy and co-workers have found precisely the same DH from a Flory-scaling analysis of the loop random walk, our results show that Shenoy's theory is exact if dynamic scaling is exact.

  10. Nonlinear dynamics: Challenges and perspectives

    Indian Academy of Sciences (India)

    M Lakshmanan

    2005-04-01

    The study of nonlinear dynamics has been an active area of research since 1960s, after certain path-breaking discoveries, leading to the concepts of solitons, integrability, bifurcations, chaos and spatio-temporal patterns, to name a few. Several new techniques and methods have been developed to understand nonlinear systems at different levels. Along with these, a multitude of potential applications of nonlinear dynamics have also been enunciated. In spite of these developments, several challenges, some of them fundamental and others on the efficacy of these methods in developing cutting edge technologies, remain to be tackled. In this article, a brief personal perspective of these issues is presented.

  11. Numerical analysis of the dynamics of distributed vortex configurations

    Science.gov (United States)

    Govorukhin, V. N.

    2016-08-01

    A numerical algorithm is proposed for analyzing the dynamics of distributed plane vortex configurations in an inviscid incompressible fluid. At every time step, the algorithm involves the computation of unsteady vortex flows, an analysis of the configuration structure with the help of heuristic criteria, the visualization of the distribution of marked particles and vorticity, the construction of streamlines of fluid particles, and the computation of the field of local Lyapunov exponents. The inviscid incompressible fluid dynamic equations are solved by applying a meshless vortex method. The algorithm is used to investigate the interaction of two and three identical distributed vortices with various initial positions in the flow region with and without the Coriolis force.

  12. Vortex dynamics and their interactions in quantum trajectories

    Energy Technology Data Exchange (ETDEWEB)

    Wisniacki, D A [Departamento de Fisica ' J. J. Giambiagi' , FCEN, UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Pujals, E R [IMPA-OS, Dona Castorina 110, 22460-320, Rio de Janeiro (Brazil); Borondo, F [Departamento de Quimica C-IX, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain)

    2007-12-30

    Vortices are known to play a key role in many important processes in physics and chemistry. Here, we study vortices in connection with the quantum trajectories that can be defined in the framework provided by the de Broglie-Bohm formalism of quantum mechanics. In a previous work, it was shown that the presence of a single moving vortex is enough to induce chaos in these trajectories. Here, this situation is explored in more detail by discussing the relationship between Lyapunov exponents and the parameters characterizing the vortex dynamics. We also consider the issue when more than one vortex exists. In this case, the interaction among them can annihilate or create pairs of vortices with opposite vorticity. This phenomenon is analyzed from a dynamical point of view, showing how the size of the regular regions in phase space grows, as vortices disappear.

  13. Nonlinear dynamics in biological systems

    CERN Document Server

    Carballido-Landeira, Jorge

    2016-01-01

    This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...

  14. WAVE BOTTOM LAYERS DYNAMIC WITH SUSPENDED SEDIMENT OVER VORTEX RIPPLES

    Institute of Scientific and Technical Information of China (English)

    JIANG Chang-bo; BAI Yu-chuan; ZHAO Zi-dan; ZHANG Hong-wu

    2004-01-01

    Vortex ripple is widely formed in the coastal region, and the dynamic of vortex is quite important because it is responsible for sediment transport. The flow structure around the vortex ripples can be modeled as 2D flow due to the geometry of the flow boundaries. In this paper, 2D Large-Ed dy-Simulation (LES) method was used to predict the flow structure and the dynamic of vortex in the bottom layers under the action of the wave, the numerical simulation results show a completely process of vortex formation, evolvement and disappearance. Based on the study of flow structure, the suspended sediment transport was modeled in present paper. The simulated sediment concentrations were compared to measurements from the literature. The agreement between the time averaged simulated concentration profiles and measurements is satisfactory. For a high setting velocity, the suspended sediment is confined to the vicinity of the bed, and it is dominated by the local bottom shear stress. For a small setting velocity,the suspension is more dominated by the characteristic of vor tex. There are two suspended sediment transport peaks observed in the cross-section at the trough and crest in the half period, the second peak is due to the separation bubble taking the sediment.

  15. Molecular shear heating and vortex dynamics in thermostatted two-dimensional Yukawa liquids

    CERN Document Server

    Gupta, Akanksha; Joy, Ashwin

    2016-01-01

    It is well known that two-dimensional macroscale shear flows are susceptible to instabilities leading to macroscale vortical structures. The linear and nonlinear fate of such a macroscale flow in a strongly coupled medium is a fundamental problem. A popular example of a strongly coupled medium is a dusty plasma, often modelled as a Yukawa liquid. Recently, laboratory experiments and MD studies of shear flows in strongly coupled Yukawa liquids, indicated occurrence of strong molecular shear heating, which is found to reduce the coupling strength exponentially leading to destruction of macroscale vorticity. To understand the vortex dynamics of strongly coupled molecular fluids undergoing macroscale shear flows and molecular shear heating, MD simulation has been performed, which allows the macroscopic vortex dynamics to evolve while at the same time, "removes" the microscopically generated heat without using the velocity degrees of freedom. We demonstrate that by using a configurational thermostat in a novel way...

  16. Vortex Nucleation in a Dissipative Variant of the Nonlinear Schroedinger Equation Under Rotation

    Science.gov (United States)

    2014-12-01

    Vortices in Nonlinear Fields (Clarendon, UK, 1999). [2] Yu.S. Kivshar and B. Luther -Davies, Physics Reports 298, 81–197 (1998). [3] Y.S. Kivshar, J...Christou, V. Tikhonenko, B. Luther -Davies and L. Pismen, Optics Comm. 152, 198–206 (1998). [4] H.J. Lugt, Vortex Flow in Nature and Technology (John

  17. Point vortex dynamics: A classical mathematics playground

    DEFF Research Database (Denmark)

    Aref, Hassan

    2007-01-01

    The idealization of a two-dimensional, ideal flow as a collection of point vortices embedded in otherwise irrotational flow yields a surprisingly large number of mathematical insights and connects to a large number of areas of classical mathematics. Several examples are given including...... the integrability of the three-vortex problem, the interplay of relative equilibria of identical vortices and the roots of certain polynomials, addition formulas for the cotangent and the Weierstrass zeta function, projective geometry, and other topics. The hope and intent of the article is to garner further...

  18. Targeted energy transfer in laminar vortex-induced vibration of a sprung cylinder with a nonlinear dissipative rotator

    Science.gov (United States)

    Blanchard, Antoine; Bergman, Lawrence A.; Vakakis, Alexander F.

    2017-07-01

    We computationally investigate the dynamics of a linearly-sprung circular cylinder immersed in an incompressible flow and undergoing transverse vortex-induced vibration (VIV), to which is attached a rotational nonlinear energy sink (NES) consisting of a mass that freely rotates at constant radius about the cylinder axis, and whose motion is restrained by a rotational linear viscous damper. The inertial coupling between the rotational motion of the attached mass and the rectilinear motion of the cylinder is ;essentially nonlinear;, which, in conjunction with dissipation, allows for one-way, nearly irreversible targeted energy transfer (TET) from the oscillating cylinder to the nonlinear dissipative attachment. At the intermediate Reynolds number Re = 100, the NES-equipped sprung cylinder undergoes repetitive cycles of slowly decaying oscillations punctuated by intervals of chaotic instabilities. During the slowly decaying portion of each cycle, the dynamics of the cylinder is regular and, for large enough values of the ratio ε of the NES mass to the total mass (i.e., NES mass plus cylinder mass), can lead to significant vortex street elongation with partial stabilization of the wake. As ε approaches zero, no such vortex elongation is observed and the wake patterns appear similar to that for a sprung cylinder with no NES. We apply proper orthogonal decomposition (POD) to the velocity flow field during a slowly decaying portion of the solution and show that, in situations where vortex elongation occurs, the NES, though not in direct contact with the surrounding fluid, has a drastic effect on the underlying flow structures, imparting significant and continuous passive redistribution of energy among POD modes. We construct a POD-based reduced-order model for the lift coefficient to characterize energy transactions between the fluid and the cylinder throughout the slowly decaying cycle. We introduce a quantitative signed measure of the work done by the fluid on the

  19. Exchange-mediated, nonlinear, out-of-plane magnetic field dependence of the ferromagnetic vortex gyrotropic mode frequency driven by core deformation

    Science.gov (United States)

    Fried, Jasper P.; Fangohr, Hans; Kostylev, Mikhail; Metaxas, Peter J.

    2016-12-01

    We have performed micromagnetic simulations of low-amplitude gyrotropic dynamics of magnetic vortices in the presence of spatially uniform out-of-plane magnetic fields. For disks having small lateral dimensions, we observe a frequency drop-off when approaching the disk's out-of-plane saturation field. This nonlinear frequency response is shown to be associated with a vortex core deformation driven by nonuniform demagnetizing fields that act on the shifted core. The deformation results in an increase in the average out-of-plane magnetization of the displaced vortex state (contrasting the effect of gyrofield-driven deformation at low field), which causes the exchange contribution to the vortex stiffness to switch from positive to negative. This generates an enhanced reduction of the core stiffness at high field, leading to a nonlinear field dependence of the gyrotropic mode frequency.

  20. Dynamics of vortex interactions in two-dimensional flows

    DEFF Research Database (Denmark)

    Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.

    2002-01-01

    a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 a(c) ...The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...

  1. The mechanism of vortex switching in magnetic nanodots under circular magnetic field. II. The dynamics of spin plaquette with vortex

    CERN Document Server

    Kovalev, A S

    2003-01-01

    A plaquette spin system in a vortex configuration is considered analytically and numerically to treat theoretically the vortex switching in magnetic nanodots due to the action of external circular magnetic field. The initial (linear) stage of the switching is analyzed. The analytical results obtained confirm the numerical data on the plaquette dynamics. Both the numerical analysis and the analytical consideration of the initial activation stage show the importance of taking into account the system azimuthal modes. At the frequencies of these modes the most rapid amplification of the vortex energy and the total out-of-plane magnetization occurs. The growth of the modes amplitudes gives rise to a parametrical activation of the low-frequency symmetric mode, and in turn causes the vortex switching. The results obtained provide a qualitative explanation of the numerical data on vortex switching in large-sized magnetic systems and may be used in experiments on guided effect on vortex polarization in magnetic nanodo...

  2. Vortex dynamics of particle-wall collisions

    Science.gov (United States)

    Leweke, Thomas; Thompson, Mark C.; Hourigan, Kerry

    2003-11-01

    We present results from an experimental and numerical study of the flow generated by a particle impacting onto a solid wall at low Reynolds numbers. Experimentally, a 3/4" bronze sphere attached to an inelastic string was lowered onto a Plexiglas plate inside a glass tank, using a stepper motor. Direct Numerical Simulations were carried out using either an axisymmetric or a fully 3D spectral-element code. The parameters varied were the running distance before impact, the sphere Reynolds number during motion, and the stopping distance away from the wall. For running lengths less than 7.5 diameters, the sphere wake remains axisymmetric in the form of an attached vortex ring. At impact, this ring overtakes the sphere and spreads out along the wall. When the sphere stops more than 0.3 diameters away from the wall, the secondary vorticity generated at the sphere surface rolls up into a second vortex ring persisting over a long time. At Reynolds number above 1000, the flow after impact exhibits a 3D instability with azimuthal wave numbers of around 20. Flow visualizations, vorticity fields, and quantitative information on the flow topology will be shown to illustrate the different regimes. The effect of a rebound of the sphere is also discussed.

  3. Sparse Identification of Nonlinear Dynamics (SINDy)

    Science.gov (United States)

    Brunton, Steven; Proctor, Joshua; Kutz, Nathan

    2016-11-01

    This work develops a general new framework to discover the governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The so-called sparse identification of nonlinear dynamics (SINDy) method results in models that are parsimonious, balancing model complexity with descriptive ability while avoiding over fitting. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including the chaotic Lorenz system, to the canonical fluid vortex shedding behind an circular cylinder at Re=100. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an increasingly important role in the characterization and control of fluid dynamics.

  4. The Arctic Vortex in March 2011: A Dynamical Perspective

    Science.gov (United States)

    Hurwitz, Margaret M.; Newman, Paul A.; Garfinkel,Chaim I.

    2011-01-01

    Despite the record ozone loss observed in March 2011, dynamical conditions in the Arctic stratosphere were unusual but not unprecedented. Weak planetary wave driving in February preceded cold anomalies in t he polar lower stratosphere in March and a relatively late breakup of the Arctic vortex in April. La Nina conditions and the westerly phas e of the quasi-biennial oscillation (QBO) were observed in March 201 1. Though these conditions are generally associated with a stronger vortex in mid-winter, the respective cold anomalies do not persist t hrough March. Therefore, the La Nina and QBO-westerly conditions cannot explain the observed cold anomalies in March 2011. In contrast, po sitive sea surface temperature anomalies in the North Pacific may ha ve contributed to the unusually weak tropospheric wave driving and s trong Arctic vortex in late winter 2011.

  5. Vortex dynamics in superfluids governed by an interacting gauge theory

    Science.gov (United States)

    Butera, Salvatore; Valiente, Manuel; Öhberg, Patrik

    2016-08-01

    We study the dynamics of a vortex in a quasi two-dimensional Bose gas consisting of light-matter coupled atoms forming two-component pseudo spins. The gas is subject to a density dependent gauge potential, hence governed by an interacting gauge theory, which stems from a collisionally induced detuning between the incident laser frequency and the atomic energy levels. This provides a back-action between the synthetic gauge potential and the matter field. A Lagrangian approach is used to derive an expression for the force acting on a vortex in such a gas. We discuss the similarities between this force and the one predicted by Iordanskii, Lifshitz and Pitaevskii when scattering between a superfluid vortex and the thermal component is taken into account.

  6. Vortex Pinning and Dynamics in the Neutron Star Crust.

    Science.gov (United States)

    Wlazłowski, Gabriel; Sekizawa, Kazuyuki; Magierski, Piotr; Bulgac, Aurel; Forbes, Michael McNeil

    2016-12-02

    The nature of the interaction between superfluid vortices and the neutron star crust, conjectured by Anderson and Itoh in 1975 to be at the heart vortex creep and the cause of glitches, has been a long-standing question in astrophysics. Using a qualitatively new approach, we follow the dynamics as superfluid vortices move in response to the presence of "nuclei" (nuclear defects in the crust). The resulting motion is perpendicular to the force, similar to the motion of a spinning top when pushed. We show that nuclei repel vortices in the neutron star crust, and characterize the force per unit length of the vortex line as a function of the vortex element to the nucleus separation.

  7. Device Applications of Nonlinear Dynamics

    CERN Document Server

    Baglio, Salvatore

    2006-01-01

    This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.

  8. NONLINEAR DYNAMICS RESPONSE OF CASING PIPE UNDER COMBINED WAVE-CURRENT

    Institute of Scientific and Technical Information of China (English)

    TANG You-gang; GU Jia-yang; ZUO Jian-li; MIN Jian-qin

    2005-01-01

    The vortex-induced nonlinear vibration of casing pipes in the deep water was studied considering the loads of current and combined wave-current. The vortex-induced vibration equation of a casing pipe was set up considering the beam mode and Morison's nonlinear fluid loads as well as the vortex-excited loads. The approach of calculating vortex-excited nonlinear vibration by Galerkin's method was proposed. The natural vibration frequencies and modes were obtained, and the response including primary resonance induced by current and the composite resonance under combined wave-current for the 170 m long casing pipe in the 160 m depth of water were investigated. The results show that the dynamics response of casing pipe obviously increases, and the complicated response behaviors of casing pipe are described under combined wave-current.

  9. Simulation of Dynamics in Two-Dimensional Vortex Systems in Random Media

    Institute of Scientific and Technical Information of China (English)

    ZHANG Wei; SUN Li-Zhen; LUO Meng-Bo

    2009-01-01

    Dynamics in two-dimensional vortex systems with random pinning centres is investigated using molecular dy-namical simulations. The driving force and temperature dependences of vortex velocity are investigated. Below the critical depinning force Fc, a creep motion of vortex is found at low temperature. At forces slightly above Fc, a part of vortices flow in winding channels at zero temperature. In the vortex channel flow region, we ob-serve the abnormal behaviour of vortex dynamics: the velocity is roughly independent of temperature or even decreases with temperature at low temperatures. A phase diagram that describes different dynamics of vortices is presented.

  10. Nonlinear Deformable-body Dynamics

    CERN Document Server

    Luo, Albert C J

    2010-01-01

    "Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...

  11. Electron vortex magnetic holes: a nonlinear coherent plasma structure

    CERN Document Server

    Haynes, Christopher T; Camporeale, Enrico; Sundberg, Torbjorn

    2014-01-01

    We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional PIC simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is ...

  12. Vortex dynamics in plasmas and fluids

    DEFF Research Database (Denmark)

    Juul Rasmussen, J.; Lynov, Jens-Peter; Hesthaven, J.S.;

    1994-01-01

    The existence and dynamics of vortical structures in both homogeneous and inhomogeneous systems will be discussed. In particular the dynamics of monopolar and dipolar vortices in a plasma with nonuniform density and in a rotating fluid with varying Coriolis force is described. The role of vortical...

  13. Edge detection by nonlinear dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Wong, Yiu-fai

    1994-07-01

    We demonstrate how the formulation of a nonlinear scale-space filter can be used for edge detection and junction analysis. By casting edge-preserving filtering in terms of maximizing information content subject to an average cost function, the computed cost at each pixel location becomes a local measure of edgeness. This computation depends on a single scale parameter and the given image data. Unlike previous approaches which require careful tuning of the filter kernels for various types of edges, our scheme is general enough to be able to handle different edges, such as lines, step-edges, corners and junctions. Anisotropy in the data is handled automatically by the nonlinear dynamics.

  14. Electron vortex magnetic holes: A nonlinear coherent plasma structure

    Science.gov (United States)

    Haynes, Christopher T.; Burgess, David; Camporeale, Enrico; Sundberg, Torbjorn

    2015-01-01

    We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.

  15. Electron vortex magnetic holes: A nonlinear coherent plasma structure

    Energy Technology Data Exchange (ETDEWEB)

    Haynes, Christopher T., E-mail: c.t.haynes@qmul.ac.uk; Burgess, David; Sundberg, Torbjorn [School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Camporeale, Enrico [Multiscale Dynamics, Centrum Wiskunde and Informatica (CWI), Amsterdam (Netherlands)

    2015-01-15

    We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.

  16. Visualization and computation of hovering mode vortex dynamics

    Science.gov (United States)

    Freymuth, Peter; Gustafson, Karl E.; Leben, Robert

    Results from experimental and numerical simulations of the unsteady hovering flight of small birds or insects are presented in extensive photographs and computer graphics and discussed in detail. In the flow-visualization experiments, an airfoil in combined pitching and plunging motion is used to generate a thrusting jet in still air, producing in addition a vortex street with rotation opposite to that of a Karman street. The numerical studies are based on an extension of the robust multigrid method of Gustafson and Leben (1986 and 1988) to hovering-mode vortex dynamics. The derivation of the governing equations is outlined, and it is shown that the numerical and experimental results are in good qualitative agreement.

  17. Statistical methods in nonlinear dynamics

    Indian Academy of Sciences (India)

    K P N Murthy; R Harish; S V M Satyanarayana

    2005-03-01

    Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.

  18. Nonlinear dynamics by mode superposition

    Energy Technology Data Exchange (ETDEWEB)

    Nickell, R.E.

    1976-01-01

    A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly. The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matric half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.

  19. The dynamics of straight vortex filaments in a Bose-Einstein condensate with a Gaussian density profile

    CERN Document Server

    Ruban, V P

    2016-01-01

    The dynamics of interacting quantized vortex filaments in a rotating trapped Bose-Einstein condensate, which is in the Thomas-Fermi regime at zero temperature and described by the Gross-Pitaevskii equation, is considered in the hydrodynamical "anelastic" approximation. In the presence of a smoothly inhomogeneous array of filaments (vortex lattice), a non-canonical Hamiltonian equation of motion is derived for the macroscopically averaged vorticity, with taking into account the spatial non-uniformity of the equilibrium condensate density determined by the trap potential. A minimum of the corresponding Hamiltonian describes a static configuration of deformed vortex lattice against a given density background. The minimum condition is reduced to a vector nonlinear partial differential equation of the second order, for which some approximate and exact solutions are found. It is shown that if the condensate density has an anisotropic Gaussian profile then equation of motion for the averaged vorticity admits solutio...

  20. Biped control via nonlinear dynamics

    Science.gov (United States)

    Hmam, Hatem M.

    1992-09-01

    This thesis applies nonlinear techniques to actuate a biped system and provides a rigorous analysis of the resulting motion. From observation of human locomotion, it is believed that the 'complex' dynamics developed by the aggregation of multiple muscle systems can be generated by a reduced order system which captures the rough details of the locomotion process. The investigation is begun with a simple model of a biped system. Since the locomotion process is cyclic in nature, we focus on applying the topologically similar concept of limit cycles to the simple model in order to generate the desired gaits. A rigorous analysis of the biped dynamics shows that the controlled motion is robust against dynamical disturbances. In addition, different biped gaits are generated by merely adjusting some of the limit cycle parameters. More dynamical and actuation complexities are then added for realism. First, two small foot components are added and the overall biped motion under the same control actuation is analyzed. Due to the physical constraints on the feet, it is shown using singular perturbation theory how the gross behavior of the biped dynamics are dictated by those of the reduced model. Next, an analysis of the biped dynamics under added nonlinear elasticities in the legs is carried out. Moreover, using a slightly modified model, forward motion is generated in the sagittal plane. At each step, a small amount of energy is consistently derived from the vertical plane and converted into a forward motion. Stability of the forward dynamics is guaranteed by appropriate foot placement. Finally, the robustness of the controlled biped dynamics is rigorously analyzed and illustrated through extensive computer simulations.

  1. Vortex Dynamics Studies in Type II Superconductors

    Science.gov (United States)

    Xu, Zhigang

    1993-03-01

    Vibrating reed, ac susceptibility and resistance measurements have been used to study the dynamics of vortices in type II superconductors. In Nb measurements, in spite of the low T _{c}'s and long coherence lengths compared to the high T_{c} superconductors, we find an extended region of temperature and field over which reversible flux line motion occurs when the Nb reed is oriented with its long dimension perpendicular to the applied field. We observe a strong, frequency-independent depression of the "irreversibility temperature" T _{Q}(H) below the resistively determined critical temperature T_{R}. The results of the ac susceptibility measurements also support these results. We concluded that observation of an extended region of magnetic reversibility is not restricted to high T_{c} or extremely anisotropic materials, and depends upon the geometry of samples with respect to the applied field direction. In NbSe_2 measurements, vibrating reed measurements were performed with the hexagonal c-axis approximately parallel or perpendicular to an applied magnetic field. Field-cooling data revealed an unusual peak in the frequency shift of the reed, accompanied by two peaks in reed dissipation. The upper peak occurs near the temperature where R~ 0, and the lower peak is very sample and amplitude dependent and hysteretic. The ac susceptibility results also show that corresponding features. The interplay of superconductivity and density waves were investigated by comparing data for NbSe _2 with the results for NbS_2 , which has a comparable superconducting T _{c } and crystal structure. In NbS_2 measurements, we did not see such a peak in the frequency shift nor the double peak feature in the dissipation in either vibrating reed measurements or ac susceptibility measurements. We have also studied the (Ba,K)BiO_3 system. It is cubic at its superconducting composition, but exhibits a moderately high T_{c }=30 K that is intermediate between conventional and high T_{rm c

  2. NONLINEAR FLUID DAMPING IN STRUCTURE-WAKE OSCILLATORS IN MODELING VORTEX-INDUCED VIBRATIONS

    Institute of Scientific and Technical Information of China (English)

    LIN Li-ming; LING Guo-can; WU Ying-xiang; ZENG Xiao-hui

    2009-01-01

    A Nonlinear Fluid Damping(NFD)in the form of the square-velocity is applied in the response analysis of Vortex-Induced Vibrations(VIV).Its nonlinear hydrodynamic effects on the coupled wake and structure oscillators are investigated.A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics,such as the amplification of body displacement at lock-in and frequency lock-in,both at high and low mass ratios.Particularly,the predicted peak amplitude of the body in the Griffin plot is in good agreement with experimental data and empirical equation,indicating the significant effect of the NFD on the structure motion.

  3. Vortex String Dynamics in an External Antisymmetric Tensor Field

    CERN Document Server

    Lee, K; Shin, H J

    1999-01-01

    We study the Lund-Regge equation that governs the motion of strings in a constant background antisymmetric tensor field by using the duality between the Lund-Regge equation and the complex sine-Gordon equation. Similar to the cases of vortex filament configurations in fluid dynamics, we find various exact solitonic string configurations which are the analogue of the Kelvin wave, the Hasimoto soliton and the smoke ring. In particular, using the duality relation, we obtain a completely new type of configuration which corresponds to the breather of the complex sine-Gordon equation.

  4. Nernst effect, Seebeck effect, and vortex dynamics in the mixed state of superconductors

    Energy Technology Data Exchange (ETDEWEB)

    Ao, P. [Umea Univ. (Sweden)

    1997-05-01

    The author demonstrates that in the presence of pinning a simple relation exists between Nernst and Seebeck coefficients and the resistivity tensor, based on the vortex equation of motion and the two-fluid model. Thus the combination of the electric and thermoelectric transport experiments can be used to test the basic models for the vortex dynamics in superconductors. Then the author shows how two different vortex dynamics models can be subjected to these tests. The vortex dynamics model without various normal fluid drag forces is consistent with those experiments, and that the alternative model with those drag forces is not.

  5. A comparative numerical analysis of linear and nonlinear aerodynamic sound generation by vortex disturbances in homentropic constant shear flows

    Energy Technology Data Exchange (ETDEWEB)

    Hau, Jan-Niklas, E-mail: hau@fdy.tu-darmstadt.de; Oberlack, Martin [Chair of Fluid Dynamics, Department of Mechanical Engineering, Technische Universität Darmstadt, Otto-Berndt-Strasse 2, 64287 Darmstadt (Germany); GSC CE, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt (Germany); Chagelishvili, George [Chair of Fluid Dynamics, Department of Mechanical Engineering, Technische Universität Darmstadt, Otto-Berndt-Strasse 2, 64287 Darmstadt (Germany); Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0160, Georgia (United States); M. Nodia Institute of Geophysics, Tbilisi State University, Tbilisi 0128, Georgia (United States); Khujadze, George [Chair of Fluid Mechanics, Universität Siegen, Paul-Bonatz-Str. 9-11, 57068 Siegen (Germany); Tevzadze, Alexander [Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi 0128, Georgia (United States)

    2015-12-15

    Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, “Linear mechanism of wave emergence from vortices in smooth shear flows,” Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, “Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow,” Phys. Fluids 12, 3021-3028 (2000); N. A. Bakas, “Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow,” J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, “Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow,” Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber

  6. A comparative numerical analysis of linear and nonlinear aerodynamic sound generation by vortex disturbances in homentropic constant shear flows

    Science.gov (United States)

    Hau, Jan-Niklas; Chagelishvili, George; Khujadze, George; Oberlack, Martin; Tevzadze, Alexander

    2015-12-01

    Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, "Linear mechanism of wave emergence from vortices in smooth shear flows," Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, "Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow," Phys. Fluids 12, 3021-3028 (2000); N. A. Bakas, "Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow," J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, "Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow," Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber plane, which

  7. Vortex dynamics equation in type-II superconductors in a temperature gradient

    Energy Technology Data Exchange (ETDEWEB)

    Vega Monroy, R.; Sarmiento Castillo, J. [Universidad del Atlantico, Barranquilla (Colombia). Facultad de Ciencias Basicas; Puerta Torres, D. [Universidad de Cartagena (Colombia). Facultad de Ciencias Exactas

    2010-12-15

    In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)

  8. IUTAM Symposium on Vortex Dynamics: Formation, Structure and Function, 10-14 March 2013, Fukuoka, Japan

    Science.gov (United States)

    Fukumoto, Yasuhide

    2014-06-01

    , Professor Meleshko unexpectedly passed away in a tragic traffic accident on 14 November 2011. This symposium was dedicated to the memory of Professors Aref and Meleshko, and started with a session commemorating the legacy of their work, organized by Professors P K Newton and G J F van Heijst. Professors Aref (1950-2011) and Meleshko (1951-2011) made fundamental contributions to fluid mechanics and vortex dynamics throughout their respective distinguished careers. Although mathematical in their fundamental approaches, both sought the connections between theory and experiment and searched for physical explanations in their work. With strong, warm, and embracing personalities, they each played key roles in developing and enriching international collaborations in the field of vortex dynamics through their considerable organizational and cooperative skills, and both made enormous contribution to the development of the IUTAM. Their scientific interests and personal lives overlapped considerably, and their impact in the field of vortex dynamics was honoured in the memorial session. The following sessions presented the development of new mathematical methods and theoretical concepts, bringing in novel techniques in vortex dynamics, stimulated by the continuous development of numerical method and new experimental results, in such aspects as vortex equilibria, spectra, instability and nonlinear dynamics of vortices in barotropic and baroclinic fluids, chaos, classical and quantum turbulence, and wall turbulence, flow separation and vortex-body interactions. Topical applications include biological locomotion, environmental problems, and Bose-Einstein condensates in condensed matter theory. Central fundamental issues in theoretical, numerical and experimental aspects of vortex dynamics were also covered during the symposium such as (1) The dynamics of point vortices in domains of non-trivial topology, its Hamiltonian formulation and new statistical approaches, (2) 3D instability of

  9. Vortex Dynamics and Shear-Layer Instability in High-Intensity Cyclotrons

    Science.gov (United States)

    Cerfon, Antoine J.

    2016-04-01

    We show that the space-charge dynamics of high-intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam breakup behavior observed in experiments and in simulations. Specifically, we demonstrate that beam breakup is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps.

  10. Nonlinear dynamics of cardiovascular ageing

    Energy Technology Data Exchange (ETDEWEB)

    Shiogai, Y. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom); Stefanovska, A. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom); Faculty of Electrical Engineering, University of Ljubljana, Ljubljana (Slovenia); McClintock, P.V.E. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom)], E-mail: p.v.e.mcclintock@lancaster.ac.uk

    2010-03-15

    The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in

  11. International Conference on Applications in Nonlinear Dynamics

    CERN Document Server

    Longhini, Patrick; Palacios, Antonio

    2017-01-01

    This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

  12. The Dynamics of Nonlinear Inference

    Science.gov (United States)

    Kadakia, Nirag

    The determination of the hidden states of coupled nonlinear systems is frustrated by the presence of high-dimensionality, chaos, and sparse observability. This problem resides naturally in a Bayesian context: an underlying physical process produces a data stream, which - though noisy and incomplete - can in principle be inverted to express the likelihood of the underlying process itself. A large class of well-developed methods treat this problem in a sequential predict-and-correct manner that alternates information from the presumed dynamical model with information from the data. One might instead formulate this problem in a temporally global, non-sequential manner, which suggests new avenues of approach within an optimization context, but also poses new challenges in numerical implementation. The variational annealing (VA) technique is proposed to address these problems by leveraging an inherent separability between the convex and nonconvex contributions of the resulting functional forms. VA is shown to reliably track unobservable states in sparsely observed chaotic systems, as well as in minimally-observed biophysical neural models. Second, this problem can be formally cast in continuous time as a Wiener path integral, which then suggests classical solutions derived from Hamilton's principle. These solutions come with their own difficulties in that they comprise an unstable boundary-value problem. Accordingly, a further technique called Hamiltonian variational annealing is proposed, which again exploits an existing separability of convexity and nonlinearity, this time in a an enlarged manifold constrained by underlying symmetries. A running theme in this thesis is that the optimal estimate of a nonlinear system is itself a dynamical system that lives in an unstable, symplectic manifold. When this system is recast in a variational context, instability is manifested as nonconvexity, the central idea being that when this nonconvexity is incorporated in a systematic

  13. Nonlinear dynamics of resistive electrostatic drift waves

    DEFF Research Database (Denmark)

    Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.

    1999-01-01

    The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... is perturbed by a small amplitude incoherent wave-field. The initial evolution is exponential, following the growth of perturbations predicted by linear stability theory. The fluctuations saturate at relatively high amplitudes, by forming a pair of magnetic field aligned vortex-like structures of opposite...

  14. A new non-linear vortex lattice method:Applications to wing aerodynamic optimizations

    Institute of Scientific and Technical Information of China (English)

    Oliviu S? ugar Gabor; Andreea Koreanschi; Ruxandra Mihaela Botez

    2016-01-01

    This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM) approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.

  15. A new non-linear vortex lattice method: Applications to wing aerodynamic optimizations

    Directory of Open Access Journals (Sweden)

    Oliviu Şugar Gabor

    2016-10-01

    Full Text Available This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.

  16. Vortex dynamics in ruptured and unruptured intracranial aneurysms

    Science.gov (United States)

    Trylesinski, Gabriel

    Intracranial aneurysms (IAs) are a potentially devastating pathological dilation of brain arteries that affect 1.5-5 % of the population. Causing around 500 000 deaths per year worldwide, their detection and treatment to prevent rupture is critical. Multiple recent studies have tried to find a hemodynamics predictor of aneurysm rupture, but concluded with distinct opposite trends using Wall Shear Stress (WSS) based parameters in different clinical datasets. Nevertheless, several research groups tend to converge for now on the fact that the flow patterns and flow dynamics of the ruptured aneurysms are complex and unstable. Following this idea, we investigated the vortex properties of both unruptured and ruptured cerebral aneurysms. A brief comparison of two Eulerian vortex visualization methods (Q-criterion and lambda 2 method) showed that these approaches gave similar results in our complex aneurysm geometries. We were then able to apply either one of them to a large dataset of 74 patient specific cases of intracranial aneurysms. Those real cases were obtained by 3D angiography, numerical reconstruction of the geometry, and then pulsatile CFD simulation before post-processing with the mentioned vortex visualization tools. First we tested the two Eulerian methods on a few cases to verify their implementation we made as well as compare them with each other. After that, the Q-criterion was selected as method of choice for its more obvious physical meaning (it shows the balance between two characteristics of the flow, its swirling and deformation). Using iso-surfaces of Q, we started by categorizing the patient-specific aneurysms based on the gross topology of the aneurysmal vortices. This approach being unfruitful, we found a new vortex-based characteristic property of ruptured aneurysms to stratify the rupture risk of IAs that we called the Wall-Kissing Vortices, or WKV. We observed that most ruptured aneurysms had a large amount of WKV, which appears to agree with

  17. Spectral large-eddy simulations and vortex dynamics in turbulence

    CERN Document Server

    Lesieur, M

    1999-01-01

    We present a point of view of large-eddy simulations (LES) in Fourier space, where the eddy coefficients are expressed thanks to a two- point spectral closure of isotropic turbulence, the EDQNM theory. Returning to real space, this leads to models of the structure- function family (plain, selective or filtered). These models are applied with success to predict the statistical distributions and coherent-vortex dynamics for a wide variety of turbulent flows. In three-dimensional decaying isotropic turbulence, we confirm the existence of a k/sup 4/ infrared backscatter in the kinetic-energy spectrum, and predict a new k/sup 2/ law for the pressure spectrum in this range. In the mixing layer (temporal or spatial), we show how to manipulate the topology of Kelvin-Helmholtz vortices, from quasi two- dimensionality to helical pairing. The latter vortex organization is found in a backward-facing step just behind the step, and yields big staggered Lambda -vortices which are carried away downstream. In a developed turb...

  18. Investigation of Vortex Structures in Gas-Discharge Nonneutral Electron Plasma: II. Vortex Formation, Evolution and Dynamics

    CERN Document Server

    Kervalishvili, N A

    2015-01-01

    The results of experimental investigations of inhomogeneities of gas-discharge nonneutral electron plasma obtained by using the nonperturbing experimental methods [N.A. Kervalishvili, arXiv:1502.02516 [physics.plasm-ph] (2015)] have been presented. Inhomogeneities are the dense solitary vortex structures stretched along the magnetic field, the lifetime of which is much greater than the time of electron-neutral collisions. The processes of formation, evolution and dynamics of vortex structures were studied. The periodic sequence of these processes is described for different geometries of discharge device.

  19. Nonlinear Dynamical Friction in a Gaseous Medium

    CERN Document Server

    Kim, Hyosun

    2009-01-01

    Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber M_p moving at velocity V_p through a uniform gaseous medium of adiabatic sound speed a_0. We model the perturber as a Plummer potential with softening radius r_s, and run various models with differing A=GM_p/(a_0^2 r_s) and M=V_p/a_0 by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibr...

  20. RESEARCH ON NONLINEAR PROBLEMS IN STRUCTURAL DYNAMICS.

    Science.gov (United States)

    Research on nonlinear problems structural dynamics is briefly summarized. Panel flutter was investigated to make a critical comparison between theory...panel flutter in aerospace vehicles, plausible simplifying assumptions are examined in the light of experimental results. Structural dynamics research

  1. Nonlinear dynamics in human behavior

    Energy Technology Data Exchange (ETDEWEB)

    Huys, Raoul [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Jirsa, Viktor K. (eds.) [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Florida Atlantic Univ., Boca Raton, FL (United States). Center for Complex Systems and Brain Sciences

    2010-07-01

    Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints - informational, mechanical, neural, metabolic, and so on - operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music. (orig.)

  2. Nonlinear Dynamical Analysis of Fibrillation

    Science.gov (United States)

    Kerin, John A.; Sporrer, Justin M.; Egolf, David A.

    2013-03-01

    The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.

  3. Nonlinear Approach in Nuclear Dynamics

    Science.gov (United States)

    Gridnev, K. A.; Kartavenko, V. G.; Greiner, W.

    2002-11-01

    Attention is focused on the various approaches that use the concept of nonlinear dispersive waves (solitons) in nonrelativistic nuclear physics. The problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is shown that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh-Taylor type) instability, with the dispersion terms in the evolution equations. The both instabilities may compensate each other and lead to stable solutions (solitons). A static scission configuration in cold ternary fission is considered in the framework of mean field approach. We suggest to use the inverse mean field method to solve single-particle Schrödinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system in the approximation of reflectless single-particle potentials. The soliton-like solutions of the Korteweg-de Vries equation are using to describe collective excitations of nuclei observed in inelastic alpha-particle and proton scattering. The analogy between fragmentation into parts of nuclei and buckyballs has led us to the idea of light nuclei as quasi-crystals. We establish that the quasi-crystalline structure can be formed when the distance between the alpha-particles is comparable with the length of the De Broglia wave of the alpha-particle. Applying this model to the scattering of alpha-particles we obtain that the form factor of the clusterized nucleus can be factorized into the formfactor of the cluster and the density of clusters in the nucleus. It gives possibility to study the distribution of clusters in nuclei and to resolve what kind of distribution we are dealing with: a surface or volume one.

  4. Nonlinear Chemical Dynamics and Synchronization

    Science.gov (United States)

    Li, Ning

    Alan Turing's work on morphogenesis, more than half a century ago, continues to motivate and inspire theoretical and experimental biologists even today. That said, there are very few experimental systems for which Turing's theory is applicable. In this thesis we present an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions in which droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants are dispersed in oil. The BZ reaction has become the prototype of nonlinear dynamics in chemistry and a preferred system for exploring the behavior of coupled nonlinear oscillators. Our system consists of a surfactant stabilized monodisperse emulsion of drops of aqueous BZ solution dispersed in a continuous phase of oil. In contrast to biology, here the chemistry is understood, rate constants are measured and interdrop coupling is purely diffusive. We explore a large set of parameters through control of rate constants, drop size, spacing, and spatial arrangement of the drops in lines and rings in one-dimension (1D) and hexagonal arrays in two-dimensions (2D). The Turing model is regarded as a metaphor for morphogenesis in biology but not for prediction. Here, we develop a quantitative and falsifiable reaction-diffusion model that we experimentally test with synthetic cells. We quantitatively establish the extent to which the Turing model in 1D describes both stationary pattern formation and temporal synchronization of chemical oscillators via reaction-diffusion and in 2D demonstrate that chemical morphogenesis drives physical differentiation in synthetic cells.

  5. Dynamics and vibrations progress in nonlinear analysis

    CERN Document Server

    Kachapi, Seyed Habibollah Hashemi

    2014-01-01

    Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...

  6. Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow

    Science.gov (United States)

    Choudhari, Meelan; Duck, Peter W.

    1996-01-01

    We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.

  7. Symbolic dynamics applied to a numerical simulation of a perturbed Hill's spherical vortex

    Science.gov (United States)

    Arenson, Joshua; Smith, Spencer; Mitchell, Kevin

    2016-11-01

    In the classic Hill's spherical vortex flow an invariant sphere prevents material inside the vortex from mixing with material outside. Here, we apply an additional shear and rotational flow to break the symmetry of the vortex, thereby allowing mixing of the material inside and outside. The resulting system exhibits fully 3D chaotic advection. We consider the scattering of passive tracers that are drawn into and then ejected from the vortex. Here we focus on the numerical computation of fractal scattering functions-the time trapped within the vortex as a function of two impact parameters. We then compare the fractal self-similarity of these scattering functions to those predicted by 3D homotopic lobe dynamics-a new symbolic method of describing topological dynamics.

  8. Research on Nonlinear Dynamical Systems.

    Science.gov (United States)

    1983-01-10

    investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear

  9. Nonlinear and nonequilibrium dynamics in geomaterials.

    Science.gov (United States)

    TenCate, James A; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A

    2004-08-01

    The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.

  10. Quantum Dynamics of Nonlinear Cavity Systems

    OpenAIRE

    Nation, Paul D.

    2010-01-01

    We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprised of a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing a flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal ...

  11. Vortex dynamics in the wake of a mechanical fish

    Energy Technology Data Exchange (ETDEWEB)

    Bruecker, Christoph [TU Bergakademie Freiberg, Lehrstuhl fuer Stroemungslehre und Stroemungsmaschinen, Freiberg (Germany); Bleckmann, Horst [Poppelsdorfer Schloss, Zoologisches Institut Bonn, Bonn (Germany)

    2007-11-15

    This study focuses on the three-dimensional flow around a mechanical fish model, which reproduces the typical undulatory body and fin motion of a carangiform swimmer. The mechanical model consists of a flexible skeleton embedded in a soft transparent silicone body, which is connected with two cams to a flapping and bending hinge generating a traveling wave motion with increasing amplitude from anterior to posterior, extending to a combined heaving and pitching motion at the fin. The model is submerged in a water tank and towed at the characteristic swimming speed for the neutral swimming mode at U/V = 1. The method of Scanning Particle Image Velocimetry was used to analyze the three-dimensional time-dependent flow field in the axial and saggital planes. The results confirm the earlier observations that the wake develops into a chain of vortex rings which travel sidewards perpendicular to the swimming direction. However, instead of one single vortex shed at each tail beat half-cycle we observed a pair of two vortex rings being shed. Each pair consists of a larger main vortex ring corresponding to the tail beat start-stop vortex, while the second vortex ring is due to the body bending motion. The existence of the second vortex reflects the role of the body in undulatory swimming. A simplified model of the fish body comparing it to a plate with a hinged flap demonstrates the link between the sequence of kinematics and vortex shedding. (orig.)

  12. Dynamical critical behavior in a cellular model of superconducting vortex avalanches

    Science.gov (United States)

    Vadakkan, Tegy John

    Bak, Tang, and Wiesenfeld showed that certain driven dissipative systems with many degrees of freedom organize into a critical state characterized by avalanche dynamics and power law distribution of avalanche sizes and durations. They called this phenomenon self-organized criticality and sandpile became the prototype of such dynamical systems. Universality in these systems is not yet well established. Forty years ago, de Gennes noted that the Bean state in a type-II superconductor is similar to a sandpile. Motivated by strong experimental evidences, Bassler and Paczuski (BP) proposed a 2D sandpile model to study self-organization in the dynamics of vortices in superconductors. In this dissertation, the effect of anisotropy in the vortex-vortex interaction, stochasticity in the vortex toppling rule, and the configuration of the pinning centers on the scaling properties of the avalanches in the BP model is studied. Also, universality in the cellular model of vortex dynamics is investigated.

  13. Kelvin Waves and Dynamic Knots on Perturbative Helical Vortex Lines

    CERN Document Server

    Kou, Su-Peng

    2016-01-01

    Vortex lines are one-dimensional extended objects in three-dimensional superfluids. Vortex lines have many interesting properties, including Kelvin waves, exotic statistics, and possible entanglement. In this paper, an emergent "quantum world" is explored by projecting helical vortex lines. A one-dimensional quantum Fermionic model is developed to effectively describe the local fluctuations of helical vortex lines. The elementary excitations are knots with half winding-number that obey emergent quantum mechanics. The Biot-Savart equation, and its Kelvin wave solutions on helical vortex lines become Schrodinger equation, and the wave functions of probability waves for finding knots, respectively. This work shows an alternative approach to simulating quantum many-body physics based on classical systems.

  14. Nonlinear Dynamic Model Explains The Solar Dynamic

    Science.gov (United States)

    Kuman, Maria

    Nonlinear mathematical model in torus representation describes the solar dynamic. Its graphic presentation shows that without perturbing force the orbits of the planets would be circles; only perturbing force could elongate the circular orbits into ellipses. Since the Hubble telescope found that the planetary orbits of other stars in the Milky Way are also ellipses, powerful perturbing force must be present in our galaxy. Such perturbing force is the Sagittarius Dwarf Galaxy with its heavy Black Hole and leftover stars, which we see orbiting around the center of our galaxy. Since observations of NASA's SDO found that magnetic fields rule the solar activity, we can expect when the planets align and their magnetic moments sum up, the already perturbed stars to reverse their magnetic parity (represented graphically as periodic looping through the hole of the torus). We predict that planets aligned on both sides of the Sun, when their magnetic moments sum-up, would induce more flares in the turbulent equatorial zone, which would bulge. When planets align only on one side of the Sun, the strong magnetic gradient of their asymmetric pull would flip the magnetic poles of the Sun. The Sun would elongate pole-to-pole, emit some energy through the poles, and the solar activity would cease. Similar reshaping and emission was observed in stars called magnetars and experimentally observed in super-liquid fast-spinning Helium nanodroplets. We are certain that NASA's SDO will confirm our predictions.

  15. Nonlinear dynamics of the left ventricle.

    Science.gov (United States)

    Munteanu, Ligia; Chiroiu, Calin; Chiroiu, Veturia

    2002-05-01

    The cnoidal method is applied to solve the set of nonlinear dynamic equations of the left ventricle. By using the theta-function representation of the solutions and a genetic algorithm, the ventricular motion can be described as a linear superposition of cnoidal pulses and additional terms, which include nonlinear interactions among them.

  16. NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM

    Institute of Scientific and Technical Information of China (English)

    A.Y.T.Leung; WuGuorong; ZhongWeifang

    2004-01-01

    The nonlinear dynamic equations of a multibody system composed of flexible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation effect is employed and its deformation field is described by exact vibration modes. A numerical procedure for solving the dynamic equations is presented based on the Newmark direct integration method combined with Newton-Raphson iterative method. The results of numerical examples prove the correctness and efficiency of the method proposed.

  17. Dissipative Nonlinear Dynamics in Holography

    CERN Document Server

    Basu, Pallab

    2013-01-01

    We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behaviour very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behaviour, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of the operator dual to the scalar field. Our setup can also be used to study quench-like behaviour in strongly coupled nonlinear systems.

  18. Dynamics of the vortex wakes of flying and swimming vertebrates.

    Science.gov (United States)

    Rayner, J M

    1995-01-01

    The vortex wakes of flying and swimming animals provide evidence of the history of aero- and hydrodynamic force generation during the locomotor cycle. Vortex-induced momentum flux in the wake is the reaction of forces the animal imposes on its environment, which must be in equilibrium with inertial and external forces. In flying birds and bats, the flapping wings generate lift both to provide thrust and to support the weight. Distinct wingbeat and wake movement patterns can be identified as gaits. In flow visualization experiments, only two wake patterns have been identified: a vortex ring gait with inactive upstroke, and a continuous vortex gait with active upstroke. These gaits may be modelled theoretically by free vortex and lifting line theory to predict mechanical energy consumption, aerodynamic forces and muscle activity. Longer-winged birds undergo a distinct gait change with speed, but shorter-winged species use the vortex ring gait at all speeds. In swimming fish, the situation is more complex: the wake vortices form a reversed von Kármán vortex street, but little is known about the mechanism of generation of the wake, or about how it varies with speed and acceleration or with body form and swimming mode. An unresolved complicating factor is the interaction between the drag wake of the flapping fish body and the thrusting wake from the tail.

  19. Spin torque and critical currents for magnetic vortex nano-oscillator in nanopillars

    Energy Technology Data Exchange (ETDEWEB)

    Guslienko, K Y; Gonzalez, J [Dpto. Fisica de Materiales, Universidad del Pais Vasco, 20018 Donostia-San Sebastian (Spain); Aranda, G R, E-mail: sckguslk@ehu.es [Centro de Fisica de Materiales UPV/EHU-CSIC, 20018 San Sebastian (Spain)

    2011-04-01

    We calculated the main dynamic parameters of the spin polarized current induced magnetic vortex oscillations in nanopillars, such as the range of current density, where vortex steady oscillations exist, the oscillation frequency and orbit radius. We accounted for both the non-linear vortex frequency and non-linear vortex damping. To describe the vortex excitations by the spin polarized current we used a generalized Thiele approach to motion of the vortex core as a collective coordinate. All the calculation results are represented via the free layer sizes, saturation magnetization, and the Gilbert damping. Predictions of the developed model can be checked experimentally.

  20. Vortex dynamics of stratospheric sudden warmings: a reanalysis data study using PV contour integral diagnostics

    Science.gov (United States)

    Beaumont, Robin; Thuburn, John; Kwasniok, Frank

    2015-04-01

    The dynamics of the polar vortex behind stratospheric sudden warming events is investigated in a data-based study. Potential vorticity contour integral diagnostics of mass and circulation are calculated from ERA-40 reanalysis data for the stratosphere. The edge of the vortex is easily identifiable in these diagnostics as a high gradient of potential vorticity, and the warming events are clearly visible. The amount of air stripped from the vortex as part of a preconditioning leading up to the warming events is determined using the balance equation of the mass integral. Significant persistent removal of mass from the vortex is found, with several such stripping events identifiable through the winter, especially in those during which a major sudden warming event occurred. These stripping episodes are visible in corresponding potential vorticity maps, where tongues of potential vorticity can be seen to be stripped from the vortex and mixed into the sorrounding surf zone of turbulent air.

  1. Vortex dynamics in 3D shock-bubble interaction

    Science.gov (United States)

    Hejazialhosseini, Babak; Rossinelli, Diego; Koumoutsakos, Petros

    2013-11-01

    The dynamics of shock-bubble interaction involve an interplay of vortex stretching, dilation, and baroclinic vorticity generation. Here, we quantify the interplay of these contributions through high resolution 3D simulations for several Mach and Atwood numbers. We present a volume rendering of density and vorticity magnitude fields of shock-bubble interaction at M = 3 and air/helium density ratio η = 7.25 to elucidate the evolution of the flow structures. We distinguish the vorticity growth rates due to baroclinicity, stretching, and dilatation at low and high Mach numbers as well as the late time evolution of the circulation. The results demonstrate that a number of analytical models need to be revised in order to predict the late time circulation of shock-bubble interactions at high Mach numbers. To this effect, we propose a simple model for the dependence of the circulation to Mach number and ambient to bubble density ratio for air/helium shock-bubble interactions.

  2. Nonlinear dynamics as an engine of computation.

    Science.gov (United States)

    Kia, Behnam; Lindner, John F; Ditto, William L

    2017-03-06

    Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'.

  3. Nonlinear dynamics as an engine of computation

    Science.gov (United States)

    Kia, Behnam; Lindner, John F.; Ditto, William L.

    2017-03-01

    Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue 'Horizons of cybernetical physics'.

  4. Teaching nonlinear dynamics through elastic cords

    Energy Technology Data Exchange (ETDEWEB)

    Chacon, R; Galan, C A; Sanchez-Bajo, F, E-mail: rchacon@unex.e [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz (Spain)

    2011-01-15

    We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.

  5. MEMS linear and nonlinear statics and dynamics

    CERN Document Server

    Younis, Mohammad I

    2011-01-01

    MEMS Linear and Nonlinear Statics and Dynamics presents the necessary analytical and computational tools for MEMS designers to model and simulate most known MEMS devices, structures, and phenomena. This book also provides an in-depth analysis and treatment of the most common static and dynamic phenomena in MEMS that are encountered by engineers. Coverage also includes nonlinear modeling approaches to modeling various MEMS phenomena of a nonlinear nature, such as those due to electrostatic forces, squeeze-film damping, and large deflection of structures. The book also: Includes examples of nume

  6. Mathematical modeling and applications in nonlinear dynamics

    CERN Document Server

    Merdan, Hüseyin

    2016-01-01

    The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

  7. Nonlinear Dynamics of Structures with Material Degradation

    Science.gov (United States)

    Soltani, P.; Wagg, D. J.; Pinna, C.; Whear, R.; Briody, C.

    2016-09-01

    Structures usually experience deterioration during their working life. Oxidation, corrosion, UV exposure, and thermo-mechanical fatigue are some of the most well-known mechanisms that cause degradation. The phenomenon gradually changes structural properties and dynamic behaviour over their lifetime, and can be more problematic and challenging in the presence of nonlinearity. In this paper, we study how the dynamic behaviour of a nonlinear system changes as the thermal environment causes certain parameters to vary. To this end, a nonlinear lumped mass modal model is considered and defined under harmonic external force. Temperature dependent material functions, formulated from empirical test data, are added into the model. Using these functions, bifurcation parameters are defined and the corresponding nonlinear responses are observed by numerical continuation. A comparison between the results gives a preliminary insight into how temperature induced properties affects the dynamic response and highlights changes in stability conditions of the structure.

  8. Nonlinear dynamics and chaotic phenomena an introduction

    CERN Document Server

    Shivamoggi, Bhimsen K

    2014-01-01

    This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics  -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special...

  9. Advance Ratio Effects on the Dynamic-stall Vortex of a Rotating Blade in Steady Forward Flight

    Science.gov (United States)

    2014-08-06

    Office P.O. Box 12211 Research Triangle Park , NC 27709-2211 Leading-edge vortex, Dynamic stall vortex, Vortex flows, Rotating wing REPORT...observed on rotating insect wing investigations2,9–13. A common theme among most of these investigations is the existence of a strong span-wise flow...structures by considering only the topology of the flow field. It is specifically designed to identify a large scale vortex superposed on a small-scale

  10. PREDICTION OF VORTEX-INDUCED VIBRATION OF LONG FLEXIBLE CYLINDERS MODELED BY A COUPLED NONLINEAR OSCILLATOR:INTEGRAL TRANSFORM SOLUTION

    Institute of Scientific and Technical Information of China (English)

    GU Ji-jun; AN Chen; LEVI Carlos; SU Jian

    2012-01-01

    The Generalized Integral Transform Technique (GITT) was applied to predict dynamic response of Vortex-Induced Vibration (VIV) of a long flexible cylinder.A nonlinear wake oscillator model was used to represent the cross-flow force acting on the cylinder,leading to a coupled system of second-order Partial Differential Equations (PDEs) in temporal variable.The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs),which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL).Numerical results were presented for comparison to those given by the finite difference method and experimental results,allowing a critical evaluation of the technique performance.The influence of variation of mean axial tension induced by elongation of flexible cylinder was evaluated,which was shown to be not negligible in numerical simulation of VIV of a long flexible cylinder.

  11. Nonlinear dynamics new directions models and applications

    CERN Document Server

    Ugalde, Edgardo

    2015-01-01

    This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: ·         Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...

  12. Dynamic disturbance decoupling for nonlinear systems

    NARCIS (Netherlands)

    Huijberts, H.J.C.; Nijmeijer, H.; Wegen, van der L.L.M.

    1992-01-01

    In analogy with the dynamic input-output decoupling problem the dynamic disturbance decoupling problem for nonlinear systems is introduced. A local solution of this problem is obtained in the case that the system under consideration is invertible. The solution is given in algebraic as well as in geo

  13. Nonlinear-dynamical arrhythmia control in humans.

    Science.gov (United States)

    Christini, D J; Stein, K M; Markowitz, S M; Mittal, S; Slotwiner, D J; Scheiner, M A; Iwai, S; Lerman, B B

    2001-05-08

    Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.

  14. Dynamical systems analysis of fluid transport in time-periodic vortex ring flows

    OpenAIRE

    Shariff, Karim; Leonard, Anthony; Ferziger, Joel H.

    2006-01-01

    It is known that the stable and unstable manifolds of dynamical systems theory provide a powerful tool for understanding Lagrangian aspects of time-periodic flows. In this work we consider two time-periodic vortex ring flows. The first is a vortex ring with an elliptical core. The manifolds provide information about entrainment and detrainment of irrotational fluid into and out of the volume transported with the ring. The likeness of the manifolds with features observed in flow visualization ...

  15. A possible quantum fluid-dynamical approach to vortex motion in nuclei

    CERN Document Server

    Nishiyama, Seiya

    2016-01-01

    The essential point of Bohr-Mottelson theory is to assume a irrotational flow. As was already suggested by Marumori and Watanabe, the internal rotational motion, i.e., the vortex motion, however, may exist also in nuclei. So, we have a necessity of taking the vortex motion into consideration. In a classical fluid dynamics, there are various ways to treat the internal rotational velocity. The Clebsch representation, v(x) = -\

  16. Nonlinear amplitude dynamics in flagellar beating

    CERN Document Server

    Oriola, David; Casademunt, Jaume

    2016-01-01

    The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive crosslinkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatiotemporal dynamics of dynein populations and flagell...

  17. Passive Tracer Dynamics in 4 Point-Vortex Flow

    CERN Document Server

    Laforgia, A; Kuznetsov, L V; Zaslavsky, G M

    2000-01-01

    The advection of passive tracers in a system of 4 identical point vortices is studied when the motion of the vortices is chaotic. The phenomenon of vortex-pairing has been observed and statistics of the pairing time is computed. The distribution exhibits a power-law tail with exponent (\\sim 3.6), implying finite average pairing time. Tracer motion is studied for a chosen initial condition of the vortex system. Accessible phase space is investigated. The size of the cores around the vortices is well approximated by the minimum inter-vortex distance and stickiness to these cores is observed. We investigate the origin of stickiness which we link to the phenomenon of vortex pairing and jumps of tracers between cores. Motion within the core is considered and fluctuations are shown to scale with tracer-vortex distance (r) as (r^{6}). No outward or inward diffusion of tracers are observed. This investigation allows the separation of the accessible phase space in four distinct regions, each with its own specific prop...

  18. Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration

    Science.gov (United States)

    Prasad, G.

    2017-06-01

    Relativistic formulation of Helmholtz's vorticity transport equation is presented on the basis of Maxwell-like version of Euler's equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg's theory of spacelike congruence of vortex lines and 1+1+(2) decomposition of the gradient of fluid's 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid's angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid's angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid's rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.

  19. Nonlinear Dynamics and Control of Flexible Structures

    Science.gov (United States)

    1991-03-01

    Freedom," Ph.D. Thesis, Department of Theoretical and Applied Mechanics, Cornell University, in preparation. 5I I URI Reorts Islam , Saiful and Mircea...Theoretical and Applied Mechanics I S. Islam Civil and Environmental Engineering I 2! I 3 URI Accomplishments 3 -Nonlinear Dynamics and Chaos in Flexible...Structures with Symmetry," 31 (1991) 265-285. Islam , S. and M. Grigoriu, "Nonlinear Random Vibration of Pin-Jointed Trusses with Imperfections," in

  20. On the Nonlinear Evolution of a Stationary Cross-Flow Vortex in a Fully Three-Dimensional Boundary Layer Flow

    Science.gov (United States)

    Gajjar, J. S. B.

    1995-01-01

    We consider the nonlinear stability of a fully three-dimensional boundary layer flow in an incompressible fluid and derive an equation governing the nonlinear development of a stationary cross-flow vortex. The amplitude equation is a novel integro-differential equation which has spatial derivatives of the amplitude occurring in the kernal function. It is shown that the evolution of the cross-flow vortex is strongly coupled to the properties of an unsteady wall layer which is in fact driven by an unknown slip velocity, proportional to the amplitude of the cross-flow vortex. The work is extended to obtain the corresponding equation for rotating disk flow. A number of special cases are examined and the numerical solution for one of cases, and further analysis, demonstrates the existence of finite-distance as well as focussing type singularities. The numerical solutions also indicate the presence of a new type of nonlinear wave solution for a certain set of parameter values.

  1. Dynamical Imaging using Spatial Nonlinearity

    Science.gov (United States)

    2014-01-29

    Imin )/ (Imax + Imin ) = 0.15 for detection of the bars (from maxima to central dip). For our experimental measurements, the best linear visibility is...Statistical theory for incoherent light propagation in nonlinear media, Physical Review E, 65 (2002) 035602. [52] M.J. Bastiaans, Application of the...1238. [53] M.E. Testorf, B.M. Hennelly, J. Ojeda-Castañeda, Phase-space optics : fundamentals and applications , McGraw-Hill, New York, 2010. [54] K.H

  2. Nonlinear dynamic vibration absorbers with a saturation

    Science.gov (United States)

    Febbo, M.; Machado, S. P.

    2013-03-01

    The behavior of a new type of nonlinear dynamic vibration absorber is studied. A distinctive characteristic of the proposed absorber is the impossibility to extend the system to infinity. The mathematical formulation is based on a finite extensibility nonlinear elastic potential to model the saturable nonlinearity. The absorber is attached to a single degree-of-freedom linear/nonlinear oscillator subjected to a periodic external excitation. In order to solve the equations of motion and to analyze the frequency-response curves, the method of averaging is used. The performance of the FENE absorber is evaluated considering a variation of the nonlinearity of the primary system, the damping and the linearized frequency of the absorber and the mass ratio. The numerical results show that the proposed absorber has a very good efficiency when the nonlinearity of the primary system increases. When compared with a cubic nonlinear absorber, for a large nonlinearity of the primary system, the FENE absorber shows a better effectiveness for the whole studied frequency range. A complete absence of quasi-periodic oscillations is also found for an appropriate selection of the parameters of the absorber. Finally, direct integrations of the equations of motion are performed to verify the accuracy of the proposed method.

  3. Structural optimization for nonlinear dynamic response.

    Science.gov (United States)

    Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S

    2015-09-28

    Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.

  4. Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity

    CERN Document Server

    Kartashov, Y V; Shnir, Y; Torner, L

    2014-01-01

    Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist, s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis m, appear in many fields, including the field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multi-component systems, or as trapped quasi-linear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0,1,2 are produced. They are stable for m1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented...

  5. Vortex dynamics in the presence of excess energy for the Landau-Lifschitz-Gilbert equation

    CERN Document Server

    Kurzke, Matthias; Moser, Roger; Spirn, Daniel

    2012-01-01

    We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic vortex system. We present a PDE-based method for proving vortex dynamics that does not rely on strong well-preparedness of the initial data and allows for instantaneous changes in the strength of the gyrovector force due to bubbling events. The main tools are estimates of the Hodge decomposition of the supercurrent and an analysis of the defect measure of weak convergence of the stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the presence of excess energy are also discussed.

  6. Linear and Nonlinear Dynamical Chaos

    CERN Document Server

    Chirikov, B V

    1997-01-01

    Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal results of the studies into chaos in classical mechanics are presented in some detail, including the strong local instability and robustness of the motion, continuity of both the phase space as well as the motion spectrum, and time reversibility but nonrecurrency of statistical evolution, within the general picture of chaos as a specific case of dynamical behavior. Analysis of the apparently very deep and challenging contradictions of this picture with the quantum principles is given. The quantum view of dynamical chaos, as an attempt to resolve these contradictions guided by the correspondence principle and based upon the characteristic time scales of quantum evolution, is explained. The picture of the quantum chaos as a new generic dynamical phenomenon is outlined together wit...

  7. Formation and Dynamics of Vortex Structures in Pure and Gas-Discharge Nonneutral Collisionless Electron Plasmas

    CERN Document Server

    Kervalishvili, N A

    2013-01-01

    The comparative analysis of the results of experimental investigations of the processes of formation, interaction and dynamics of vortex structures in pure electron and gas-discharge electron nonneutral plasmas taking place for the period of time much less than the electron-neutral collision time has been given. The general processes of formation and behavior of vortex structures in these two plasmas were considered. The phenomena, taking place only in one of these plasmas were also considered. It is shown that the existing difference in behavior of vortex structures is caused by different initial states of nonneutral electron plasmas. The role of vortex structures in the processes taking place in nonneutral electron plasma is discussed.

  8. Nonlinear dynamics of cell orientation

    Science.gov (United States)

    Safran, S. A.; de, Rumi

    2009-12-01

    The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, τc , for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, τc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.

  9. Delta-singular vortex dynamics on a rotating sphere and stability of coupled atmospheric centers of action

    CERN Document Server

    Mokhov, I I; Chefranov, A G

    2010-01-01

    Existence of a stationary mode for a Hamiltonian dynamic system of two point vortexes with different signs on different latitudes of a uniform rotating sphere complying with observed data is stated. It is shown that such mode realization is possible only in the case when the more intensive cyclonic vortex has greater latitude than that of the anticyclonic vortex. A criterion of exponential instability of the stationary vortex mode taken into account impact of the polar vortexes is obtained. Compliance of the theory to observed data and reanalysis for coupled quasi-stationary systems of cyclonic and anticyclonic atmosphere action centers above oceans in the Northern Hemisphere is considered.

  10. Vortex dynamics in coherently coupled Bose-Einstein condensates

    Science.gov (United States)

    Calderaro, Luca; Fetter, Alexander L.; Massignan, Pietro; Wittek, Peter

    2017-02-01

    In classical hydrodynamics with uniform density, vortices move with the local fluid velocity. This description is rewritten in terms of forces arising from the interaction with other vortices. Two such positive straight vortices experience a repulsive interaction and precess in a positive (anticlockwise) sense around their common centroid. A similar picture applies to vortices in a two-component, two-dimensional uniform Bose-Einstein condensate (BEC) coherently coupled through rf Rabi fields. Unlike the classical case, however, the rf Rabi coupling induces an attractive interaction and two such vortices with positive signs now rotate in the negative (clockwise) sense. Pairs of counter-rotating vortices are instead found to translate with uniform velocity perpendicular to the line joining their cores. This picture is extended to a single vortex in a two-component trapped BEC. Although two uniform vortex-free components experience familiar Rabi oscillations of particle-number difference, such behavior is absent for a vortex in one component because of the nonuniform vortex phase. Instead the coherent Rabi coupling induces a periodic vorticity transfer between the two components.

  11. Dynamics of vortex matter in YBCO sub-micron bridges

    Energy Technology Data Exchange (ETDEWEB)

    Papari, G., E-mail: papari@fisica.unina.it [Dipartimento di Fisica, Università degli Studi di Napoli Federico II, I-80126 Napoli (Italy); Carillo, F. [NEST, CNR-NANO and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa (Italy); Stornaiuolo, D.; Massarotti, D. [Dipartimento di Fisica, Università degli Studi di Napoli Federico II, I-80126 Napoli (Italy); CNR-SPIN UOS Napoli, Complesso Universitario di Monte SantAngelo, via Cinthia, 80126 Napoli (Italy); Longobardi, L. [American Physical Society, 1 Research Road, Ridge, NY 11961 (United States); Beltram, F. [NEST, CNR-NANO and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa (Italy); Tafuri, F. [CNR-SPIN UOS Napoli, Complesso Universitario di Monte SantAngelo, via Cinthia, 80126 Napoli (Italy); Dipartimento di Ingegneria Industriale e dell' informazione, Seconda Universit‘a di Napoli, via Roma 29, 81031 Aversa (CE) (Italy)

    2014-11-15

    Highlights: • Superconducting properties of YBCO nanowires in the width range ξvortex lattice melting temperature. • Magnetoresistence oscillations: entrance of vortex rows and modulation of screening currents. - Abstract: We have developed a fabrication process that allows us to realize pure YBCO nanowires displaying robust superconductivity at widths w as low as 160 nm. We can modify the process in order to maintain a Au protective layer. This allows us to scale our nanowires even further to widths as low as 50 nm. We have studied how the presence of vortices and the occurrence of phase slips affect the transport properties of nanowires in the width range ξVortex entry barrier is found to scale with the width. Our findings confirm that for widths ξvortex flow.

  12. Structural optimization for nonlinear dynamic response

    DEFF Research Database (Denmark)

    Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.

    2015-01-01

    condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped–clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...... by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance...

  13. Dynamics of Nonlinear Waves on Bounded Domains

    CERN Document Server

    Maliborski, Maciej

    2016-01-01

    This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy to concentrate on smaller scales leading to a turbulent behaviour. Which of these two possibilities occurs depends on a model and the initial conditions. In the quasiperiodic scenario there exist very special time-periodic solutions. They result for a delicate balance between dispersion and nonlinear interaction. The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains. While turbulence is mainly associated with hydrodynamics, recent research in General Relativity has also revealed turbulent phenomena. Numerical studies of a self-gravitating massless scalar field in spherical symmetry gave evidence that anti-de Sitter space ...

  14. Phase slips and vortex dynamics in Josephson oscillations between Bose-Einstein condensates

    Science.gov (United States)

    Abad, M.; Guilleumas, M.; Mayol, R.; Piazza, F.; Jezek, D. M.; Smerzi, A.

    2015-02-01

    We study the relation between Josephson dynamics and topological excitations in a dilute Bose-Einstein condensate confined in a double-well trap. We show that the phase slips responsible for the self-trapping regime are created by vortex rings entering and annihilating inside the weak-link region or created at the center of the barrier and expanding outside the system. Large amplitude oscillations just before the onset of self-trapping are also strictly connected with the dynamics of vortex rings at the edges of the inter-well barrier. Our results extend and analyze the dynamics of the vortex-induced phase slippages suggested a few decades ago in relation to the “ac” Josephson effect of superconducting and superfluid helium systems.

  15. Nonlinear dynamics in the study of birdsong

    Science.gov (United States)

    Mindlin, Gabriel B.

    2017-09-01

    Birdsong, a rich and complex behavior, is a stellar model to understand a variety of biological problems, from motor control to learning. It also enables us to study how behavior emerges when a nervous system, a biomechanical device and the environment interact. In this review, I will show that many questions in the field can benefit from the approach of nonlinear dynamics, and how birdsong can inspire new directions for research in dynamics.

  16. Nonlinear dynamics in particle accelerators

    CERN Document Server

    Dilão, Rui

    1996-01-01

    This book is an introductory course to accelerator physics at the level of graduate students. It has been written for a large audience which includes users of accelerator facilities, accelerator physicists and engineers, and undergraduates aiming to learn the basic principles of construction, operation and applications of accelerators.The new concepts of dynamical systems developed in the last twenty years give the theoretical setting to analyse the stability of particle beams in accelerator. In this book a common language to both accelerator physics and dynamical systems is integrated and dev

  17. Ontology of Earth's nonlinear dynamic complex systems

    Science.gov (United States)

    Babaie, Hassan; Davarpanah, Armita

    2017-04-01

    As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.

  18. Some Nonlinear Dynamic Inequalities on Time Scales

    Indian Academy of Sciences (India)

    Wei Nian Li; Weihong Sheng

    2007-11-01

    The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736--751).

  19. Estimating the uncertainty in underresolved nonlinear dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Chorin, Alelxandre; Hald, Ole

    2013-06-12

    The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise term that describes the uncertainty turns out to be neither Markovian nor Gaussian. It is argued that this is the general situation.

  20. Nonlinear dynamics and quantitative EEG analysis.

    Science.gov (United States)

    Jansen, B H

    1996-01-01

    Quantitative, computerized electroencephalogram (EEG) analysis appears to be based on a phenomenological approach to EEG interpretation, and is primarily rooted in linear systems theory. A fundamentally different approach to computerized EEG analysis, however, is making its way into the laboratories. The basic idea, inspired by recent advances in the area of nonlinear dynamics and chaos theory, is to view an EEG as the output of a deterministic system of relatively simple complexity, but containing nonlinearities. This suggests that studying the geometrical dynamics of EEGs, and the development of neurophysiologically realistic models of EEG generation may produce more successful automated EEG analysis techniques than the classical, stochastic methods. A review of the fundamentals of chaos theory is provided. Evidence supporting the nonlinear dynamics paradigm to EEG interpretation is presented, and the kind of new information that can be extracted from the EEG is discussed. A case is made that a nonlinear dynamic systems viewpoint to EEG generation will profoundly affect the way EEG interpretation is currently done.

  1. A Computational Fluid Dynamics Study of Swirling Flow Reduction by Using Anti-Vortex Baffle

    Science.gov (United States)

    Yang, H. Q.; Peugeot, John W.; West, Jeff S.

    2017-01-01

    An anti-vortex baffle is a liquid propellant management device placed adjacent to an outlet of the propellant tank. Its purpose is to substantially reduce or eliminate the formation of free surface dip and vortex, as well as prevent vapor ingestion into the outlet, as the liquid drains out through the flight. To design an effective anti-vortex baffle, Computational Fluid Dynamic (CFD) simulations were undertaken for the NASA Ares I vehicle LOX tank subjected to the simulated flight loads with and without the anti-vortex baffle. The Six Degree-Of-Freedom (6-DOF) dynamics experienced by the Crew Launch Vehicle (CLV) during ascent were modeled by modifying the momentum equations in a CFD code to accommodate the extra body forces from the maneuvering in a non-inertial frame. The present analysis found that due to large moments, the CLV maneuvering has a significant impact on the vortical flow generation inside the tank. Roll maneuvering and side loading due to pitch and yaw are shown to induce swirling flow. The vortical flow due to roll is symmetrical with respect to the tank centerline, while those induced by pitch and yaw maneuverings showed two vortices side by side. The study found that without the anti-vortex baffle, the swirling flow caused surface dip during the late stage of drainage and hence early vapor ingestion. The flow can also be non-uniform in the drainage pipe as the secondary swirling flow velocity component can be as high as 10% of the draining velocity. An analysis of the vortex dynamics shows that the swirling flow in the drainage pipe during the Upper Stage burn is mainly the result of residual vortices inside the tank due to the conservation of angular momentum. The study demonstrated that the swirling flow in the drainage pipe can be effectively suppressed by employing the anti-vortex baffle.

  2. Vortex dynamics in coherently coupled Bose-Einstein condensates

    CERN Document Server

    Calderaro, Luca; Massignan, Pietro; Wittek, Peter

    2016-01-01

    In classical hydrodynamics with uniform density, vortices move with the local fluid velocity. This description is rewritten in terms of forces arising from the interaction with other vortices. Two such positive straight vortices experience a repulsive interaction and precess in a positive (anticlockwise) sense around their common centroid. A similar picture applies to vortices in a two-component two-dimensional uniform Bose-Einstein condensate (BEC) coherently coupled through rf Rabi fields. Unlike the classical case, however, the rf Rabi coupling induces an attractive interaction and two such vortices with positive signs now rotate in the negative (clockwise) sense. Pairs of counter-rotating vortices are instead found to translate with uniform velocity perpendicular to the line joining their cores. This picture is extended to a single vortex in a two-component trapped BEC. Although two uniform vortex-free components experience familiar Rabi oscillations of particle-number difference, such behavior is absent ...

  3. Dynamic evolution of coherent vortex dipole in atmospheric turbulence

    Science.gov (United States)

    Li, Jinhong; Zeng, Jun

    2017-01-01

    The analytical expression for the cross-spectral density function of Gaussian Schell-model (GSM) beams with coherent vortex dipole (CVD) propagating through atmospheric turbulence is derived, which enables us to study the evolution process of CVD propagating through atmospheric turbulence, where the influences of the beams parameters and atmospheric turbulence parameters on the ratio of critical off-axis distance to the waist width are stressed. It shows that the evolution process of the CVD depends on the off-axis distance. The larger the off-axis distance is, the more the number of CVD is. When the off-axis distance is zero, the position of coherent vortices with positive and negative topological charge of CVD propagating through atmospheric turbulence is always symmetry. When the off-axis distance is big enough, compared with the situation at source plane, the orientation of the positive coherent vortex of inherent CVD and negative coherent vortex of that rotates 180° in the far field. The larger the structure constant and the waist width are, as well as the smaller the spatial correlation length and the inner scale are, the smaller the ratio ac/w0 is. Besides, the ratio ac/w0 will no longer change when the spatial correlation length or the inner scale increases to a certain value, whereas the outer scale has no effect on the ratio.

  4. Dynamical effects of overparametrization in nonlinear models

    Science.gov (United States)

    Aguirre, Luis Antonio; Billings, S. A.

    1995-01-01

    This paper is concemed with dynamical reconstruction for nonlinear systems. The effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated. It is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns. The complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters. In this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes. Moreover, some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels. In order to precisely quantify the complexity of the reconstructions, global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks.

  5. Nonlinear dynamics of a double bilipid membrane.

    Science.gov (United States)

    Sample, C; Golovin, A A

    2007-09-01

    The nonlinear dynamics of a biological double membrane that consists of two coupled lipid bilayers, typical of some intracellular organelles such as mitochondria or nuclei, is studied. A phenomenological free-energy functional is formulated in which the curvatures of the two parts of the double membrane and the distance between them are coupled to the lipid chemical composition. The derived nonlinear evolution equations for the double-membrane dynamics are studied analytically and numerically. A linear stability analysis is performed, and the domains of parameters are found in which the double membrane is stable. For the parameter values corresponding to an unstable membrane, numerical simulations are performed that reveal various types of complex dynamics, including the formation of stationary, spatially periodic patterns.

  6. Nonlinear dynamics and quantum chaos an introduction

    CERN Document Server

    Wimberger, Sandro

    2014-01-01

    The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

  7. Nonlinear adhesion dynamics of confined lipid membranes

    Science.gov (United States)

    To, Tung; Le Goff, Thomas; Pierre-Louis, Olivier

    Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems. Supported by the grand ANR Biolub.

  8. Superworldvolume dynamics of superbranes from nonlinear realizations

    Energy Technology Data Exchange (ETDEWEB)

    Bellucci, S. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, Frascati, RM (Italy); Ivanov, E. [Paris Univ., Paris (France). Lab. de Physique Theorique et des Hautes Energies]|[Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow (USSR); Krivonos, S. [Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow (USSR)

    2000-07-01

    Based on the concept of the partial breaking of global supersymmetry (PBGS), it has been derived the worldvolume superfield equations of motion for N=1, D=4 supermembrane, as well as for the space-time filling D2- and D3-branes, from nonlinear realizations of the corresponding supersymmetries. It has been argued that it is of no need to take care of the relevant automorphism groups when being interested in the dynamical equations. This essentially facilitates computations. As a by-product, it has been obtained a new polynomial representation for the d=3,4 Born-Infeld equations, with merely a cubic nonlinearity.

  9. Vortex Dynamics in a Spin-Orbit-Coupled Bose-Einstein Condensate

    Science.gov (United States)

    Fetter, Alexander L.

    2015-07-01

    Vortices in a one-component dilute atomic ultracold Bose-Einstein condensate (BEC) usually arise as a response to externally driven rotation. Apart from a few special situations, these vortices are singly quantized with unit circulation (Fetter, Rev Mod Phys 81, 647-691, 2009). Recently, the NIST group has constructed a two-component BEC with a spin-orbit-coupled Hamiltonian involving Pauli matrices (Spielman, Phys Rev A 79, 063613, 2009; Y.-J. Lin et al., Nature 462, 628-632, 2009; Y.-J. Lin et al., Nature 471, 83-87, 2011), and I here study the dynamics of a two-component vortex in such a spin-orbit-coupled condensate. These spin-orbit-coupled BECs use an applied magnetic field to split the hyperfine levels. Hence, they rely on a focused laser beam to trap the atoms. In addition, two Raman laser beams create an effective (or synthetic) gauge potential. The resulting spin-orbit Hamiltonian is discussed in some detail. The various laser beams are fixed in the laboratory, so that it is not feasible to nucleate a vortex by an applied rotation that would need to rotate all the laser beams and the magnetic field. In a one-component BEC, a vortex can also be created by a thermal quench, starting from the normal state and suddenly cooling deep into the condensed state (Freilich et al., Science 329, 1182-1185, 2010). I propose that a similar method would work for a vortex in a spin-orbit-coupled BEC. Such a vortex has two components, and each has its own circulation quantum number (typically ). If both components have the same circulation, I find that the composite vortex should execute uniform precession, like that observed in a single-component BEC (Freilich et al., Science 329, 1182-1185, 2010). In contrast, if one component has unit circulation and the other has zero circulation, then some fraction of the dynamical vortex trajectories should eventually leave the condensate, providing clear experimental evidence for this unusual vortex structure. In the context of

  10. Nonlinear Dynamics on Interconnected Networks

    Science.gov (United States)

    Arenas, Alex; De Domenico, Manlio

    2016-06-01

    Networks of dynamical interacting units can represent many complex systems, from the human brain to transportation systems and societies. The study of these complex networks, when accounting for different types of interactions has become a subject of interest in the last few years, especially because its representational power in the description of users' interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.) [1], or in representing different transportation modes in urban networks [2,3]. The general name coined for these networks is multilayer networks, where each layer accounts for a type of interaction (see Fig. 1).

  11. Nonlinear dynamics of interacting populations

    CERN Document Server

    Bazykin, Alexander D

    1998-01-01

    This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative the

  12. Dynamical systems analysis of fluid transport in time-periodic vortex ring flows

    Science.gov (United States)

    Shariff, Karim; Leonard, Anthony; Ferziger, Joel H.

    2006-04-01

    It is known that the stable and unstable manifolds of dynamical systems theory provide a powerful tool for understanding Lagrangian aspects of time-periodic flows. In this work we consider two time-periodic vortex ring flows. The first is a vortex ring with an elliptical core. The manifolds provide information about entrainment and detrainment of irrotational fluid into and out of the volume transported with the ring. The likeness of the manifolds with features observed in flow visualization experiments of turbulent vortex rings suggests that a similar process might be at play. However, what precise modes of unsteadiness are responsible for stirring in a turbulent vortex ring is left as an open question. The second situation is that of two leapfrogging rings. The unstable manifold shows striking agreement with even the fine features of smoke visualization photographs, suggesting that fluid elements in the vicinity of the manifold are drawn out along it and begin to reveal its structure. We suggest that interpretations of these photographs that argue for complex vorticity dynamics ought to be reconsidered. Recently, theoretical and computational tools have been developed to locate structures analogous to stable and unstable manifolds in aperiodic, or finite-time systems. The usefulness of these analogs is demonstrated, using vortex ring flows as an example, in the paper by Shadden, Dabiri, and Marsden [Phys. Fluids 18, 047105 (2006)].

  13. Dynamics of two-dimensional vortex system in a strong square pinning array at the second matching field

    Energy Technology Data Exchange (ETDEWEB)

    Ren, Qing-Bao [Department of Physics, Lishui University, Lishui 323000 (China); Luo, Meng-Bo, E-mail: Luomengbo@zju.edu.cn [Department of Physics, Zhejiang University, Hangzhou 310027 (China)

    2013-10-30

    We study the dynamics of a two-dimensional vortex system in a strong square pinning array at the second matching field. Two kinds of depinning behaviors, a continuous depinning transition at weak pinning and a discontinuous one at strong pinning, are found. We show that the two different kinds of vortex depinning transitions can be identified in transport as a function of the pinning strength and temperature. Moreover, interstitial vortex state can be probed from the transport properties of vortices.

  14. Bubble nonlinear dynamics and stimulated scattering process

    Science.gov (United States)

    Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu

    2016-02-01

    A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).

  15. Critical state and vortex dynamics in high temperature superconductors: Experimental and numerical investigations

    Energy Technology Data Exchange (ETDEWEB)

    Gjoelmesli, S.

    1995-05-01

    In this thesis, statics and dynamics of magnetic vortices in high temperature superconductors has been investigated by ac susceptibility, magnetic relaxation and transport measurements, using several different compounds. Measurements of the complex susceptibility of granular superconducting YBa{sub 2}Cu{sub 3}O{sub 7{sub -}x} (YBCO) reveal two distinct regimes of screening due to granular and intergranular currents respectively. In the critical state, the presence of a dc field breaks the symmetry of the experimental conditions if the critical current is field dependent. In such experiments two peaks in the loss component {chi}{sup ``}(B) of the complex susceptibility are found, both caused by intergranular currents. The symmetry breaking due to a dc field is seen directly in sampled waveforms of the pickup coil voltage, which represent the time derivative of the dynamic magnetization. In contrast to granular materials, a single crystal YBCO displays significant frequency dependence of the peak of the loss component {chi}{sup ``}(T). The power-law voltage current characteristic is equivalent to nonlinear vortex diffusion, with a characteristic length scale which reduces to the Bean depth and the classical skin-depth as the exponent tends to infinity and one, respectively. Magnetic relaxation measurements on the mercury based superconductor Hg-1212 has been done by means of a SQUID magnetometer. A new set-up for measurements of voltage-current characteristics of superconducting tapes and other samples has been constructed. Silver sheathed Bi-2223 tapes have been measured. 123 refs., 61 figs., 1 tab.

  16. Point vortex models and the dynamics of strong vortices in the atmosphere and oceans

    Energy Technology Data Exchange (ETDEWEB)

    Aref, H.; Stremler, M.A. [Illinois Univ., Urbana, IL (United States). Dept. of Theoretical and Applied Mechanics

    2001-07-01

    Point vortex dynamics has a special 'flavor' since it combines fluid mechanics, which usually entails the solution of partial differential equations, with the theory of dynamical systems, which is usually concerned with a small number of ordinary differential equations. Modern developments have shown that very complicated things can happen already for a small number of ODEs. In the case of classical point vortices on the unbounded plane, the two-vortex problem is integrable and very simple. Furthermore, one has the interesting result that the three-vortex problem is integrable. Generally, dynamical three-body problems are non-integrable unless the system in question is integrable for any number of particles. Four point vortices, on the other hand, can display chaotic motion. Indeed, the transition from integrability to chaos occurs already for the problem of passive advection of a particle in the flow field produced by the integrable three-vortex motion. The motion of the advected particle can be chaotic. This insight led to the concept of chaotic advection, which has since emerged as a general paradigm of flow kinematics and fluid mixing, and has been actively pursued in the context of very viscous flows. Here again there are important connections to geophysical fluid dynamics. Thus, Zimmerman and collaborators have emphasized that the mixing in shallow tidal basins, such as the Wadden sea, is probably more appropriately described by chaotic advection than by turbulent transport models. (orig.)

  17. Dynamical influence of vortex–antivortex pairs in magnetic vortex oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Otxoa, R.M., E-mail: ro274@cam.ac.uk [Institut d' Electronique Fondamentale, UMR CNRS 8622, Univ. Paris-Sud, 91405 Orsay (France); Hitachi Cambridge Laboratory, J. J. Thomson Avenue, CB3 OHE Cambridge (United Kingdom); Petit-Watelot, S. [Institut d' Electronique Fondamentale, UMR CNRS 8622, Univ. Paris-Sud, 91405 Orsay (France); Institut Jean Lamour, UMR CNRS 7198, Univ. de Lorraine, F-54506 Vandoeuvre-les-Nancy (France); Manfrini, M.; Radu, I.P.; Thean, A. [IMEC, Kapeldreef 75, 3001 Leuven (Belgium); Kim, Joo-Von; Devolder, T. [Institut d' Electronique Fondamentale, UMR CNRS 8622, Univ. Paris-Sud, 91405 Orsay (France)

    2015-11-15

    We study the magnetization dynamics in a nanocontact magnetic vortex oscillators as function of temperature. Low temperature experiments reveal that the dynamics at low and high currents differ qualitatively. At low currents, we excite a temperature independent standard oscillation mode, consisting of a gyrotropic motion of a vortex about the nanocontact in the free layer. Above a critical current, a sudden jump in the frequency is observed, which occurs with a substantial increase of the frequency versus current slope factor. Using micromagnetic simulation and analytical modeling, we associate this new regime to the creation of a vortex–antivortex pair in the pinned layer of the spin valve. This pair gives an additional perpendicular spin torque component that alters the free layer vortex dynamics, which can be quantitatively accounted for by an analytical model. - Highlights: • We study the magnetization dynamics in a nanocontact magnetic vortex oscillators as function of temperature. • Electrical measurements reveal the existence of a vortex–antivortex pair in the pinnel layer above certain value of the injected current. • Micromagnetic simulations confirm qualitatively this scenario.

  18. Chaotic dynamics of a body–vortex pair

    DEFF Research Database (Denmark)

    Pedersen, Johan Rønby; Aref, Hassan

    2011-01-01

    the occurrence of chaos in the system of ODEs emerging from these assumptions. It is well-known that the system consisting of a circular body with uniform mass distribution interacting with a single point vortex is integrable. Here we investigate how this integrability breaks down when the body center...... contains a finite number of point vortices of constant circulation but is otherwise irrotational. We assign a mass distribution to the body and let it move and rotate freely in response to the force and torque exerted by the fluid. Conversely, the fluid moves in response to the body motion. We study...

  19. Nonlinear Dynamics of Coiling in Viscoelastic Jets

    CERN Document Server

    Majmudar, Trushant; Hartt, William; McKinley, Gareth

    2010-01-01

    Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain less well understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in great detail; buckling instability in viscous jets leads to regular periodic coiling of the jet that exhibits a non-trivial frequency dependence with the height of the fall. Very few experimental or theoretical studies exist for continuous viscoelastic jets beyond the onset of the first instability. Here, we present a systematic study of the effects of viscoelasticity on the dynamics of free surface continuous jets of surfactant solutions that form worm-like micelles. We observe complex nonlinear spatio-temporal dynamics of the jet and uncover a transition from periodic to doubly-periodic or quasi-periodic to a multi-frequency, possibly chaotic dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the "leaping shampoo effect" or the Kaye effe...

  20. CISM course on exploiting nonlinear behaviour in structural dynamics

    CERN Document Server

    Virgin, Lawrence; Exploiting Nonlinear Behavior in Structural Dynamics

    2012-01-01

    The articles in this volume give an overview and introduction to nonlinear phenomena in structural dynamics. Topics treated are approximate methods for analyzing nonlinear systems (where the level of nonlinearity is assumed to be relatively small), vibration isolation, the mitigation of undesirable torsional vibration in rotating systems utilizing specifically nonlinear features in the dynamics, the vibration of nonlinear structures in which the motion is sufficiently large amplitude and structural systems with control.

  1. Cluster-based control of nonlinear dynamics

    CERN Document Server

    Kaiser, Eurika; Spohn, Andreas; Cattafesta, Louis N; Morzynski, Marek

    2016-01-01

    The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a Markov model. The Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is de...

  2. Non-Linear Dynamics and Fundamental Interactions

    CERN Document Server

    Khanna, Faqir

    2006-01-01

    The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.

  3. Single Cavity Trapped Vortex Combustor Dynamics – Part-1: Experiments

    Directory of Open Access Journals (Sweden)

    Atul Singhal

    2011-03-01

    Full Text Available In the present work, a water-cooled, modular, atmospheric pressure Trapped Vortex Combustor (TVC test rig is designed and fabricated for reacting and non-reacting flow experiments. The unique features of this rig consist of a continuously variable length-to-depth ratio (L/D of the cavity and optical access through quartz plates provided on three sides for visualization. Flame stabilization in the single cavity TVC was successfully achieved with methane as fuel and the range of flow conditions for stable operation were identified. From these, a few cases were selected for detailed experimentation. Reacting flow experiments for the selected cases indicated that reducing L/D ratio and increasing cavity-air velocity favour stable combustion. The pressure drop across the single cavity TVC is observed to be lower as compared to conventional combustors. Temperatures are measured at the exit using thermocouples and corrected for radiative losses. Species concentrations are measured at the exit using an exhaust gas analyzer. The combustion efficiency is observed to be around 97-99 % and the pattern factor is observed to be in the range of 0.08 to 0.13. High-speed imaging made possible by the optical access indicates that the overall combustion is fairly steady, and there is no vortex shedding downstream.

  4. Vortex Lattice Transition Dynamics in MgB2

    Science.gov (United States)

    Rastovski, C.; Das, P.; Schlesinger, K.; Eskildsen, M. R.; Gannon, W. J.; Dewhurst, C. D.; Zhigadlo, N. D.; Karpinski, J.

    2012-02-01

    We present small-angle neutron scattering (SANS) studies of the vortex lattice (VL) in MgB2 with H c. This material has three different VL phases, all with triangular symmetry but oriented differently with respect to the crystalline axes. Furthermore, a high degree of metastability between the VL phases of MgB2 has been observed as the sample is cooled or heated across the equilibrium phase transitions. Here we present detailed studies of how the metastable (MS) VL phases transition to the ground state (GS), either driven by small changes of the DC magnetic field or by a transverse AC field. Our results show that the MS VL is not due to vortex pinning, and results are inconsistent with predictions based on the Bean model. Instead, we speculate that a ``jamming'' of counter rotated VL domains is responsible for the VL metastability. This is further supported by a power law dependence of the GS VL domain population upon the number of applied AC cycles. This work was supported by the Department of Energy, Basic Energy Sciences under Award No. DE-FG02-10ER46783.

  5. Nonlinear Dynamics in Double Square Well Potential

    CERN Document Server

    Khomeriki, Ramaz; Ruffo, Stefano; Wimberger, Sandro; 10.1007/s11232-007-0096-y

    2009-01-01

    Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.

  6. Geometrodynamics: The Nonlinear Dynamics of Curved Spacetime

    OpenAIRE

    Scheel, Mark A.; Thorne, Kip S.

    2017-01-01

    We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of spacetime curvature near singularities, the instability of black strings in 5 spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observation of gravitational waves.

  7. Time Series Forecasting: A Nonlinear Dynamics Approach

    OpenAIRE

    Sello, Stefano

    1999-01-01

    The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cy...

  8. Dynamics and Interaction of Vortex Lines in an Elongated Bose-Einstein Condensate

    Science.gov (United States)

    Serafini, S.; Barbiero, M.; Debortoli, M.; Donadello, S.; Larcher, F.; Dalfovo, F.; Lamporesi, G.; Ferrari, G.

    2015-10-01

    We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.

  9. Vortex dynamics in self-dual Chern-Simons Higgs systems

    CERN Document Server

    Kim, Y; Kim, Yoonbai; Lee, Kimyeong

    1994-01-01

    We consider vortex dynamics in self-dual Chern-Simons Higgs systems. We show that the naive Aharanov-Bohm phase is the inverse of the statistical phase expected from the vortex spin, and that the self-dual configurations of vortices are degenerate in energy but not in angular momentum. We also use the path integral formalism to derive the dual formulation of Chern-Simons Higgs systems in which vortices appear as charged particles. We argue that besides the electromagnetic interaction, there is an additional interaction between vortices, the so-called Magnus force, and that these forces can be put together into a single `dual electromagnetic' interaction. This dual electromagnetic interaction leads to the right Aharanov-Bohm phase. We also derive and study the effective action for slowly moving vortices, which contains terms both linear and quadratic in the vortex velocity.

  10. DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    MA TIAN; WANG SHOUHONG

    2005-01-01

    The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.

  11. Dynamic Associations in Nonlinear Computing Arrays

    Science.gov (United States)

    Huberman, B. A.; Hogg, T.

    1985-10-01

    We experimentally show that nonlinear parallel arrays can be made to compute with attractors. This leads to fast adaptive behavior in which dynamical associations can be made between different inputs which initially produce sharply distinct outputs. We first define a set of simple local procedures which allow a general computing structure to change its state in time so as to produce classical Pavlovian conditioning. We then examine the dynamics of coalescence and dissociation of attractors with a number of quantitative experiments. We also show how such arrays exhibit generalization and differentiation of inputs in their behavior.

  12. Nonlinear dynamic analysis of sandwich panels

    Science.gov (United States)

    Lush, A. M.

    1984-01-01

    Two analytical techniques applicable to large deflection dynamic response calculations for pressure loaded composite sandwich panels are demonstrated. One technique utilizes finite element modeling with a single equivalent layer representing the face sheets and core. The other technique utilizes the modal analysis computer code DEPROP which was recently modified to include transverse shear deformation in a core layer. The example problem consists of a simply supported rectangular sandwich panel. Included are comparisons of linear and nonlinear static response calculations, in addition to dynamic response calculations.

  13. Vortex rings and jets recent developments in near-field dynamics

    CERN Document Server

    Yu, Simon

    2015-01-01

    In this book, recent developments in our understanding of fundamental vortex ring and jet dynamics will be discussed, with a view to shed light upon their near-field behaviour which underpins much of their far-field characteristics. The chapters provide up-to-date research findings by their respective experts and seek to link near-field flow physics of vortex ring and jet flows with end-applications in mind. Over the past decade, our knowledge on vortex ring and jet flows has grown by leaps and bounds, thanks to increasing use of high-fidelity, high-accuracy experimental techniques and numerical simulations. As such, we now have a much better appreciation and understanding on the initiation and near-field developments of vortex ring and jet flows under many varied initial and boundary conditions. Chapter 1 outlines the vortex ring pinch-off phenomenon and how it relates to the initial stages of jet formations and subsequent jet behaviour, while Chapter 2 takes a closer look at the behaviour resulting from vor...

  14. Stochastic Vortex Dynamics in Two-Dimensional Easy Plane Ferromagnets: Multiplicative Versus Additive Noise

    Energy Technology Data Exchange (ETDEWEB)

    Kamppeter, T.; Mertens, F.G.; Moro, E.; Sanchez, A.; Bishop, A.R.

    1998-09-01

    We study how thermal fluctuations affect the dynamics of vortices in the two-dimensional anisotropic Heisenberg model depending on their additive or multiplicative character. Using a collective coordinate theory, we analytically show that multiplicative noise, arising from fluctuations in the local field term of the Landau-Lifshitz equations, and Langevin-like additive noise have the same effect on vortex dynamics (within a very plausible assumption consistent with the collective coordinate approach). This is a highly non-trivial result as multiplicative and additive noises usually modify the dynamics in very different ways. We also carry out numerical simulations of both versions of the model finding that they indeed give rise to very similar vortex dynamics.

  15. Nonlinear dynamics non-integrable systems and chaotic dynamics

    CERN Document Server

    Borisov, Alexander

    2017-01-01

    This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.

  16. Nonlinear and stochastic dynamics in the heart

    Energy Technology Data Exchange (ETDEWEB)

    Qu, Zhilin, E-mail: zqu@mednet.ucla.edu [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Hu, Gang [Department of Physics, Beijing Normal University, Beijing 100875 (China); Garfinkel, Alan [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Integrative Biology and Physiology, University of California, Los Angeles, CA 90095 (United States); Weiss, James N. [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States)

    2014-10-10

    In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

  17. Nonlinear dynamics analysis of a new autonomous chaotic system

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper, a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nuchaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.

  18. Gradient-based optimization in nonlinear structural dynamics

    DEFF Research Database (Denmark)

    Dou, Suguang

    The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider, fr...

  19. Dynamic vortex interactions with flexible fibers and edges for prediction of owl noise suppression

    Science.gov (United States)

    Korykora, Sarah; Jaworski, Justin

    2015-11-01

    The compliant trailing-edge fringe of owls and the soft downy material on their upper wing surfaces are thought to enable their silent flight by weakening the interaction of boundary layer turbulence with these flexible structures. Previous analysis of turbulence noise generation by wave-bearing elastic edges have shown that the far-field acoustic power scaling can be weakened by up to the square of the Mach number relative to a rigid edge. However, it is unclear whether or not the wave-bearing feature or simply the flexible nature of the edge scatterer produces this noise suppression. To assess this distinction, a dynamic vortex interaction model is developed whereby the motion of a line vortex round a rigid but elastically-restrained wall-mounted fiber or trailing edge is determined numerically. Special attention is paid to the dynamic interaction between the flexible structure and vortex, which is accomplished via a conformal mapping relationship determined in closed form. Results from this analysis seek to develop a vortex sound model to discern the effect of flexible versus wave-bearing scatterers on turbulence noise suppression and help explain the mechanisms of silent owl flight.

  20. Vortex formation and dynamics in two-dimensional driven-dissipative condensates

    Science.gov (United States)

    Hebenstreit, F.

    2016-12-01

    We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum many-body systems that determines the time evolution of the Wigner function. Using the truncated Wigner approximation, in which quantum fluctuations are only taken into account in the initial state whereas the dynamics is governed by classical evolution equations, we study the buildup of long-range correlations due to the action of non-Hermitean quantum jump operators that constitute a mechanism for dissipative cooling. Starting from an initially disordered state corresponding to a vortex condensate, the dissipative process results in the annihilation of vortex-antivortex pairs and the establishment of quasi-long-range order at late times. We observe that a finite vortex density survives the cooling process, which disagrees with the analytically constructed vortex-free Bose-Einstein condensate at asymptotic times. This indicates that quantum fluctuations beyond the truncated Wigner approximation need to be included to fully capture the physics of dissipative Bose-Einstein condensation.

  1. Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake.

    Science.gov (United States)

    Mantič-Lugo, Vladislav; Arratia, Cristóbal; Gallaire, François

    2014-08-22

    The Bénard-von Kármán vortex shedding instability in the wake of a cylinder is perhaps the best known example of a supercritical Hopf bifurcation in fluid dynamics. However, a simplified physical description that accurately accounts for the saturation amplitude of the instability is still missing. Here, we present a simple self-consistent model that provides a clear description of the saturation mechanism and quantitatively predicts the saturated amplitude and flow fields. The model is formally constructed by a set of coupled equations governing the mean flow together with its most unstable eigenmode with finite size. The saturation amplitude is determined by requiring the mean flow to be neutrally stable. Without requiring any input from numerical or experimental data, the resolution of the model provides a good prediction of the amplitude and frequency of the vortex shedding as well as the spatial structure of the mean flow and the Reynolds stress.

  2. Nonlinear dynamics of neural delayed feedback

    Energy Technology Data Exchange (ETDEWEB)

    Longtin, A.

    1990-01-01

    Neural delayed feedback is a property shared by many circuits in the central and peripheral nervous systems. The evolution of the neural activity in these circuits depends on their present state as well as on their past states, due to finite propagation time of neural activity along the feedback loop. These systems are often seen to undergo a change from a quiescent state characterized by low level fluctuations to an oscillatory state. We discuss the problem of analyzing this transition using techniques from nonlinear dynamics and stochastic processes. Our main goal is to characterize the nonlinearities which enable autonomous oscillations to occur and to uncover the properties of the noise sources these circuits interact with. The concepts are illustrated on the human pupil light reflex (PLR) which has been studied both theoretically and experimentally using this approach. 5 refs., 3 figs.

  3. Digital Communications Using Chaos and Nonlinear Dynamics

    CERN Document Server

    Larson, Lawrence E; Liu, Jia-Ming

    2006-01-01

    This book introduces readers to a new and exciting cross-disciplinary field of digital communications with chaos. This field was born around 15 years ago, when it was first demonstrated that nonlinear systems which produce complex non-periodic noise-like chaotic signals, can be synchronized and modulated to carry useful information. Thus, chaotic signals can be used instead of pseudo-random digital sequences for spread-spectrum and private communication applications. This deceptively simple idea spun hundreds of research papers, and many novel communication schemes based on chaotic signals have been proposed. However, only very recently researchers have begun to make a transition from academic studies toward practical implementation issues, and many "promising" schemes had to be discarded or re-formulated. This book describes the state of the art (both theoretical and experimental) of this novel field. The book is written by leading experts in the fields of Nonlinear Dynamics and Electrical Engineering who pa...

  4. Rossler Nonlinear Dynamical Machine for Cryptography Applications

    CERN Document Server

    Pandey, Sunil; Shrivastava, Dr S C

    2009-01-01

    In many of the cryptography applications like password or IP address encryption schemes, symmetric cryptography is useful. In these relatively simpler applications of cryptography, asymmetric cryptography is difficult to justify on account of the computational and implementation complexities associated with asymmetric cryptography. Symmetric schemes make use of a single shared key known only between the two communicating hosts. This shared key is used both for the encryption as well as the decryption of data. This key has to be small in size besides being a subset of a potentially large keyspace making it convenient for the communicating hosts while at the same time making cryptanalysis difficult for the potential attackers. In the present work, an abstract Rossler nonlinear dynamical machine has been described first. The Rossler system exhibits chaotic dynamics for certain values of system parameters and initial conditions. The chaotic dynamics of the Rossler system with its apparently erratic and irregular ...

  5. Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation

    Science.gov (United States)

    Van Gorder, Robert A.

    2016-05-01

    Very recent experimental work has demonstrated the existence of Kelvin waves along quantized vortex filaments in superfluid helium. The possible configurations and motions of such filaments is of great physical interest, and Svistunov previously obtained a Hamiltonian formulation for the dynamics of quantum vortex filaments in the low-temperature limit under the assumption that the vortex filament is essentially aligned along one axis, resulting in a two-dimensional (2D) problem. It is standard to approximate the dynamics of thin filaments by employing the local induction approximation (LIA), and we show that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, we immediately obtain solutions to the two-dimensional LIA, such as helix, planar, and self-similar solutions. These solutions are obtained in a rather direct manner from the WKIS equation and then mapped into the 2D-LIA framework. Furthermore, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA. One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. Implications of the results for the physics of experimentally studied solitary waves, Kelvin waves, and postvortex reconnection events are mentioned.

  6. Nonlinear dynamics of hydrostatic internal gravity waves

    Energy Technology Data Exchange (ETDEWEB)

    Stechmann, Samuel N.; Majda, Andrew J. [New York University, Courant Institute of Mathematical Sciences, NY (United States); Khouider, Boualem [University of Victoria, Department of Mathematics and Statistics, Victoria, BC (Canada)

    2008-11-15

    Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the resulting equations are thus referred to here as the two-mode shallow water equations (2MSWE). A key aspect of the nonlinearities of the 2MSWE is that they allow for interactions between a background wind shear and propagating waves. This is important in the tropical atmosphere where horizontally propagating gravity waves interact together with wind shear and have source terms due to convection. It is shown here that the 2MSWE have nonlinear internal bore solutions, and the behavior of the nonlinear waves is investigated for different background wind shears. When a background shear is included, there is an asymmetry between the east- and westward propagating waves. This could be an important effect for the large-scale organization of tropical convection, since the convection is often not isotropic but organized on large scales by waves. An idealized illustration of this asymmetry is given for a background shear from the westerly wind burst phase of the Madden-Julian oscillation; the potential for organized convection is increased to the west of the existing convection by the propagating nonlinear gravity waves, which agrees qualitatively with actual observations. The ideas here should be useful for other physical applications as well. Moreover, the 2MSWE have several interesting mathematical properties: they are a system of nonconservative PDE with a conserved energy, they are conditionally hyperbolic, and they are neither genuinely nonlinear nor linearly degenerate over all of state space. Theory and numerics are developed to illustrate these features, and these features are

  7. Nonlinear dynamical triggering of slow slip

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, Paul A [Los Alamos National Laboratory; Knuth, Matthew W [WISCONSIN; Kaproth, Bryan M [PENN STATE; Carpenter, Brett [PENN STATE; Guyer, Robert A [Los Alamos National Laboratory; Le Bas, Pierre - Yves [Los Alamos National Laboratory; Daub, Eric G [Los Alamos National Laboratory; Marone, Chris [PENN STATE

    2010-12-10

    Among the most fascinating, recent discoveries in seismology have been the phenomena of triggered slip, including triggered earthquakes and triggered-tremor, as well as triggered slow, silent-slip during which no seismic energy is radiated. Because fault nucleation depths cannot be probed directly, the physical regimes in which these phenomena occur are poorly understood. Thus determining physical properties that control diverse types of triggered fault sliding and what frictional constitutive laws govern triggered faulting variability is challenging. We are characterizing the physical controls of triggered faulting with the goal of developing constitutive relations by conducting laboratory and numerical modeling experiments in sheared granular media at varying load conditions. In order to simulate granular fault zone gouge in the laboratory, glass beads are sheared in a double-direct configuration under constant normal stress, while subject to transient perturbation by acoustic waves. We find that triggered, slow, silent-slip occurs at very small confining loads ({approx}1-3 MPa) that are smaller than those where dynamic earthquake triggering takes place (4-7 MPa), and that triggered slow-slip is associated with bursts of LFE-like acoustic emission. Experimental evidence suggests that the nonlinear dynamical response of the gouge material induced by dynamic waves may be responsible for the triggered slip behavior: the slip-duration, stress-drop and along-strike slip displacement are proportional to the triggering wave amplitude. Further, we observe a shear-modulus decrease corresponding to dynamic-wave triggering relative to the shear modulus of stick-slips. Modulus decrease in response to dynamical wave amplitudes of roughly a microstrain and above is a hallmark of elastic nonlinear behavior. We believe that the dynamical waves increase the material non-affine elastic deformation during shearing, simultaneously leading to instability and slow-slip. The inferred

  8. Application of the nonlinear vortex-lattice concept to aircraft-interference problems

    Science.gov (United States)

    Kandil, O. A.; Mook, D. T.; Nayfeh, A. H.

    1976-01-01

    A discrete-vortex model was developed to account for the hazardous effects of the vortex trail issued from the edges of separation of a large leading wing on a small trailing wing. The model is divided into three main parts: the leading wing and its near wake, the near and far wakes of the leading wing, and the trailing wing and the portion of the far wake in its vicinity. The normal force, pitching moment, and rolling moment coefficients for the trailing wing are calculated. The circulation distribution in the vortex trail is calculated in the first part of the model where the leading wing is far upstream and hence is considered isolated. A numerical example is solved to demonstrate the feasibility of using this method to study interference between aircraft. The numerical results show the correct trends: The following wing experiences a loss in lift between the wing-tip vortex systems of the leading wing, a gain outside this region, and strong rolling moments which can change sign as the lateral relative position changes. All the results are strongly dependent on the vertical relative position.

  9. Current-vortex filament model of nonlinear Alfven perturbations in a finite-pressure plasma

    NARCIS (Netherlands)

    Lakhin, V. P.; Schep, T. J.; Westerhof, E.

    1998-01-01

    A low-beta, two-fluid model is shown to possess solutions in the form of current-vortex filaments. The model can be viewed as that of reduced magnetohydrodynamics, extended with electron inertia, the Hall term and parallel electron pressure. These drift-Alfven filaments are the plasma analogs of poi

  10. Nonlinear dynamics new directions theoretical aspects

    CERN Document Server

    Ugalde, Edgardo

    2015-01-01

    This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: ·         Presents a rigorous treatment of fluctuations in dynamical systems and explores a range of topics in fractal analysis, among other fundamental topics ·         Features recent developments on...

  11. Direct numerical simulations of vortex rings at ReΓ = 7500

    OpenAIRE

    Bergdorf, Michael; Koumoutsakos, Petros; Leonard, Anthony

    2007-01-01

    We present direct numerical simulations of the turbulent decay of vortex rings with ReΓ = 7500. We analyse the vortex dynamics during the nonlinear stage of the instability along with the structure of the vortex wake during the turbulent stage. These simulations enable the quantification of vorticity dynamics and their correlation with structures from dye visualization and the observations of circulation decay that have been reported in related experimental works. Movies are available with th...

  12. Adaptive explicit Magnus numerical method for nonlinear dynamical systems

    Institute of Scientific and Technical Information of China (English)

    LI Wen-cheng; DENG Zi-chen

    2008-01-01

    Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.

  13. Nonlinear dynamics from lasers to butterflies

    CERN Document Server

    Ball, R

    2003-01-01

    This book is an inspirational introduction to modern research directions and scholarship in nonlinear dynamics, and will also be a valuable reference for researchers in the field. With the scholarly level aimed at the beginning graduate student, the book will have broad appeal to those with an undergraduate background in mathematical or physical sciences.In addition to pedagogical and new material, each chapter reviews the current state of the area and discusses classic and open problems in engaging, surprisingly non-technical ways. The contributors are Brian Davies (bifurcations in maps), Nal

  14. Beam stability & nonlinear dynamics. Formal report

    Energy Technology Data Exchange (ETDEWEB)

    Parsa, Z. [ed.

    1996-12-31

    his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.

  15. Research on nonlinear stochastic dynamical price model

    Energy Technology Data Exchange (ETDEWEB)

    Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)

    2008-09-15

    In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.

  16. Nonlinear dynamic macromodeling techniques for audio systems

    Science.gov (United States)

    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.

  17. Nonlinear Dynamics of Electrostatically Actuated MEMS Arches

    KAUST Repository

    Al Hennawi, Qais M.

    2015-05-01

    In this thesis, we present theoretical and experimental investigation into the nonlinear statics and dynamics of clamped-clamped in-plane MEMS arches when excited by an electrostatic force. Theoretically, we first solve the equation of motion using a multi- mode Galarkin Reduced Order Model (ROM). We investigate the static response of the arch experimentally where we show several jumps due to the snap-through instability. Experimentally, a case study of in-plane silicon micromachined arch is studied and its mechanical behavior is measured using optical techniques. We develop an algorithm to extract various parameters that are needed to model the arch, such as the induced axial force, the modulus of elasticity, and the initially induced initial rise. After that, we excite the arch by a DC electrostatic force superimposed to an AC harmonic load. A softening spring behavior is observed when the excitation is close to the first resonance frequency due to the quadratic nonlinearity coming from the arch geometry and the electrostatic force. Also, a hardening spring behavior is observed when the excitation is close to the third (second symmetric) resonance frequency due to the cubic nonlinearity coming from mid-plane stretching. Then, we excite the arch by an electric load of two AC frequency components, where we report a combination resonance of the summed type. Agreement is reported among the theoretical and experimental work.

  18. Nonlinear dynamical characteristics of bed load motion

    Institute of Scientific and Technical Information of China (English)

    BAI; Yuchuan; XU; Haijue; XU; Dong

    2006-01-01

    Bed forms of various kinds that evolve naturally on the bottom of sandy coasts and rivers are a result of the kinematics of bed load transport. Based on the group motion of particles in the bed load within the bottom layer, a study on the nonlinear dynamics of bed load transport is presented in this paper. It is found that some development stages, such as the initiation, the equilibrium sediment transport, and the transition from a smooth bed to sand dunes, can be accounted for by different states in the nonlinear system of the bed load transport. It is verified by comparison with experimental data reported by Laboratoire Nationae D'Hydraulique, Chatou, France, that the evolution from a smooth bed to sand dunes is determined by mutation in the bed load transport. This paper presents results that may offer theoretical explanations to the experimental observations. It is also an attempt to apply the state-of-the-art nonlinear science to the classical sediment transport mechanics.

  19. Studying Vortex Dynamics of Rotating Convection with High-resolution PIV Measurement

    Science.gov (United States)

    Fu, Hao; Sun, Shiwei; Wang, Yu; Zhou, Bowen; Wang, Yuan

    2016-11-01

    A novel experimental setup for studying vortex dynamics in rotating Rayleigh-Benard convection has been made in School of Atmospheric Sciences, Nanjing University. With water as the working fluid, three lasers with different frequencies and the corresponding three CCDs have been placed to complete 2D2C (two dimensions, two components) PIV measurement. The lasers are fixed on two crossing guiding ways and can move up and down to scan the flow field. An algorithm has been made to reconstruct 3D velocity field based on multiple 2D2C PIV data. This time, we are going to present the details of this new machine and algorithm, as well as some scientific understanding of vortex dynamics owing to this high-resolution velocity measurement system. This work was supported by "LMSWE Lab Funding No. 14380001".

  20. Application of the lifting line vortex wake method to dynamic load case simulations

    Science.gov (United States)

    Boorsma, K.; Hartvelt, M.; Orsi, L. M.

    2016-09-01

    Within the EU AVATAR project, the added benefit of using the vortex line method is researched by calculating aero-elastic response for a variety of IEC load cases. A comparison is made to BEM to identify differences. Results are presented for yawed flow, extreme transient shear, half wake and turbulent inflow conditions. In addition to that also a dynamic pitch step case is performed including a comparison to experimental data. The aerodynamic code used for this purpose allows to easily switch between BEM and vortex line models whilst keeping the external input the same. The comparison indicates that taking into account vortex wake models can yield a significantly different aero-elastic response compared to BEM models, often acting as a damper to fluctuations. As such estimated fatigue loads are reduced for selected load cases. Since the free vortex wake simulations come at a substantial increase of CPU-time, a hybrid approach prescribing the far wake is shown to offer a promising compromise.

  1. Nonlinear Dynamic Characteristics of the Railway Vehicle

    Science.gov (United States)

    Uyulan, Çağlar; Gokasan, Metin

    2017-06-01

    The nonlinear dynamic characteristics of a railway vehicle are checked into thoroughly by applying two different wheel-rail contact model: a heuristic nonlinear friction creepage model derived by using Kalker 's theory and Polach model including dead-zone clearance. This two models are matched with the quasi-static form of the LuGre model to obtain more realistic wheel-rail contact model. LuGre model parameters are determined using nonlinear optimization method, which it's objective is to minimize the error between the output of the Polach and Kalker model and quasi-static LuGre model for specific operating conditions. The symmetric/asymmetric bifurcation attitude and stable/unstable motion of the railway vehicle in the presence of nonlinearities which are yaw damping forces in the longitudinal suspension system are analyzed in great detail by changing the vehicle speed. Phase portraits of the lateral displacement of the leading wheelset of the railway vehicle are drawn below and on the critical speeds, where sub-critical Hopf bifurcation take place, for two wheel-rail contact model. Asymmetric periodic motions have been observed during the simulation in the lateral displacement of the wheelset under different vehicle speed range. The coexistence of multiple steady states cause bounces in the amplitude of vibrations, resulting instability problems of the railway vehicle. By using Lyapunov's indirect method, the critical hunting speeds are calculated with respect to the radius of the curved track parameter changes. Hunting, which is defined as the oscillation of the lateral displacement of wheelset with a large domain, is described by a limit cycle-type oscillation nature. The evaluated accuracy of the LuGre model adopted from Kalker's model results for prediction of critical speed is higher than the results of the LuGre model adopted from Polach's model. From the results of the analysis, the critical hunting speed must be resolved by investigating the track tests

  2. Dynamics of Nonlinear Time-Delay Systems

    CERN Document Server

    Lakshmanan, Muthusamy

    2010-01-01

    Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...

  3. Chaotic Discrimination and Non-Linear Dynamics

    Directory of Open Access Journals (Sweden)

    Partha Gangopadhyay

    2005-01-01

    Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.

  4. Synchronization of Nonlinear Oscillators Over Networks with Dynamic Links

    NARCIS (Netherlands)

    De Persis, Claudio

    2015-01-01

    In this paper we investigate the problem of synchronization of homogeneous nonlinear oscillators coupled by dynamic links. The output of the nonlinear oscillators is the input to the dynamic links, while the output of these dynamics links is the quantity available to the distributed controllers at t

  5. Neuromechanical tuning of nonlinear postural control dynamics

    Science.gov (United States)

    Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.

    2009-06-01

    Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

  6. Bubble and Drop Nonlinear Dynamics (BDND)

    Science.gov (United States)

    Trinh, E. H.; Leal, L. Gary; Thomas, D. A.; Crouch, R. K.

    1998-01-01

    Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.

  7. Time Series Forecasting A Nonlinear Dynamics Approach

    CERN Document Server

    Sello, S

    1999-01-01

    The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cycle. Starting from a previous recent work, we checked the reliability and accuracy of a forecasting model based on concepts of nonlinear dynamical systems applied to experimental time series, such as embedding phase space,Lyapunov spectrum,chaotic behaviour. The model is based on a locally hypothesis of the behaviour on the embedding space, utilizing an optimal number k of neighbour vectors to predict the future evolution of the current point with the set of characteristic parameters determined by several previous paramet...

  8. New Insights on Insect's Silent Flight. Part I: Vortex Dynamics and Wing Morphing

    Science.gov (United States)

    Ren, Yan; Liu, Geng; Dong, Haibo; Geng, Biao; Zheng, Xudong; Xue, Qian

    2016-11-01

    Insects are capable of conducting silent flights. This is attributed to its specially designed wing material properties for the control of vibration and surface morphing during the flapping flight. In current work, we focus on the roles of dynamic wing morphing on the unsteady vortex dynamics of a cicada in steady flight. A 3D image-based surface reconstruction method is used to obtain kinematical and morphological data of cicada wings from high-quality high-speed videos. The observed morphing wing kinematics is highly complex and a singular value decomposition method is used to decompose the wing motion to several dominant modes with distinct motion features. A high-fidelity immersed-boundary-based flow solver is then used to study the vortex dynamics in details. The results show that vortical structures closely relate to the morphing mode, which plays key role in the development and attachment of leading-edge vortex (LEV), thus helps the silent flapping of the cicada wings. This work is supported by AFOSR FA9550-12-1-0071 and NSF CBET-1313217.

  9. Non-Linear Dynamics of Saturn's Rings

    Science.gov (United States)

    Esposito, L. W.

    2015-12-01

    Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from

  10. Heave-roll-pitch coupled nonlinear internal resonance response of a spar platform considering wave and vortex exciting loads

    Science.gov (United States)

    Li, Wei; Tang, Yougang; Liu, Liqin; Liu, Shuxiao; Cai, Runbo

    2017-04-01

    Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model. In fact, in addition to the heave and pitch which are in one plane, the nonlinear unstable motion will also occur in roll. From the results of the experiments, the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch. The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force. The nonlinear coupled equations in heave, roll and pitch are established by considering time-varying wet surface and coupling. The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency. Numerical integration of the motion equations has been performed to verify the first-order perturbation solution. The results are confirmed by model test. There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch. It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value. The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch. The energy transfers from heave to pitch and then transfers from pitch to roll. Due to the influence of the low-frequency vortex-excited force, the response of roll is more complicated than that of pitch.

  11. Ultrafast vortex core dynamics investigated by finite-element micromagnetic simulations

    Energy Technology Data Exchange (ETDEWEB)

    Gliga, Sebastian

    2010-07-01

    The investigations carried out in this thesis concern the ultrafast dynamics of a fundamental micromagnetic configuration: the vortex. Over the past decade, a detailed understanding of the dynamic and static properties of such magnetic nanostructures has been achieved as a result of close interplay between experiments, theory and numeric simulations. Here, micromagnetic simulations were performed based on the finite-element method. The vortex structure arises in laterally-confined ferromagnets, in particular in thin-film elements, and is characterized by an in-plane curling of the magnetic moments around a very stable and narrow core. In the present study, a novel process in micromagnetism was found: the ultrafast reversal of the vortex core. The possibility of easily switching the core orientation by means of short in-plane field pulses is surprising in view of the very high stability of the core. Moreover, the simulations presented here showed that this reversal process unfolds on a time scale of only a few tens of picoseconds, which leads to the prediction of the fastest and most complex micromagnetic reversal process known to date. Indeed, the vortex core is not merely switched: it is destroyed and recreated in the immediate vicinity with an opposite direction. This is mediated by a rapid sequence of vortex-antivortex pair creation and annihilation subprocesses and results in a sudden burst-like emission of spin waves. Equally fascinating is the ultrafast dynamics of an isolated magnetic antivortex, the topological counterpart of the vortex. The simulations performed here showed that the static complementarity between vortices and antivortices is equally reflected in their ultrafast dynamics, which leads to the reversal of the antivortex core. A promising means for the control of the magnetization on the nanoscale consists in exploiting the spin-transfer torque effect. The study of the current-induced dynamics of vortices showed that the core reversal can be

  12. Consensus tracking for multiagent systems with nonlinear dynamics.

    Science.gov (United States)

    Dong, Runsha

    2014-01-01

    This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.

  13. Self-organized Vortex State in Two-dimensional $Dictyostelium$ Dynamics

    CERN Document Server

    Rappel, W J; Sarkisian, A; Levine, H; Loomis, W F; Rappel, Wouter-Jan; Nicol, Alastair; Sarkissian, Armand; Levine, Herbert; Loomis, William F.

    1999-01-01

    We present results of experiments on the dynamics of {\\it Dictyostelium discoideum} in a novel set-up which constraints cell motion to a plane. After aggregation, the amoebae collect into round ''pancake" structures in which the cells rotate around the center of the pancake. This vortex state persists for many hours and we have explicitly verified that the motion is not due to rotating waves of cAMP. To provide an alternative mechanism for the self-organization of the {\\it Dictyostelium} cells, we have developed a new model of the dynamics of self-propelled deformable objects. In this model, we show that cohesive energy between the cells, together with a coupling between the self-generated propulsive force and the cell's configuration produces a self-organized vortex state. The angular velocity profiles of the experiment and of the model are qualitatively similar. The mechanism for self-organization reported here can possibly explain similar vortex states in other biological systems.

  14. Knotted Vortices: Entropic Lattice Boltzmann Method for Simulation of Vortex dynamics

    Science.gov (United States)

    Boesch, Fabian; Chikatamarla, Shyam; Karlin, Ilya

    2013-11-01

    Knotted and interlinked vortex structures in real fluids are conjectured to play a major role in hydrodynamic flow dissipation. Much interest lies in determining their temporal stability and the mechanism through which knots dissolve. Kleckner and Irvine recently have shown the existence of such knotted vortices experimentally by accelerating hydrofoils in water. In the present work we employ the entropic lattice Boltzmann method (ELBM) to perform DNS simulations of the creation and dynamics of knotted vortex rings inspired by the experimental setup in. ELBM renders LBM scheme unconditionally stable by restoring the second law of thermodynamics (the Boltzmann H-theorem), and thus enables simulations of large domains and high Reynolds numbers with DNS quality. The results presented in this talk provide an in-depth study of the dynamics of knotted vortices and vortex reconnection events and confirm the existence of trefoil knots in silicio for the first time. This work was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID s347.

  15. Dynamic scattering of electron vortex beams – A Bloch wave analysis

    Energy Technology Data Exchange (ETDEWEB)

    Mendis, B.G., E-mail: b.g.mendis@durham.ac.uk

    2015-02-15

    Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum () transfer between the vortex beam and the specimen due to dynamic scattering is critical. In general the pendellösung consists of short and long wavelength oscillations. The former is due to interference between the tightly bound 1s and more dispersive non-1s Bloch states, while the latter is due to interference between the non-1s states. For EMCD experiments with ±ħ angular momentum beams, momentum transfer can be minimised by selecting the appropriate aperture size, so that the probe wavefunction approximately matches that of the 2p-type Bloch states. For manipulating nanoparticles with large angular momentum beams small apertures are required to excite the 1s state and thereby enhance the short wavelength oscillations in . This enables efficient momentum transfer to the specimen, provided the nanoparticle dimension corresponds to a minimum in the pendellösung. - Highlights: • Dynamic scattering of vortex beams is analysed using Bloch waves. • Fundamental origins of pendellösung oscillations are identified. • Effect on magnetic dichroism measurements and nanoparticle manipulation is discussed.

  16. The dynamics of the stratospheric polar vortex and its relation to springtime ozone depletions

    Science.gov (United States)

    Schoeberl, Mark R.; Hartmann, Dennis L.

    1991-01-01

    Recent aircraft observations have determined the structure of polar vortices during winter and their relationship to polar ozone depletions, based on high dynamical isolation and the extremely low temperatures required for stratospheric cloud formation. The aircraft data reveal large gradients of potential vorticity and concentrations of conservative trace species at the transition from high-latitude to polar air, implying that the inward mixing of heat and constituents is strongly inhibited, and that the perturbed polar stratospheric chemistry associated with the ozone hole is isolated from the rest of the stratosphere until the vortex breaks up in late spring. It is therefore the overall polar vortex which limits the annual polar ozone depletions' maximum area-coverage.

  17. Vortex-induced dynamic loads on a non-spinning volleyball

    Science.gov (United States)

    Qing-ding, Wei; Rong-sheng, Lin; Zhi-jie, Liu

    1988-09-01

    An experiment on vortex-induced dynamic loads on a non-spinning Volleyball was conducted in a wind tunnel. The flow past the Volleyball was visualized, and the aerodynamic load was measured by use of a strain gauge balance. The separation on the Volleyball was measured with hot-film. The experimental results suggest that under the action of an unstable tail vortex system the separation region is changeable, and that the fluctuation of drag and lateral forces is the same order of magnitude as the mean drag, no matter whether the seam of the Volleyball is symmetric or asymmetric, with regard to the flow. Based on the experimental data a numerical simulation of Volleyball swerve motion was made.

  18. Linear and nonlinear dynamics of current-driven waves in dusty plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Ahmad, Ali [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Department of Physics, COMSATS Institute of Information Technology (CIIT), Islamabad (Pakistan); Theoretical Plasma Physics Division, PINSTECH, P. O. Nilore, Islamabad (Pakistan); Ali Shan, S.; Haque, Q. [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Theoretical Plasma Physics Division, PINSTECH, P. O. Nilore, Islamabad (Pakistan); Saleem, H. [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Department of Physics, COMSATS Institute of Information Technology (CIIT), Islamabad (Pakistan)

    2012-09-15

    The linear and nonlinear dynamics of a recently proposed plasma mode of dusty plasma is studied using kappa distribution for electrons. This electrostatic wave can propagate in the plasma due to the sheared flow of electrons and ions parallel to the external magnetic field in the presence of stationary dust. The coupling of this wave with the usual drift wave and ion acoustic wave is investigated. D'Angelo's mode is also modified in the presence of superthermal electrons. In the nonlinear regime, the wave can give rise to dipolar vortex structures if the shear in flow is weaker and tripolar vortices if the flow has steeper gradient. The results have been applied to Saturn's magnetosphere corresponding to negatively charged dust grains. But the theoretical model is applicable for positively charged dust as well. This work will be useful for future observations and studies of dusty environments of planets and comets.

  19. Magnetic vortex dynamics in the non-circular potential of a thin ellipticferromagnetic nanodisk with applied fields

    Directory of Open Access Journals (Sweden)

    G. M. Wysin

    2017-03-01

    Full Text Available Spontaneous vortex motion in thin ferromagnetic nanodisks of elliptical shape is dominated by a natural gyrotropic orbital part, whose resonance frequency $\\omega_G=\\overline{k}/G$ depends on a force constant and gyrovector charge, both of which change with the disk size and shape and applied in-plane or out-of-plane fields. The system is analyzed via a dynamic Thiele equation and also using numerical simulations of the Landau-Lifshitz-Gilbert (LLG equations for thin systems, including temperature via stochastic fields in a Langevin equation for the spin dynamics. A vortex is found to move in an elliptical potential with two principal axis force constants $k_x$ and $k_y$, whose ratio determines the eccentricity of the vortex motion, and whose geometric mean $\\overline{k}=\\sqrt{k_x k_y}$ determines the frequency. The force constants can be estimated from the energy of quasi-static vortex configurations or from an analysis of the gyrotropic orbits. $k_x$ and $k_y$ get modified either by an applied field perpendicular to the plane or by an in-plane applied field that changes the vortex equilibrium location. Notably, an out-of-plane field also changes the vortex gyrovector $G$, which directly influences $\\omega_G$. The vortex position and velocity distributions in thermal equilibrium are found to be Boltzmann distributions in appropriate coordinates, characterized by the force constants.

  20. Nonlinear Dynamics and Optimization of Spur Gears

    Science.gov (United States)

    Pellicano, Francesco; Bonori, Giorgio; Faggioni, Marcello; Scagliarini, Giorgio

    In the present study a single degree of freedom oscillator with clearance type non-linearity is considered. Such oscillator represents the simplest model able to analyze a single teeth gear pair, neglecting: bearings and shafts stiffness and multi mesh interactions. One of the test cases considered in the present work represents an actual gear pair that is part of a gear box of an agricultural vehicle; such gear pair gave rise to noise problems. The main gear pair characteristics (mesh stiffness and inertia) are evaluated after an accurate geometrical modelling. The meshing stiffness of the gear pair is piecewise linear and time varying (in particular periodic); it is evaluated numerically using nonlinear finite element analysis (with contact mechanics) for different positions along one mesh cycle, then it is expanded in Fourier series. A direct numerical integration approach and a smoothing technique have been considered to obtain the dynamic scenario. Bifurcation diagrams of Poincaré maps are plotted according to some sample case study from literature. Optimization procedures are proposed, in order to find optimal involute modifications that reduce gears vibration.

  1. On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

    DEFF Research Database (Denmark)

    True, Hans

    1999-01-01

    We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed....

  2. Nonlinear dynamics of electron-positron clusters

    CERN Document Server

    Manfredi, Giovanni; Haas, Fernando; 10.1088/1367-2630/14/7/075012

    2012-01-01

    Electron-positron clusters are studied using a quantum hydrodynamic model that includes Coulomb and exchange interactions. A variational Lagrangian method is used to determine their stationary and dynamical properties. The cluster static features are validated against existing Hartree-Fock calculations. In the linear response regime, we investigate both dipole and monopole (breathing) modes. The dipole mode is reminiscent of the surface plasmon mode usually observed in metal clusters. The nonlinear regime is explored by means of numerical simulations. We show that, by exciting the cluster with a chirped laser pulse with slowly varying frequency (autoresonance), it is possible to efficiently separate the electron and positron populations on a timescale of a few tens of femtoseconds.

  3. Chua's Nonlinear Dynamics Perspective of Cellular Automata

    Science.gov (United States)

    Pazienza, Giovanni E.

    2013-01-01

    Chua's `Nonlinear Dynamics Perspective of Cellular Automata' represents a genuine breakthrough in this area and it has had a major impact on the recent scientific literature. His results have been accurately described in a series of fourteen papers appeared over the course of eight years but there is no compendious introduction to his work. Therefore, here for the first time, we present Chua's main ideas as well as a few unpublished results that have not been included in his previous papers. This overview illustrates the essence of Chua's work by using a clear terminology and a consistent notation, and it is aimed at those who want to approach this subject through a concise but thorough exposition.

  4. Unusual vortex dynamics in the quantum-liquid phase of a-MoSi1− films

    Indian Academy of Sciences (India)

    S Okuma

    2006-01-01

    We find the unusual vortex dynamics in the low-temperature liquid phase of amorphous MoSi1− films by measuring the fluctuating component of the flux-flow voltage () about the average voltage. For the thick film, in which the quantum-vortexliquid (QVL) phase has been well-determined in the field–temperature plane, () originating from the vortex motion is clearly visible in the QVL phase, where the distribution of () is anomalously asymmetric, implying large velocity and/or number fluctuations of driven vortices. For the thin film, in which the QVL phase has not been determined from the static transport measurements, similar unusual vortex motion is observed in nearly the same reduced-temperature regime. We suggest that vortex dynamics in the low-temperature liquid phase of thick and thin films is dominated by common physical mechanisms related to quantum-fluctuation effects.

  5. Nonlinear Dynamics: Integrability, Chaos and Patterns

    Energy Technology Data Exchange (ETDEWEB)

    Grammaticos, B [GMPIB, Universite Paris VII, Tour 24--14, 5e etage, Case 7021, 75251 Paris (France)

    2004-02-06

    When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like 'verify the relation 14.81'. Others are less so, such as 'prepare a write-up on a) frequency

  6. Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.

    Science.gov (United States)

    Shemer, Keren; Voloch-Bloch, Noa; Shapira, Asia; Libster, Ana; Juwiler, Irit; Arie, Ady

    2013-12-15

    We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump's radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new "virtual beam" having multiple values of OAM that are determined by the nonlinear process.

  7. Surfactant and nonlinear drop dynamics in microgravity

    Science.gov (United States)

    Jankovsky, Joseph Charles

    2000-11-01

    Large amplitude drop dynamics in microgravity were conducted during the second United States Microgravity Laboratory mission carried onboard the Space Shuttle Columbia (20 October-5 November 1995). Centimeter- sized drops were statically deformed by acoustic radiation pressure and released to oscillate freely about a spherical equilibrium. Initial aspect ratios of up to 2.0 were achieved. Experiments using pure water and varying aqueous concentrations of Triton-X 100 and bovine serum albumin (BSA) were performed. The axisymmetric drop shape oscillations were fit using the degenerate spherical shape modes. The frequency and decay values of the fundamental quadrupole and fourth order shape mode were analyzed. Several large amplitude nonlinear oscillation dynamics were observed. Shape entrainment of the higher modes by the fundamental quadrupole mode occurred. Amplitude- dependent effects were observed. The nonlinear frequency shift, where the oscillation frequency is found to decrease with larger amplitudes, was largely unaffected by the presence of surfactants. The percentage of time spent in the prolate shape over one oscillation cycle was found to increase with oscillation amplitude. This prolate shape bias was also unaffected by the addition of surfactants. These amplitude-dependent effects indicate that the nonlinearities are a function of the bulk properties and not the surface properties. BSA was found to greatly enhance the surface viscoelastic properties by increasing the total damping of the oscillation, while Triton had only a small influence on damping. The surface concentration of BSA was found to be diffusion-controlled over the time of the experiments, while the Triton diffusion rate was very rapid. Using the experimental frequency and decay values, the suface viscoelastic properties of surface dilatational viscosity ( ks ) and surface shear viscosity ( ms ) were found for varying surfactant concentrations using the transcendental equation of Lu

  8. Dynamics and Instabilities of Free Surface and Vortex Flows

    DEFF Research Database (Denmark)

    Tophøj, Laust Emil Hjerrild

    2012-01-01

    This PhD thesis consists of two main parts. The first part describes the dynamics of an ideal fluid on a stationary free surface of a given shape. It turns out that one can formulate a set of self-contained equations of momentum conservation for the tangential flow, with no reference to the flow...... of the fluid bulk. With these equations, one can in principle predict the surface flow on a given free surface, once its shape has been measured. The equations are expressed for a general surface using Riemannian geometry and their solutions are discussed, including some difficulties that may arise...

  9. Dust vortex flows in plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Shukla, P.K

    2002-12-30

    Coherent nonlinear structures in the form of dust vortex flows have been observed in unmagnetized laboratory dusty plasmas. Our objective here is show that the dynamics of such dust vortices is governed by a modified Navier-Stokes equation (MNSE) and that the stationary solutions of the MNSE can be represented as monopolar as well as a row of identical Stuart and a row of counter-rotating vortices.

  10. XXIII International Conference on Nonlinear Dynamics of Electronic Systems

    CERN Document Server

    Stoop, Ruedi; Stramaglia, Sebastiano

    2017-01-01

    This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.

  11. A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT

    Institute of Scientific and Technical Information of China (English)

    陶华学; 郭金运

    2000-01-01

    The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non-derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.

  12. Interactions between nonlinear spur gear dynamics and surface wear

    Science.gov (United States)

    Ding, Huali; Kahraman, Ahmet

    2007-11-01

    In this study, two different dynamic models, a finite elements-based deformable-body model and a simplified discrete model, and a surface wear model are combined to study the interaction between gear surface wear and gear dynamic response. The proposed dynamic gear wear model includes the influence of worn surface profiles on dynamic tooth forces and transmission error as well as the influence of dynamic tooth forces on wear profiles. This paper first introduces the nonlinear dynamic models that include gear backlash and time-varying gear mesh stiffness, and a wear model separately. It presents a comparison to experiments for validation of the dynamic models. The dynamic models are combined with the wear model to study the interaction of surface wear and dynamic behavior in both linear and nonlinear response regimes. At the end, several sets of simulation results are used to demonstrate the two-way relationship between nonlinear gear dynamics and surface wear.

  13. Reversed propagation dynamics of vortex field in a left-handed material slab

    CERN Document Server

    Luo, Hailu

    2007-01-01

    On the basis of angular spectrum representation, a formalism describing reversed propagation dynamics of vortex field in an isotropic left-handed material (LHM) slab is presented. Because of the negative refractive index of LHM slab, the reversed Gouy-phase shift and the reversed Rayleigh length in a paraxial Laguerre-Gaussian beam are proposed. The negative phase velocity and reversed Gouy-phase shift caused inverse screw of wave-front, inverse spiral of Poynting vector, and reversed rotation of optical vortex. It is found that the positive mode ($l>0$) Laguerre-Gaussian beam in LHM will present the same fashion of rotation as the negative mode ($l<0$) one in RHM. It is shown that the phase difference caused by the Gouy-phase shift in regular right-handed material (RHM) can be compensated by that caused by the inverse Gouy phase shift in LHM. If certain matching conditions are satisfied, the intensity and phase distributions of the vortex field at object plane can be completely reconstructed at the image ...

  14. Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids

    Science.gov (United States)

    Shilko, Evgeny V.; Grinyaev, Yurii V.; Popov, Mikhail V.; Popov, Valentin L.; Psakhie, Sergey G.

    2016-05-01

    We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P -wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004), 10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001), 10.1103/PhysRevE.64.036128].

  15. Universality in the Self Organized Critical behavior of a cellular model of superconducting vortex dynamics

    Science.gov (United States)

    Sun, Yudong; Vadakkan, Tegy; Bassler, Kevin

    2007-03-01

    We study the universality and robustness of variants of the simple model of superconducting vortex dynamics first introduced by Bassler and Paczuski in Phys. Rev. Lett. 81, 3761 (1998). The model is a coarse-grained model that captures the essential features of the plastic vortex motion. It accounts for the repulsive interaction between vortices, the pining of vortices at quenched disordered locations in the material, and the over-damped dynamics of the vortices that leads to tearing of the flux line lattice. We report the results of extensive simulations of the critical ``Bean state" dynamics of the model. We find a phase diagram containing four distinct phases of dynamical behavior, including two phases with distinct Self Organized Critical (SOC) behavior. Exponents describing the avalanche scaling behavior in the two SOC phases are determined using finite-size scaling. The exponents are found to be robust within each phase and for different variants of the model. The difference of the scaling behavior in the two phases is also observed in the morphology of the avalanches.

  16. Dynamic analysis of a liquid droplet and optimization of helical angles for vortex drainage gas recovery

    Directory of Open Access Journals (Sweden)

    Xiaodong Wu

    2016-10-01

    Full Text Available Downhole vortex drainage gas recovery is a new gas production technology. So far, however, the forces and motions of liquid phase in the swirling flow field of wellbores during its field application have not been figured out. In this paper, the forces of liquid droplets in the swirling flow field of wellbores were analyzed on the basis of two-phase fluid dynamics theories. Then, the motion equations of fluid droplets along axial and radical directions were established. Magnitude comparison was performed on several typical acting forces, including Basset force, virtual mass force, Magnus force, Saffman force and Stokes force. Besides, the formula for calculating the optimal helical angle of vortex tools was established according to the principle that the vertical resultant force on fluid droplets should be the maximum. And afterwards, each acting force was comprehensively analyzed in terms of its origin, characteristics and direction based on the established force analysis model. Magnitude comparison indicates that the forces with less effect can be neglected, including virtual mass force, Basset force and convection volume force. Moreover, the vertically upward centrifugal force component occurs on the fluid droplets in swirling flow field instead of those in the conventional flow field of wellbores, which is favorable for the fluid droplets to move upward. The reliability of optimal helical angle calculation formula was verified by means of case analysis. It is demonstrated that with the decrease of well depth, the fluid-carrying capability of gas and the optimal helical angle increase. The research results in this paper have a guiding significance to the optimization design of downhole vortex tools and the field application of downhole vortex drainage gas recovery technology.

  17. COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Y.; Borland, Michael

    2017-06-25

    Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.

  18. Analysis of the Nonlinear Static and Dynamic Behavior of Offshore Structures

    KAUST Repository

    Alfosail, Feras

    2015-07-01

    Understanding static and dynamic nonlinear behavior of pipes and risers is crucial for the design aspects in offshore engineering fields. In this work, we examine two nonlinear problems in offshore engineering field: vortex Induced vibration of straight horizontal pipes, and boundary layer static solution of inclined risers. In the first study, we analyze the effect of the internal velocity of straight horizontal pipe and obtain the vortex induced vibration forces via coupling the pipe equation of motion with the recently modified Van Der Pol oscillator governing the lift coefficient. Our numerical results are obtained for two different pipe configurations: hinged-hinged, and clamped- clamped. The results show that the internal velocity reduces the vibration and the oscillation amplitudes. Also, it is shown that the clamped-clamped pipe configuration offers a wider range of internal velocities before buckling instability occurs. The results also demonstrate the effect of the end condition on the amplitudes of vibration. In the second study, we develop a boundary layer perturbation static solution to govern and simulate the static behavior of inclined risers. In the boundary layer analysis, we take in consideration the effects of the axial stretch, applied tension, and internal velocity. Our numerical simulation results show good agreement with the exact solutions for special cases. In addition, our developed method overcomes the mathematical and numerical limitations of the previous methods used before.

  19. Dynamic modeling and analysis of vortex filament motion using a novel curve-fitting method

    Directory of Open Access Journals (Sweden)

    Chang-Joo Kim

    2016-02-01

    Full Text Available Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The governing equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary differential equations. The applicability of Bézier curves, B-spline, and Lagrange interpolating polynomials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot–Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the proposed method.

  20. Energy flow theory of nonlinear dynamical systems with applications

    CERN Document Server

    Xing, Jing Tang

    2015-01-01

    This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

  1. Nonlinear dynamics of the wake of an oscillating cylinder

    Science.gov (United States)

    Olinger, D. J.; Sreenivasan, K. R.

    1988-02-01

    The wake of an oscillating cylinder at low Reynolds numbers is a nonlinear system in which a limit cycle due to natural vortex shedding is modulated, generating in phase space a flow on a torus. It is experimentally shown that the system displays Arnol'd tongues for rational frequency ratios, and approximates the devil's staircase along the critical line. The 'singularity spectrum' as well as spectral peaks at various Fibonacci sequences accompanying quasi-periodic transition to chaos shows that the system belongs to the same universality class as the sine circle map.

  2. Light dynamics in nonlinear trimers ans twisted multicore fibers

    CERN Document Server

    Castro-Castro, Claudia; Srinivasan, Gowri; Aceves, Alejandro B; Kevrekidis, Panayotis G

    2016-01-01

    Novel photonic structures such as multi-core fibers and graphene based arrays present unique opportunities to manipulate and control the propagation of light. Here we discuss nonlinear dynamics for structures with a few (2 to 6) elements for which linear and nonlinear properties can be tuned. Specifically we show how nonlinearity, coupling, and parity-time PT symmetric gain/loss relate to existence, stability and in general, dynamical properties of nonlinear optical modes. The main emphasis of our presentation will be on systems with few degrees of freedom, most notably couplers, trimers and generalizations thereof to systems with 6 nodes.

  3. Applications of Nonlinear Dynamics Model and Design of Complex Systems

    CERN Document Server

    In, Visarath; Palacios, Antonio

    2009-01-01

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

  4. Dynamics of two-dimensional vortex pairs in a spatially varying potential

    Science.gov (United States)

    Lee, H. H.; Gunn, J. M. F.

    1992-10-01

    We consider the dynamics of vortices in a superfluid 4He film flowing over a substrate at zero temperature. The vortex trajectories are assumed to be governed by the Magnus-force equation with the effect of the substrate incorporated via the gradient of a potential. We use an equivalent Hamiltonian formulation to show that two vortices in a slowly varying potential can exhibit stochastic behavior. In this regard, there are differences between the cases of two vortices of the same sign and those of the opposite sign, the latter becoming stochastic more readily.

  5. Management of the orbital angular momentum of vortex beams in a quadratic nonlinear interaction

    CERN Document Server

    Bovino, Fabio A; Bertolotti, Mario; Sibilia, Concita

    2011-01-01

    Light intensity control of the orbital angular momentum of the fundamental beam in a quadratic nonlinear process is theoretically and numerically presented. In particular we analyzed a seeded second harmonic generation process in presence of orbital angular momentum of the interacting beams due both to on axis and off axis optical vortices. Examples are proposed and discussed.

  6. Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Algebraic dynamics approach and algebraic dynamics algorithm for the solution of nonlinear partial differential equations are applied to the nonlinear advection equa-tion. The results show that the approach is effective for the exact analytical solu-tion and the algorithm has higher precision than other existing algorithms in nu-merical computation for the nonlinear advection equation.

  7. Chaotic behavior in nonlinear polarization dynamics

    Energy Technology Data Exchange (ETDEWEB)

    David, D.; Holm, D.D.; Tratnik, M.V. (Los Alamos National Lab., NM (USA))

    1989-01-01

    We analyze the problem of two counterpropagating optical laser beams in a slightly nonlinear medium from the point of view of Hamiltonian systems; the one-beam subproblem is also investigated as a special case. We are interested in these systems as integrable dynamical systems which undergo chaotic behavior under various types of perturbations. The phase space for the two-beam problem is C{sup 2} {times} C{sup 2} when we restricted the the regime of travelling-wave solutions. We use the method of reduction for Hamiltonian systems invariant under one-parameter symmetry groups to demonstrate that the phase space reduces to the two-sphere S{sup 2} and is therefore completely integrable. The phase portraits of the system are classified and we also determine the bifurcations that modify these portraits; some new degenerate bifurcations are presented in this context. Finally, we introduce various physically relevant perturbations and use the Melnikov method to prove that horseshoe chaos and Arnold diffusion occur as consequences of these perturbations. 10 refs., 7 figs., 1 tab.

  8. Vortex formation in coalescence of droplets with a reservoir using molecular dynamics simulations.

    Science.gov (United States)

    Taherian, Fereshte; Marcon, Valentina; Bonaccurso, Elmar; van der Vegt, Nico F A

    2016-10-01

    The flow patterns generated by the coalescence of aqueous ethanol droplets with a water reservoir are investigated using molecular dynamics simulations. The influence of surface tension gradient, which leads to the spreading of the droplet along the liquid-vapor interface of the reservoir, is studied by changing the ethanol concentration of the droplet. The internal circulation (vortex strength) of the droplet and the reservoir are analyzed separately. Simulation results reveal the formation of swirling flows within the droplet at early times when the radius of the coalescence neck due to the capillary forces increases rapidly with time. The vortex strength is found to be higher at lower concentrations of ethanol (higher liquid-vapor surface tension of the droplet), where the driving force for the contact line movement (capillary force) is stronger. The circulation diminishes by moving the center of mass of the droplet toward the reservoir. The lower surface tension of the droplet compared to the reservoir leads to surface tension gradient driven flow, which transports the droplet molecules along the liquid-vapor interface of the reservoir. Such a flow motion results in the generation of convective flows in the underlying water, which forms swirling flows within the reservoir. Therefore, the vortex strength of the reservoir is higher at higher ethanol concentrations of the droplet. The reservoir circulation decays to zero as soon as the ethanol concentration becomes homogeneous along the interface of the pool. The time evolution of circulation within the droplet and the reservoir are correlated with the center of mass motion of the droplet toward the surface, the time variation of the precursor film radius and the dynamic surface tension of the reservoir.

  9. Nonlinear dynamical model of an automotive dual mass flywheel

    Directory of Open Access Journals (Sweden)

    Lei Chen

    2015-06-01

    Full Text Available The hysteresis, stick–slip, and rotational speed-dependent characteristics in a basic dual mass flywheel are obtained from a static and a dynamic experiments. Based on the experimental results, a nonlinear model of the transferred torque in this dual mass flywheel is developed, with the overlying form of nonlinear elastic torque and frictional torque. The nonlinearities of stiffness are investigated, deriving a nonlinear model to describe the rotational speed-dependent stiffness. In addition, Bouc–Wen model is used to model the hysteretic frictional torque. Thus, the nonlinear 2-degree-of-freedom system of this dual mass flywheel is set up. Then, the Levenberg–Marquardt method is adopted for the parameter estimation of the frictional torque. Finally, taking the nonlinear stiffness in this model into account, the parameters of Bouc–Wen model are estimated based on the dynamic test data.

  10. Transistor-based metamaterials with dynamically tunable nonlinear susceptibility

    Science.gov (United States)

    Barrett, John P.; Katko, Alexander R.; Cummer, Steven A.

    2016-08-01

    We present the design, analysis, and experimental demonstration of an electromagnetic metamaterial with a dynamically tunable effective nonlinear susceptibility. Split-ring resonators loaded with transistors are shown theoretically and experimentally to act as metamaterials with a second-order nonlinear susceptibility that can be adjusted through the use of a bias voltage. Measurements confirm that this allows for the design of a nonlinear metamaterial with adjustable mixing efficiency.

  11. Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

    Science.gov (United States)

    Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

    2016-06-01

    This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

  12. Vortex Dynamics

    Science.gov (United States)

    1989-08-07

    present requires careful consideration, particularly since added nonuniqueness enrters in such circumstances, and the consistency requirement or the... nonuniqueness of steady, axiallv svmmetric. inviscid tlo,,s with closed streamlines. When closed streamsurfaces exist. the specification of the...Jac.obian be nonsinzular and Lipschitz continuous. this iteration wiil converge to the exact solution at quadratic rate I Dennis & Schnabei. theorem 5.2.1 1

  13. The numerical dynamic for highly nonlinear partial differential equations

    Science.gov (United States)

    Lafon, A.; Yee, H. C.

    1992-01-01

    Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

  14. Nonlinear switching dynamics in a photonic-crystal nanocavity

    DEFF Research Database (Denmark)

    Yu, Yi; Palushani, Evarist; Heuck, Mikkel;

    2014-01-01

    the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms......We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...

  15. Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets

    Science.gov (United States)

    Yang, Hai-Hua; Zhou, Lin; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun

    2016-10-01

    A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley-Goldstein (L-G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L-G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable.

  16. AC current driven dynamic vortex state in YBa{sub 2}Cu{sub 3}O{sub 7-x}

    Energy Technology Data Exchange (ETDEWEB)

    Lucarelli, A.; Frey, A.; Yang, R.; Luepke, G. [The College of William and Mary, Department of Applied Science, Williamsburg, VA (United States); Grilli, F. [Los Alamos National Laboratory, Superconductivity Technology Center, Los Alamos, NM (United States); Haugan, T.; Levin, G.; Barnes, P. [Air Force Research Laboratory, Wright-Patterson AFB, OH (United States)

    2007-09-15

    Time-resolved magneto-optical imaging measurements show that an ac current enables the vortex matter in YBa{sub 2}Cu{sub 3}O{sub 7-x} thin films to reorganize into two coexisting steady states of driven vortex motion with different characteristics: a quasi-static disordered glassy state in the sample interior and a dynamic state of plastic motion near the edges. Finite-element calculations consistent with the critical state model show good agreement with the measured field profiles in the quasi-static state but predict a larger hysteretic behavior in the dynamic state. (orig.)

  17. Nonlinear dynamics of zigzag molecular chains (in Russian)

    DEFF Research Database (Denmark)

    Savin, A. V.; Manevitsch, L. I.; Christiansen, Peter Leth;

    1999-01-01

    Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry-dependent...

  18. Non-linear wave packet dynamics of coherent states

    Indian Academy of Sciences (India)

    J Banerji

    2001-02-01

    We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.

  19. Dynamical diagnosis of the breakup of the stratospheric polar vortex in the Northern Hemisphere

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The research on climate change in polar regions, especially on the role of polar in the global climate system, has gain unprecedented level of interest. It has been the key scientific issue of the International Polar Year program (IPY, 2007―2008). In this paper, we dealt with the debate upon the breakup time of the stratospheric polar vortex in boreal spring. An observational study of the relation between stratospheric polar vortex breakup and the extra-tropical circulation was performed. The mean breakup date―when the winter westerly at the core of polar jet turns to summer easterly―is about April 10. The breakup time has large interannual variation with a time span of about 2 months. It also has a long-term trend with the 1990s and 2000s witnessing more and more late breakups of polar vortex. Composite of wind speed at the core of polar jet for the extremely early and late breakup years shows that late years have two periods of westerly weakening while early breakup years have only one. The first weakening in the late years happens in middle January with wind speed dropping sharply from more than 40 m s-1 to about 15 m s-1. This is accompanied with anomalous activities of planetary waves in both stratosphere and troposphere; while the second weakening in the late breaking years is mainly the results of diabatic heating with very weak wave activities. In early breakup years, the transition from westerly to easterly is rapid with wind speed dropping from more than 30 m s-1 to less than -10 m s-1 within a month. This evolution is associated with a strong bidirectional dynamical coupling of the stratosphere and troposphere. The circulation anomalies at low troposphere are also analyzed in the extremely early and late breakup years. It shows that there are significant differences between the two kinds of extreme years in the geopotential height and temperature composite analysis, indicating the dynamical coupling of stratosphere and troposphere with the

  20. Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input

    Institute of Scientific and Technical Information of China (English)

    张克勤; 庄开宇; 苏宏业; 褚健; 高红

    2002-01-01

    This paper presents a sliding mode(SM) based identifier to deal with the parameter idenfification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system;an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.

  1. Bifurcation methods of dynamical systems for handling nonlinear wave equations

    Indian Academy of Sciences (India)

    Dahe Feng; Jibin Li

    2007-05-01

    By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.

  2. NONLINEAR STOCHASTIC DYNAMICS: A SURVEY OF RECENT DEVELOPMENTS

    Institute of Scientific and Technical Information of China (English)

    朱位秋; 蔡国强

    2002-01-01

    This paper provides an overview of significant advances in nonlinearstochastic dynamics during the past two decades, including random response, stochas-tic stability, stochastic bifurcation, first passage problem and nonlinear stochasticcontrol. Topics for future research are also suggested.

  3. Unified Nonlinear Flight Dynamics and Aeroelastic Simulator Tool Project

    Data.gov (United States)

    National Aeronautics and Space Administration — ZONA Technology, Inc. (ZONA) proposes a R&D effort to develop a Unified Nonlinear Flight Dynamics and Aeroelastic Simulator (UNFDAS) Tool that will combine...

  4. The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations

    Science.gov (United States)

    David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.

    2012-11-01

    In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems.

  5. Nonlinear Dynamics of the Perceived Pitch of Complex Sounds

    CERN Document Server

    Cartwright, J H E; Piro, O; Cartwright, Julyan H. E.; Gonzalez, Diego L.; Piro, Oreste

    1999-01-01

    We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.

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

    Science.gov (United States)

    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.

  7. Dynamic and thermodynamic properties of porous vortex matter in Bi(2)Sr(2)CaCu(2)O(8) in an oblique magnetic field.

    Science.gov (United States)

    Avraham, Nurit; Goldschmidt, Y Y; Liu, J T; Myasoedov, Y; Rappaport, M; Zeldov, E; van der Beek, C J; Konczykowski, M; Tamegai, T

    2007-08-24

    Vortex matter in Bi(2)Sr(2)CaCu(2)O(8) with a low concentration of tilted columnar defects (CDs) was studied using magneto-optical measurements and molecular dynamics simulations. It is found that while the dynamic properties are significantly affected by tilting the magnetic field away from the CDs, the thermodynamic transitions are angle independent. The simulations indicate that vortex pancakes remain localized on the CDs even at large tilting angles. This preserves the vortex thermodynamics, while vortex pinning is considerably weakened due to kink sliding.

  8. Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions

    Energy Technology Data Exchange (ETDEWEB)

    Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)

    2011-01-17

    We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.

  9. Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions

    Science.gov (United States)

    Alka, W.; Goyal, Amit; Nagaraja Kumar, C.

    2011-01-01

    We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.

  10. On the simulation of tether-nets for space debris capture with Vortex Dynamics

    Science.gov (United States)

    Botta, Eleonora M.; Sharf, Inna; Misra, Arun K.; Teichmann, Marek

    2016-06-01

    Tether-nets are one of the more promising methods for the active removal of space debris. The aim of this paper is to study the dynamics of this type of systems in space, which is still not well-known and the simulation of which has multiple outstanding issues. In particular, the focus is on the deployment and capture phases of a net-based active debris removal mission, and on the effect of including the bending stiffness of the net threads on the dynamical characteristics of the net and on the computational efficiency. Lumped-parameter modeling of the net in Vortex Dynamics, without bending stiffness representation, is introduced first and validated then, against results obtained with an equivalent model in Matlab, using numerical simulations of the deployment phase. A model able to reproduce the bending stiffness of the net in Vortex Dynamics is proposed, and the outcome of a net deployment simulation is compared to the results of simulation without bending stiffness. A simulation of net-based capture of a derelict spacecraft is analyzed from the point of view of evaluating the effect of modeling the bending stiffness. From comparison of simulations with and without bending stiffness representation, it is found that bending stiffness has a significant influence both on the simulation results and on the computation time. When bending stiffness is included, the net is more resistant to the changes in its shape caused both by the motion of the corner masses (during deployment) and by the contact with the debris (during capture).

  11. Vibrational mechanics nonlinear dynamic effects, general approach, applications

    CERN Document Server

    Blekhman, Iliya I

    2000-01-01

    This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

  12. Non-linear dynamics in pulse combustor: A review

    Indian Academy of Sciences (India)

    Sirshendu Mondal; Achintya Kukhopadhyay; Swarnendu Sen

    2015-03-01

    The state of the art of non-linear dynamics applied to pulse combustor theoretically and experimentally is reviewed. Pulse combustors are a class of air-breathing engines in which pulsations in combustion are utilized to improve the performance. As no analytical solution can be obtained for most of the nonlinear systems, the whole set of solutions can be investigated with the help of dynamical system theory. Many studies have been carried out on pulse combustors whose dynamics include limit cycle behaviour, Hopf bifurcation and period-doubling bifurcation. The dynamic signature has also been used for early prediction of extinction.

  13. Employment of CB models for non-linear dynamic analysis

    Science.gov (United States)

    Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

    1990-01-01

    The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

  14. Dynamic decoupling nonlinear control method for aircraft gust alleviation

    Science.gov (United States)

    Lv, Yang; Wan, Xiaopeng; Li, Aijun

    2008-10-01

    A dynamic decoupling nonlinear control method for MIMO system is presented in this paper. The dynamic inversion method is used to decouple the multivariable system. The nonlinear control method is used to overcome the poor decoupling effect when the system model is inaccurate. The nonlinear control method has correcting function and is expressed in analytic form, it is easy to adjust the parameters of the controller and optimize the design of the control system. The method is used to design vertical transition mode of active control aircraft for gust alleviation. Simulation results show that the designed vertical transition mode improves the gust alleviation effect about 34% comparing with the normal aircraft.

  15. Research on Nonlinear Dynamics with Defense Applications

    Science.gov (United States)

    2006-04-01

    numerical verifications, we have experimentally realized the scheme by using a Duffing -type of nonlinear electronic oscillator (originally developed by C...circuits In defense applications it may be desirable to induce chaos in nonlinear oscillators operating in a stable regime. Examples of such oscillators ...evolutions of the target Duffing circuit and deliver resonant perturbations to generate robust chaotic attractors. A brief account of the work has been

  16. Nonlinear modeling of an aerospace object dynamics

    Science.gov (United States)

    Davydov, I. E.; Davydov, E. I.

    2017-01-01

    Here are presented the scientific results, obtained by motion modeling of complicated technical systems of aerospace equipment with consideration of nonlinearities. Computerized panel that allows to measure mutual influence of the system's motion and stabilization device with consideration of its real characteristics has been developed. Analysis of motion stability of a system in general has been carried out and time relationships of the system's motion taking in account nonlinearities are presented.

  17. Vortex dynamics and wall shear stress behaviour associated with an elliptic jet impinging upon a flat plate

    Science.gov (United States)

    Long, J.; New, T. H.

    2016-07-01

    Vortical structures and dynamics of a Re h = 2100 elliptic jet impinging upon a flat plate were studied at H/ d h = 1, 2 and 4 jet-to-plate separation distances. Flow investigations were conducted along both its major and minor planes using laser-induced fluorescence and digital particle image velocimetry techniques. Results show that the impingement process along the major plane largely consists of primary jet ring-vortex and wall-separated secondary vortex formations, where they subsequently separate from the flat plate at smaller H/ d h = 1 and 2 separation distances. Key vortex formation locations occur closer to the impingement point as the separation distance increases. Interestingly, braid vortices and rib structures begin to take part in the impingement process at H/ d h = 4 and wave instabilities dominate the flow field. In contrast, significantly more coherent primary and secondary vortices with physically larger vortex core sizes and higher vortex strengths are observed along the minor plane, with no signs of braid vortices and rib structures. Lastly, influences of these different flow dynamics on the major and minor plane instantaneous and mean skin friction coefficient levels are investigated to shed light on the effects of separation distance on the wall shear stress distributions.

  18. A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Pacini, Benjamin Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mayes, Randall L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Roettgen, Daniel R [Univ. of Wisconsin, Madison, WI (United States)

    2015-10-01

    Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.

  19. Dynamic characteristics of an inclined flexible cylinder undergoing vortex-induced vibrations

    Science.gov (United States)

    Han, Qinghua; Ma, Yexuan; Xu, Wanhai; Lu, Yan; Cheng, Ankang

    2017-04-01

    A series of experimental tests were conducted on vortex-induced vibrations (VIV) of a flexible inclined cylinder with a yaw angle equals 45° for investigating the response characteristics in a towing tank. The flexible cylinder model was 5.6 m in length and 16 mm in diameter with an aspect ratio of 350 and a mass ratio of 1.9. The Reynolds numbers ranged from about 800 to 16,000.The strain responses were measured directly in both cross-flow (CF) and in-line (IL) directions and corresponding displacements were obtained using a modal approach. The dynamic response characteristics of the inclined flexible cylinder excited by vortex shedding was examined from the aspect of strain response, displacement amplitudes, dominant modes, response frequencies and drag force coefficients. The experimental results indicated that the CF response amplitude could be up to a value of 3.0D and the IL one more than 1.1D. The dominant modes were from 1 to 3 in CF direction and 1 to 5 in IL direction. And it was found that dominant frequencies increased linearly with the reduced velocity. The multi-modal response of the flexible inclined cylinder model excited by VIV was observed and analyzed. Moreover, the values of drag coefficients were in the range of 0.9-2.6.

  20. On the dynamics of flame edges in diffusion-flame/vortex interactions

    Energy Technology Data Exchange (ETDEWEB)

    Hermanns, Miguel; Linan, Amable [Departamento de Motopropulsion y Termofluidodinamica, Universidad Politecnica de Madrid, Pza. Cardenal Cisneros 3, 28040 Madrid (Spain); Vera, Marcos [Area de Mecanica de Fluidos, Universidad Carlos III de Madrid, 28911 Leganes (Spain)

    2007-04-15

    We analyze the local flame extinction and reignition of a counterflow diffusion flame perturbed by a laminar vortex ring. Local flame extinction leads to the appearance of flame edges separating the burning and extinguished regions of the distorted mixing layer. The dynamics of these edges is modeled based on previous numerical results, with heat release effects fully taken into account, which provide the propagation velocity of triple and edge flames in terms of the upstream unperturbed value of the scalar dissipation. The temporal evolution of the mixing layer is determined using the classical mixture fraction approach, with both unsteady and curvature effects taken into account. Although variable density effects play an important role in exothermic reacting mixing layers, in this paper the description of the mixing layer is carried out using the constant density approximation, leading to a simplified analytical description of the flow field. The mathematical model reveals the relevant nondimensional parameters governing diffusion-flame/vortex interactions and provides the parameter range for the more relevant regime of local flame extinction followed by reignition via flame edges. Despite the simplicity of the model, the results show very good agreement with previously published experimental results. (author)

  1. Dynamic micromagnetic simulation of the magnetic spectrum of permalloy nanodot array with vortex state

    Science.gov (United States)

    Peng, Y.; Zhao, G. P.; Morvan, F. J.; Wu, S. Q.; Yue, M.

    2017-01-01

    Due to its potential applications in high-density magnetic storage and spin electronic devices, the ferromagnetic resonance absorption phenomenon has recently drawn much attention. By studying the influence of different materials with various shapes on this phenomenon, the new understandings gained could lead to other applications in the future. In this paper, dynamic magnetic susceptibilities of the vortex state in permalloy nanodot arrays have been investigated using a three-dimensional object oriented micromagnetic framework (OOMMF) code with a two-dimensional periodic boundary condition (2D-PBC) extension and compared with those of a single dot carefully. The resonance mode is excited in the vortex state of nanodot arrays by the microwave magnetic field perpendicular to the dot plane. In this case only radially symmetric spin wave modes can be excited. The influence of the geometric parameters on the resonance frequency has been studied systemically, including the dot radius, the number of repeating elements, and the dot distance. One can see that the resonance peak of the dot array is higher than that of a single dot because of the induced stronger magnetostatic coupling. A critical dot distance exists at which the dot array may be treated as a single dot. There is only one resonance peak for both the dot array and the single dot, as the radius changes.

  2. Low-field vortex dynamics in various high-c thin films

    Indian Academy of Sciences (India)

    Johan J Åkerman; K V Rao

    2002-05-01

    We present a novel ac susceptibility technique for the study of vortex creep in superconducting thin films. With this technique we study the dynamics of dilute vortices in -axis oriented Y-123, Hg-1212, and Tl-1212 thin films, as well as -axis oriented Hg-1212 thin films. Results on the Hg-1212 and Tl-1212 thin films indicate that dislocation-mediated plastic flux creep of single vortices dominates at low temperatures and fields. As the temperature (or the field) is increased, the increasing vortex–vortex interactions promote a collective behavior, which can be characterized by elastic creep with a non-zero exponent. Also, in some of these samples effects of thermally assisted quantum creep are visible up to 45 K in some of these samples. In Y-123 thin films, creep is found to be collective down to the lowest temperatures and fields investigated, while the quantum creep persists only up to 10–11 K.

  3. Dynamic scattering of electron vortex beams--a Bloch wave analysis.

    Science.gov (United States)

    Mendis, B G

    2015-02-01

    Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum (〈Lz〉) transfer between the vortex beam and the specimen due to dynamic scattering is critical. In general the 〈Lz〉 pendellösung consists of short and long wavelength oscillations. The former is due to interference between the tightly bound 1s and more dispersive non-1s Bloch states, while the latter is due to interference between the non-1s states. For EMCD experiments with ±ħ angular momentum beams, momentum transfer can be minimised by selecting the appropriate aperture size, so that the probe wavefunction approximately matches that of the 2p-type Bloch states. For manipulating nanoparticles with large angular momentum beams small apertures are required to excite the 1s state and thereby enhance the short wavelength oscillations in 〈Lz〉. This enables efficient momentum transfer to the specimen, provided the nanoparticle dimension corresponds to a minimum in the 〈Lz〉 pendellösung.

  4. Influence of vortex dynamics and atmospheric turbulence on the early evolution of a contrail

    Directory of Open Access Journals (Sweden)

    R. Paugam

    2010-04-01

    Full Text Available This study describes three-dimensional numerical simulations of the evolution of an aircraft contrail during the first 30 min following the emission of exhausts. The wake is modeled as a vortex pair descending in a stratified atmosphere where turbulent fluctuations are sustained in the late dissipation regime. The focus of the study is laid on the interactions between vortex dynamics, atmospheric turbulence and contrail microphysics, and their role in determining the growth and the distribution of ice crystals. The atmospheric turbulence is synthesized using a methodology developed to force anisotropic turbulent fluctuations. The results show the feasibility of three-dimensional simulations of the early development of a contrail in supersaturated conditions before its transition into a contrail-cirrus. %(when radiative heating and sedimentation are no more negligible. It is shown that in case of strongly supersaturated and shear-free atmosphere the optical depth is maintained as the contrail spreads by turbulent diffusion in the late dissipation regime.

  5. Numerical study of air-core vortex dynamics during liquid draining from cylindrical tanks

    Energy Technology Data Exchange (ETDEWEB)

    Mathew, Sam; Patnaik, B S V [Fluid Mechanics Laboratory, Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036 (India); Tharakan, T John, E-mail: bsvp@iitm.ac.in [Flow and Acoustics Group, Liquid Propulsion Systems Centre, Indian Space Research Organization, Trivandrum 695547 (India)

    2014-04-01

    An air core is often formed during liquid draining from cylindrical tanks. An understanding of the mechanism behind its formation and the parameters that accentuate its growth is central to the development of an air-core vortex suppression strategy. In the present study, liquid draining from a cylindrical tank is investigated with the aid of computational fluid dynamics tools. A qualitative and a quantitative comparison of the temporal variation of critical height against available experiments is reported. A systematic investigation has revealed that, drain port shape, size, pressurization, initial rotation, etc, play a vital role in the formation of an air core vortex and its growth. These variables were also observed to influence critical height and total drain time, both of which are of engineering interest. Towards the development of a gas-core suppression strategy, the circular drain port is modified to either a stepped or a bell mouth shape. Although the new drain port shapes have delayed the gas-core from entering the drain-port, they were found to be only marginally advantageous. (paper)

  6. Vortex dominated flows. Analysis and computation for multiple scale phenomena

    Energy Technology Data Exchange (ETDEWEB)

    Ting, L. [New York Univ., NY (United States). Courant Inst. of Mathematical Sciences; Klein, R. [Freie Univ. Berlin (Germany). Fachbereich Mathematik und Informatik; Knio, O.M. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Mechanical Engineering

    2007-07-01

    This monograph provides in-depth analyses of vortex dominated flows via matched and multiscale asymptotics, and demonstrates how insight gained through these analyses can be exploited in the construction of robust, efficient, and accurate numerical techniques. The book explores the dynamics of slender vortex filaments in detail, including fundamental derivations, compressible core structure, weakly non-linear limit regimes, and associated numerical methods. Similarly, the volume covers asymptotic analysis and computational techniques for weakly compressible flows involving vortex-generated sound and thermoacoustics. The book is addressed to both graduate students and researchers. (orig.)

  7. Double symbolic joint entropy in nonlinear dynamic complexity analysis

    Science.gov (United States)

    Yao, Wenpo; Wang, Jun

    2017-07-01

    Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.

  8. Practical compensation for nonlinear dynamic thrust measurement system

    Directory of Open Access Journals (Sweden)

    Chen Lin

    2015-04-01

    Full Text Available The real dynamic thrust measurement system usually tends to be nonlinear due to the complex characteristics of the rig, pipes connection, etc. For a real dynamic measuring system, the nonlinearity must be eliminated by some adequate methods. In this paper, a nonlinear model of dynamic thrust measurement system is established by using radial basis function neural network (RBF-NN, where a novel multi-step force generator is designed to stimulate the nonlinearity of the system, and a practical compensation method for the measurement system using left inverse model is proposed. Left inverse model can be considered as a perfect dynamic compensation of the dynamic thrust measurement system, and in practice, it can be approximated by RBF-NN based on least mean square (LMS algorithms. Different weights are set for producing the multi-step force, which is the ideal input signal of the nonlinear dynamic thrust measurement system. The validity of the compensation method depends on the engine’s performance and the tolerance error 0.5%, which is commonly demanded in engineering. Results from simulations and experiments show that the practical compensation using left inverse model based on RBF-NN in dynamic thrust measuring system can yield high tracking accuracy than the conventional methods.

  9. Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.

    Science.gov (United States)

    Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi

    2008-03-01

    In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.

  10. Adaptive Fuzzy Dynamic Surface Control for Uncertain Nonlinear Systems

    Institute of Scientific and Technical Information of China (English)

    Xiao-Yuan Luo; Zhi-Hao Zhu; Xin-Ping Guan

    2009-01-01

    In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of "explosion of complexity" in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globaily uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller (SMC). Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.

  11. International Conference on Structural Nonlinear Dynamics and Diagnosis

    CERN Document Server

    CSNDD 2012; CSNDD 2014

    2015-01-01

    This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics.  Researchers and engineers interested in the challenges posed and opportunities offered by nonlinearities in the development of passive and active control strategies, energy harvesting, novel design criteria, modeling and characteriz...

  12. Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

    Science.gov (United States)

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

    2016-10-01

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

  13. Nonlinear Dynamic Characteristics of Combustion Wave in SHS Process

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation,based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear.It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.

  14. Vortex cores and vortex motion in superconductors with anisotropic Fermi surfaces

    Science.gov (United States)

    Galvis, J. A.; Herrera, E.; Guillamón, I.; Vieira, S.; Suderow, H.

    2017-02-01

    Explaning static and dynamic properties of the vortex lattice in anisotropic superconductors requires a careful characterization of vortex cores. The vortex core contains Andreev bound states whose spatial extension depends on the anisotropy of the electronic band-structure and superconducting gap. This might have an impact on the anisotropy of the superconducting properties and on vortex dynamics. Here we briefly summarize basic concepts to understand anisotropic vortex cores and review vortex core imaging experiments. We further discuss moving vortex lattices and the influence of vortex core shape in vortex motion. We find vortex motion in highly tilted magnetic fields. We associate vortex motion to the vortex entry barrier and the screening currents at the surface. We find preferential vortex motion along the main axis of the vortex lattice. After travelling integers of the intervortex distance, we find that vortices move more slowly due to the washboard potential of the vortex lattice.

  15. Reconnection of superfluid vortex bundles.

    Science.gov (United States)

    Alamri, Sultan Z; Youd, Anthony J; Barenghi, Carlo F

    2008-11-21

    Using the vortex filament model and the Gross-Pitaevskii nonlinear Schroedinger equation, we show that bundles of quantized vortex lines in He II are structurally robust and can reconnect with each other maintaining their identity. We discuss vortex stretching in superfluid turbulence and show that, during the bundle reconnection process, kelvin waves of large amplitude are generated, in agreement with the finding that helicity is produced by nearly singular vortex interactions in classical Euler flows.

  16. Dynamic Analysis of Vibrating Systems with Nonlinearities

    Science.gov (United States)

    M. Kalami, Yazdi; Ahmadian, H.; Mirzabeigy, A.; Yildirim, A.

    2012-02-01

    The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.

  17. Nonlinear and stochastic dynamics of coherent structures

    DEFF Research Database (Denmark)

    Rasmussen, Kim

    1997-01-01

    system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...... phenomenon. We find numerically and analytically that the collapse can be delayed and ultimatively arrested by the fluctuations. Allowing the system to reach thermal equilibrium we further augment the model by a nonlineardamping term and find that this prohibits collapse in the strict mathematical se nse....... However a collapse like behavior still persists in the presence of the nonlinear damping . Apart from the absence of the collapse in the strict mathematical sense we find that the nonlinear damping term has rather weak influence on the interplay between fluctuations and self-focusing. The study...

  18. Nonlinear dynamics of domain walls with cross-ties

    Science.gov (United States)

    Dubovik, M. N.; Zverev, V. V.; Filippov, B. N.

    2016-07-01

    The dynamic behavior of a domain wall with cross-ties is analyzed on the basis of micromagnetic simulation with exact allowance for all main (exchange, magnetoanisotropic, and magnetostatic) interactions in thin magnetically uniaxial ferromagnetic films with planar anisotropy. It is found that the peculiarities of motion of such domain walls are closely related to the behavior of topological defects in the magnetization distribution (generation, motion, and annihilation of vortex-antivortex pairs on the film surface and Bloch points). We observe three different regimes of motion (stationary, periodic, and turbulent regimes), each of which is realized in a certain range of fields oriented along the easy magnetization axis. It is shown that the experimentally observed dynamic bends of the walls with cross-ties are determined by the type of motion of vortices and antivortices. The velocities of domain walls in different regimes are calculated, and the dynamic configurations of the magnetization and existing dynamic transitions between them are investigated.

  19. Field topologies in ideal and near ideal magnetohydrodynamics and vortex dynamics

    CERN Document Server

    Low, B C

    2014-01-01

    Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near ideal MHD are reviewed in two parts. The first part gives a physically complete description of the frozen in field topology, taking magnetic flux conservation as fundamental and treating four topics, Eulerian and Lagrangian descriptions of MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics in comparison to ideal MHD. A corollary clarifies the challenge of achieving a high degree of the frozen in condition in numerical MHD. The second part treats field topology breakage centered on the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global constraint readily results in formation of tangential magnetic discontinuities, i.e., electric current sheets of zero thickness. A similar incompatibil...

  20. Incremental approximate dynamic programming for nonlinear flight control design

    NARCIS (Netherlands)

    Zhou, Y.; Van Kampen, E.J.; Chu, Q.P.

    2015-01-01

    A self-learning adaptive flight control design for non-linear systems allows reliable and effective operation of flight vehicles in a dynamic environment. Approximate dynamic programming (ADP) provides a model-free and computationally effective process for designing adaptive linear optimal

  1. Nonlinear dynamics of a microelectromechanical oscillator with delayed feedback

    NARCIS (Netherlands)

    Van Leeuwen, R.; Karabacak, D.M.; Van der Zant, H.S.J.; Venstra, W.J.

    2013-01-01

    We study the dynamics of a nonlinear electromechanical oscillator with delayed feedback. Compared to their linear counterparts, we find that the dynamics is dramatically different. The well-known Barkhausen stability criterion ceases to exist, and two modes of operation emerge: one characterized by

  2. Nonlinear Dynamics in the Ultradian Rhythm of Desmodium motorium

    Science.gov (United States)

    Chen, Jyh-Phen; Engelmann, Wolfgang; Baier, Gerold

    1995-12-01

    The dynamics of the lateral leaflet movement of Desmodium motorium is studied. Simple periodic, quasiperiodic and aperiodic time series are observed. The long-scale dynamics may either be uniform or composed of several prototypic oscillations (one of them reminiscent of homoclinic chaos). Diffusively coupled nonlinear oscillators may account for the variety of ultradian rhythms.

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

    Science.gov (United States)

    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.

  4. Reconstructing the Nonlinear Dynamical Systems by Evolutionary Computation Techniques

    Institute of Scientific and Technical Information of China (English)

    LIU Minzhong; KANG Lishan

    2006-01-01

    We introduce a new dynamical evolutionary algorithm(DEA) based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems (mainly the Lorenz and Chen systems ). The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.

  5. NONLINEAR DYNAMICS OF CARBON NANOTUBES UNDER LARGE ELECTROSTATIC FORCE

    KAUST Repository

    Xu, Tiantian

    2015-06-01

    Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

  6. Scalar mixing and strain dynamics methodologies for PIV/LIF measurements of vortex ring flows

    Science.gov (United States)

    Bouremel, Yann; Ducci, Andrea

    2017-01-01

    Fluid mixing operations are central to possibly all chemical, petrochemical, and pharmaceutical industries either being related to biphasic blending in polymerisation processes, cell suspension for biopharmaceuticals production, and fractionation of complex oil mixtures. This work aims at providing a fundamental understanding of the mixing and stretching dynamics occurring in a reactor in the presence of a vortical structure, and the vortex ring was selected as a flow paradigm of vortices commonly encountered in stirred and shaken reactors in laminar flow conditions. High resolution laser induced fluorescence and particle imaging velocimetry measurements were carried out to fully resolve the flow dissipative scales and provide a complete data set to fully assess macro- and micro-mixing characteristics. The analysis builds upon the Lamb-Oseen vortex work of Meunier and Villermaux ["How vortices mix," J. Fluid Mech. 476, 213-222 (2003)] and the engulfment model of Baldyga and Bourne ["Simplification of micromixing calculations. I. Derivation and application of new model," Chem. Eng. J. 42, 83-92 (1989); "Simplification of micromixing calculations. II. New applications," ibid. 42, 93-101 (1989)] which are valid for diffusion-free conditions, and a comparison is made between three methodologies to assess mixing characteristics. The first method is commonly used in macro-mixing studies and is based on a control area analysis by estimating the variation in time of the concentration standard deviation, while the other two are formulated to provide an insight into local segregation dynamics, by either using an iso-concentration approach or an iso-concentration gradient approach to take into account diffusion.

  7. Nonlinear dynamics based digital logic and circuits.

    Science.gov (United States)

    Kia, Behnam; Lindner, John F; Ditto, William L

    2015-01-01

    We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two.

  8. Nonlinear ship waves and computational fluid dynamics

    National Research Council Canada - National Science Library

    MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei

    2014-01-01

    .... Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design...

  9. Nonlinear Kinetic Dynamics of Magnetized Weibel Instability

    CERN Document Server

    Palodhi, L; Pegoraro, F

    2010-01-01

    Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it and their influence on the resulting electrostatic waves are shown.

  10. High Dynamic Performance Nonlinear Source Emulator

    DEFF Research Database (Denmark)

    Nguyen-Duy, Khiem; Knott, Arnold; Andersen, Michael A. E.

    2016-01-01

    As research and development of renewable and clean energy based systems is advancing rapidly, the nonlinear source emulator (NSE) is becoming very essential for testing of maximum power point trackers or downstream converters. Renewable and clean energy sources play important roles in both terres...

  11. Photonic Nonlinear Transient Computing with Multiple-Delay Wavelength Dynamics

    Science.gov (United States)

    Martinenghi, Romain; Rybalko, Sergei; Jacquot, Maxime; Chembo, Yanne K.; Larger, Laurent

    2012-06-01

    We report on the experimental demonstration of a hybrid optoelectronic neuromorphic computer based on a complex nonlinear wavelength dynamics including multiple delayed feedbacks with randomly defined weights. This neuromorphic approach is based on a new paradigm of a brain-inspired computational unit, intrinsically differing from Turing machines. This recent paradigm consists in expanding the input information to be processed into a higher dimensional phase space, through the nonlinear transient response of a complex dynamics excited by the input information. The computed output is then extracted via a linear separation of the transient trajectory in the complex phase space. The hyperplane separation is derived from a learning phase consisting of the resolution of a regression problem. The processing capability originates from the nonlinear transient, resulting in nonlinear transient computing. The computational performance is successfully evaluated on a standard benchmark test, namely, a spoken digit recognition task.

  12. Residual Minimizing Model Reduction for Parameterized Nonlinear Dynamical Systems

    CERN Document Server

    Constantine, Paul G

    2010-01-01

    We present a method for approximating the solution of a parameterized, nonlinear dynamical (or static) system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the dynamical system. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. We prove some interesting characteristics of the scheme including uniqueness and an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and groundwater modeling - a nonlinear parabolic PDE w...

  13. Dynamic computer-generated nonlinear-optical holograms

    Science.gov (United States)

    Liu, Haigang; Li, Jun; Fang, Xiangling; Zhao, Xiaohui; Zheng, Yuanlin; Chen, Xianfeng

    2017-08-01

    We propose and experimentally demonstrate dynamic nonlinear optical holograms by introducing the concept of computer-generated holograms for second-harmonic generation of a structured fundamental wave with a specially designed wave front. The generation of Laguerre-Gaussian second-harmonic beams is investigated in our experiment. Such a method, which only dynamically controls the wave front of the fundamental wave by a spatial light modulator, does not need domain inversion in nonlinear crystals and hence is a more flexible way to achieve the off-axis nonlinear second-harmonic beams. It can also be adopted in other schemes and has potential applications in nonlinear frequency conversion, optical signal processing, and real-time hologram, etc.

  14. NONLINEAR THEORY OF DYNAMIC STABILITY FOR LAMINATED COMPOSITE CYLINDRICAL SHELLS

    Institute of Scientific and Technical Information of China (English)

    周承倜; 王列东

    2001-01-01

    Hamilton Principle was uaed to derive the general governing equations of nonlinear dynamic stability for laminated cylindrical shells in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were solved by variational method. Analysis reveals that under the action of dynamic load,laminated cylindrical shells will fall into a state of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed: i.e. T300/5 208 graphite epoxy E-glass epoxy, and ARALL shells. Results show that all factors will induce important influence for dynamic stability of laminated shells. So, in research of dynamic stability for laminated shells, to consider these factors is important.

  15. Wave-packet dynamics in one-dimensional nonlinear Schroedinger lattices: local vs. nonlocal nonlinear effects

    Energy Technology Data Exchange (ETDEWEB)

    Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)

    2014-02-15

    We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinear Schroedinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinear Schroedinger equation generalized by including a nonlocal nonlinear term, we calculate four different physical quantities as a function of time, which are the return probability to the initial excitation site, the participation number, the root-mean-square displacement from the excitation site and the spatial probability distribution. We investigate the influence of the nonlocal nonlinearity on the delocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trapping region, we find that the nonlocal nonlinearity compresses the soliton width and slows down the spreading of the wave packet. In the vicinity of the delocalization to self-trapping transition point and inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which we call partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.

  16. Non-linear Flight Dynamics at High Angles of Attack

    DEFF Research Database (Denmark)

    Granasy, P.; Sørensen, C.B.; Mosekilde, Erik

    1998-01-01

    The methods of nonlinear dynamics are applied to the longitudinal motion of a vectored thrust aircraft, in particular the behavior at high angles of attack. Our model contains analytic nonlinear aerodynamical coefficients based on NASA windtunnel experiments on the F-18 high-alpha research vehicle...... (HARV). When the aircraft is forced with small thrust deflections whilst in poststall equilibrium, chaotic motion is observed at certain frequencies. At other frequencies, several limiting states coexist....

  17. Nonlinear Dynamic Analysis of the Whole Vehicle on Bumpy Road

    Institute of Scientific and Technical Information of China (English)

    王威; 李瑰贤; 宋玉玲

    2010-01-01

    Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found.The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincaré maps were used simultaneously to derive strange super chaotic attractor.According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of ...

  18. Estimating nonlinear dynamic equilibrium economies: a likelihood approach

    OpenAIRE

    2004-01-01

    This paper presents a framework to undertake likelihood-based inference in nonlinear dynamic equilibrium economies. The authors develop a sequential Monte Carlo algorithm that delivers an estimate of the likelihood function of the model using simulation methods. This likelihood can be used for parameter estimation and for model comparison. The algorithm can deal both with nonlinearities of the economy and with the presence of non-normal shocks. The authors show consistency of the estimate and...

  19. Nonlinear laser dynamics from quantum dots to cryptography

    CERN Document Server

    Lüdge, Kathy

    2012-01-01

    A distinctive discussion of the nonlinear dynamical phenomena of semiconductor lasers. The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research.By presenting both experimental and theoretical results, the distinguished authors consider solitary lase

  20. Nonlinear Galerkin Optimal Truncated Low—dimensional Dynamical Systems

    Institute of Scientific and Technical Information of China (English)

    ChuijieWU

    1996-01-01

    In this paper,a new theory of constructing nonlinear Galerkin optimal truncated Low-Dimensional Dynamical Systems(LDDSs) directly from partial differential equations has been developed.Applying the new theory to the nonlinear Burgers' equation,it is shown that a nearly perfect LDDS can be gotten,and the initial-boundary conditions are automatically included in the optimal bases.The nonlinear Galerkin method does not have advantages within the optimization process,but it can significantly improve the results,after the Galerkin optimal bases have been gotten.

  1. NONLINEAR DYNAMICAL CHARACTERISTICS OF PILES UNDER HORIZONTAL VIBRATION

    Institute of Scientific and Technical Information of China (English)

    HU Yu-jia; CHENG Chang-jun; YANG Xiao

    2005-01-01

    The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pilesoil interaction was established-a coupling nonlinear boundary value problem. Under the case of horizontal vibration, the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain. The effects of parameters, especially the axis force on the stiffness were studied in detail. The numerical results suggest that it is possible that the pile applying an axis force will lose its stability. So, the effect of the axis force on the pile is considered.

  2. Chaos and Nonlinear Dynamics in a Quantum Artificial Economy

    CERN Document Server

    Gonçalves, Carlos Pedro

    2012-01-01

    Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.

  3. Electron dynamics with radiation and nonlinear wigglers

    Energy Technology Data Exchange (ETDEWEB)

    Jowett, J.M.

    1986-06-01

    The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches.

  4. Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

    Institute of Scientific and Technical Information of China (English)

    LIU Yu-sheng; CHEN Jiang; LI Xing-yuan

    2006-01-01

    Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties.How to control such systems effectively is one of the most challenging problems.This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems.The controller can be used in cases where there exist parameter and nonlinear uncertainties,unmodeled dynamics and unknown bounded disturbances.The design of the controller is based on the control Lyapunov function method.A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics,nonlinear uncertainties and unknown bounded disturbances.The backstepping procedure is employed to overcome the complexity in the design.With the proposed method,the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters.there are.It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system.Furthermore,all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately.Simulation results illustrate the effectiveness of the proposed robust adaptive controller.

  5. Unmodeled Dynamics in Robust Nonlinear Control

    Science.gov (United States)

    2000-08-01

    IEEE Transactions on Automatic Control , vol. 44, pp. 1975–1981, 1999. [6] D. Bestle...systems,” IEEE Transactions on Automatic Control , vol. 41, pp. 876–880, 1996. 95 [9] C.I. Byrnes and A. Isidori, “New results and examples in...Output-feedback stochastic nonlinear stabilization,” IEEE Transactions on Automatic Control , vol. 44, pp. 328–333, 1999. [14] J. Eker and K.J.

  6. Power Spectral Density Conversions and Nonlinear Dynamics

    Directory of Open Access Journals (Sweden)

    Mostafa Rassaian

    1994-01-01

    Full Text Available To predict the vibration environment of a payload carried by a ground or air transporter, mathematical models are required from which a transfer function to a prescribed input can be calculated. For sensitive payloads these models typically include linear shock isolation system stiffness and damping elements relying on the assumption that the isolation system has a predetermined characteristic frequency and damping ratio independent of excitation magnitude. In order to achieve a practical spectral analysis method, the nonlinear system has to be linearized when the input transportation and handling vibration environment is in the form of an acceleration power spectral density. Test data from commercial isolators show that when nonlinear stiffness and damping effects exist the level of vibration input causes a variation in isolator resonant frequency. This phenomenon, described by the stationary response of the Duffing oscillator to narrow-band Gaussian random excitation, requires an alternative approach for calculation of power spectral density acceleration response at a shock isolated payload under random vibration. This article details the development of a plausible alternative approach for analyzing the spectral response of a nonlinear system subject to random Gaussian excitations.

  7. Spin-dynamics simulations of vortex precession in 2-D magnetic dots

    Energy Technology Data Exchange (ETDEWEB)

    Depondt, Ph., E-mail: depondt@insp.jussieu.fr [Institut des NanoSciences de Paris, Universite Pierre et Marie Curie, UMR 7588 CNRS, 75252 Paris Cedex 05 (France); Levy, J.-C.S., E-mail: jean-claude.levy@univ-paris-diderot.fr [Materiaux et Phenomenes Quantiques, Universite Denis Diderot, UMR 7162 CNRS, 75013 Paris (France)

    2011-10-31

    Highlights: → Vortex precession was simulated in two-dimensional magnetic dots of finite size. → A simple qualitative explanation of the observed behaviors is proposed, including seemingly erratic ones. → Pinning of the vortex motion, unconnected with defects, is also observed and an explanation thereof provided. -- Abstract: Vortex precession was simulated in two-dimensional magnetic dots. The Landau-Lifshitz equation with exchange and dipolar interactions was integrated at a low temperature with initial conditions consisting in a single vortex situated aside from the central position. This vortex precesses around the center of the sample and either can be expelled or converges towards the center. These relaxation processes are systematically studied. A simple qualitative explanation of the observed behaviors is proposed, including seemingly somewhat erratic ones. Intrinsic pinning of the vortex motion, unconnected with defects, is also observed and an explanation thereof provided.

  8. Stable counter-rotating vortex pairs in saturable media

    Energy Technology Data Exchange (ETDEWEB)

    Desyatnikov, Anton S. [Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200 (Australia)]. E-mail: asd124@rsphysse.anu.edu.au; Mihalache, Dumitru [Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), Department of Theoretical Physics, 407 Atomistilor, Magurele-Bucharest 077125 (Romania); Mazilu, Dumitru [Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), Department of Theoretical Physics, 407 Atomistilor, Magurele-Bucharest 077125 (Romania); Malomed, Boris A. [Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Lederer, Falk [Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universitaet Jena, Max-Wien-Platz 1, D-07743 Jena (Germany)

    2007-04-30

    We resolve a controversial issue of the stability of composite vortex solitons in self-focusing saturable nonlinear media. Stable vortex solitons with hidden angular momentum, i.e., composed of counter-rotating beams with topological charges +1 and -1, are found, and their linear-stability region is identified. In contrast, the solitons with explicit vorticity are always unstable against splitting. The predicted linear stability of the hidden-vorticity solitons is achieved in the strong-saturation regime, when the soliton's total power exceeds a certain threshold. The dynamical stability is verified in direct simulations of nonlinear model.

  9. Magnetic vortex dynamics on a picosecond timescale in a hexagonal permalloy pattern

    Energy Technology Data Exchange (ETDEWEB)

    Shim, J.-H.; Kim, D.-H.; Mesler, B.; Moon, J.-H.; Lee, K.-J.; Anderson, E. H.; Fischer, P.

    2009-12-02

    We have observed a motion of magnetic vortex core in a hexagonal Permalloy pattern by means of Soft X-ray microscopy. Pump-probe stroboscopic observation on a picosecond timescale has been carried out after exciting a ground state vortex structure by an external field pulse of 1 ns duration. Vortex core is excited off from the center position of the hexagonal pattern but the analysis of the core trajectory reveals that the motion is nongyrotropic.

  10. Theoretical and software considerations for nonlinear dynamic analysis

    Science.gov (United States)

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

    1983-01-01

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

  11. Nonlinear dynamics and quantum entanglement in optomechanical systems.

    Science.gov (United States)

    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.

  12. Nonlinear Dynamic Characteristics of Oil-in-Water Emulsions

    Science.gov (United States)

    Yin, Zhaoqi; Han, Yunfeng; Ren, Yingyu; Yang, Qiuyi; Jin, Ningde

    2016-08-01

    In this article, the nonlinear dynamic characteristics of oil-in-water emulsions under the addition of surfactant were experimentally investigated. Firstly, based on the vertical upward oil-water two-phase flow experiment in 20 mm inner diameter (ID) testing pipe, dynamic response signals of oil-in-water emulsions were recorded using vertical multiple electrode array (VMEA) sensor. Afterwards, the recurrence plot (RP) algorithm and multi-scale weighted complexity entropy causality plane (MS-WCECP) were employed to analyse the nonlinear characteristics of the signals. The results show that the certainty is decreasing and the randomness is increasing with the increment of surfactant concentration. This article provides a novel method for revealing the nonlinear dynamic characteristics, complexity, and randomness of oil-in-water emulsions with experimental measurement signals.

  13. Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems

    CERN Document Server

    Vázquez, Luis

    2013-01-01

    Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization. This book also: Presents mechanical method for determining matrix singularity or non-independence of dimension and complexity Illustrates novel mathematical applications of classical Newton’s law Offers a new approach and insight to basic, standard problems Includes numerous examples and applications Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems is an ideal book for undergraduate and graduate students as well as researchers interested in linear problems and optimization, and nonlinear dynamics.      

  14. Nonlinear electronic circuit with neuron like bursting and spiking dynamics.

    Science.gov (United States)

    Savino, Guillermo V; Formigli, Carlos M

    2009-07-01

    It is difficult to design electronic nonlinear devices capable of reproducing complex oscillations because of the lack of general constructive rules, and because of stability problems related to the dynamical robustness of the circuits. This is particularly true for current analog electronic circuits that implement mathematical models of bursting and spiking neurons. Here we describe a novel, four-dimensional and dynamically robust nonlinear analog electronic circuit that is intrinsic excitable, and that displays frequency adaptation bursting and spiking oscillations. Despite differences from the classical Hodgkin-Huxley (HH) neuron model, its bifurcation sequences and dynamical properties are preserved, validating the circuit as a neuron model. The circuit's performance is based on a nonlinear interaction of fast-slow circuit blocks that can be clearly dissected, elucidating burst's starting, sustaining and stopping mechanisms, which may also operate in real neurons. Our analog circuit unit is easily linked and may be useful in building networks that perform in real-time.

  15. Nonlinear dynamics of zigzag molecular chains (in Russian)

    DEFF Research Database (Denmark)

    Savin, A. V.; Manevitsch, L. I.; Christiansen, Peter Leth

    1999-01-01

    Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry......-dependent anharmonism that comes into the picture. The existence or otherwise of solitons is determined in this case by the interplay between the geometrical anharmonism and the physical anharmonism of the interstitial interaction, of opposite signs. The nonlinear dynamic analysis of the three most typical zigzag...... models (two-dimensional alpha-spiral, polyethylene transzigzag backbone, and the zigzag chain of hydrogen bonds) shows that the zigzag structure essentially limits the soliton dynamics to finite, relatively narrow, supersonic soliton velocity intervals and may also result in that several acoustic soliton...

  16. A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Jay R. Johnson; Simon Wing

    2004-01-28

    Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach.

  17. Finite Element Based Lagrangian Vortex Dynamics Model for Wind Turbine Aerodynamics

    Science.gov (United States)

    McWilliam, Michael K.; Crawford, Curran

    2014-06-01

    This paper presents a novel aerodynamic model based on Lagrangian Vortex Dynamics (LVD) formulated using a Finite Element (FE) approach. The advantage of LVD is improved fidelity over Blade Element Momentum Theory (BEMT) while being faster than Numerical Navier-Stokes Models (NNSM) in either primitive or velocity-vorticity formulations. The model improves on conventional LVD in three ways. First, the model is based on an error minimization formulation that can be solved with fast root finding algorithms. In addition to improving accuracy, this eliminates the intrinsic numerical instability of conventional relaxed wake simulations. The method has further advantages in optimization and aero-elastic simulations for two reasons. The root finding algorithm can solve the aerodynamic and structural equations simultaneously, avoiding Gauss-Seidel iteration for compatibility constraints. The second is that the formulation allows for an analytical definition for sensitivity calculations. The second improvement comes from a new discretization scheme based on an FE formulation and numerical quadrature that decouples the spatial, influencing and temporal meshes. The shape for each trailing filament uses basis functions (interpolating splines) that allow for both local polynomial order and element size refinement. A completely independent scheme distributes the influencing (vorticity) elements along the basis functions. This allows for concentrated elements in the near wake for accuracy and progressively less in the far-wake for efficiency. Finally the third improvement is the use of a far-wake model based on semi-infinite vortex cylinders where the radius and strength are related to the wake state. The error-based FE formulation allows the transition to the far wake to occur across a fixed plane.

  18. Analysis of Nonlinear Dynamics by Square Matrix Method

    Energy Technology Data Exchange (ETDEWEB)

    Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II

    2016-07-25

    The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.

  19. Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseases.

    Science.gov (United States)

    Grenfell, B T; Kleczkowski, A; Gilligan, C A; Bolker, B M

    1995-06-01

    There is currently considerable interest in the role of nonlinear phenomena in the population dynamics of infectious diseases. Childhood diseases such as measles are particularly well documented dynamically, and have recently been the subject of analyses (of both models and notification data) to establish whether the pattern of epidemics is chaotic. Though the spatial dynamics of measles have also been extensively studied, spatial and nonlinear dynamics have only recently been brought together. The present review concentrates mainly on describing this synthesis. We begin with a general review of the nonlinear dynamics of measles models, in a spatially homogeneous environment. Simple compartmental models (specifically the SEIR model) can behave chaotically, under the influence of strong seasonal 'forcing' of infection rate associated with patterns of schooling. However, adding observed heterogeneities such as age structure can simplify the deterministic dynamics back to limit cycles. By contrast all current strongly seasonally forced stochastic models show large amplitude irregular fluctuations, with many more 'fadeouts' of infection that is observed in real communities of similar size. This indicates that (social and/or geographical) spatial heterogeneity is needed in the models. We review the exploration of this problem with nonlinear spatiotemporal models. The few studies to date indicate that spatial heterogeneity can help to increase the realism of models. However, a review of nonlinear analyses of spatially subdivided measles data show that more refinements of the models (particularly in representing the impact of human demographic changes on infection dynamics) are required. We conclude with a discussion of the implication of these results for the dynamics of infectious diseases in general and, in particular, the possibilities of cross fertilization between human disease epidemiology and the study of plant and animal diseases.

  20. Application of dynamic recurrent neural networks in nonlinear system identification

    Science.gov (United States)

    Du, Yun; Wu, Xueli; Sun, Huiqin; Zhang, Suying; Tian, Qiang

    2006-11-01

    An adaptive identification method of simple dynamic recurrent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteristics of system can reflect the dynamic characteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNN, and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topological structure in usual dynamic recurrent neural network.

  1. Structure-based control of complex networks with nonlinear dynamics

    CERN Document Server

    Zañudo, Jorge G T; Albert, Réka

    2016-01-01

    Given the network of interactions underlying a complex system, what can we learn about controlling such a system solely from its structure? Over a century of research in control theory has given us tools to answer this question, which were widely applied in science and engineering. Yet the current tools do not always consider the inherently nonlinear dynamics of real systems and the naturally occurring system states in their definition of "control", a term whose interpretation varies across disciplines. Here we use a new mathematical framework for structure-based control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors and which are guaranteed to be effective regardless of the dynamic details and parameters of the underlying system. We use this framework on several real networks, compar...

  2. Nonlinear dynamic phenomena in the beer model

    DEFF Research Database (Denmark)

    Mosekilde, Erik; Laugesen, Jakob Lund

    2007-01-01

    The production-distribution system or "beer game" is one of the most well-known system dynamics models. Notorious for the complex dynamics it produces, the beer game has been used for nearly five decades to illustrate how structure generates behavior and to explore human decision making. Here we...

  3. Nonlinear dynamics of the mammalian inner ear

    CERN Document Server

    Szalai, Robert; Homer, Martin

    2015-01-01

    A simple nonlinear transmission-line model of the cochlea with longitudinal coupling is introduced that can reproduce Basilar membrane response and neural tuning in the chinchilla. It is found that the middle ear has little effect on cochlear resonances, and hence conclude that the theory of coherent reflections is not applicable to the model. The model also provides an explanation of the emergence of spontaneous otoacoustic emissions (SOAEs). It is argued that SOAEs arise from Hopf bifurcations of the transmission-line model and not from localized instabilities. The paper shows that emissions can become chaotic, intermittent and fragile to perturbations.

  4. Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

    Science.gov (United States)

    Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

    2016-09-01

    It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

  5. A digital holography set-up for 3D vortex flow dynamics

    Science.gov (United States)

    Lebon, Benoît; Perret, Gaële; Coëtmellec, Sébastien; Godard, Gilles; Gréhan, Gérard; Lebrun, Denis; Brossard, Jérôme

    2016-06-01

    In the present paper, a digital in-line holography (DIH) set-up, with a converging beam, is used to take three-dimensional (3D) velocity measurements of vortices. The vortices are formed periodically at the edges of a submerged horizontal plate submitted to regular waves. They take the form of vortex filaments that extend from side to side of the channel. They undergo strongly three-dimensional instability mechanisms that remain very complicated to characterize experimentally. The experiments are performed in a 10 × 0.3 × 0.3 m3 wave flume. The DIH set-up is performed using a modulated laser diode emitting at the wavelength of 640 nm and a lensless CCD camera. The beam crosses the channel side to side. To reveal the flow dynamics, 30-μm hydrogen bubbles are generated at the edge of the plate to serve as tracers. Their locations are recorded on the holograms multiple times to access the dynamics of the flow. This method leads to an accuracy in the order of 100 μm on the axial location. Those measurements have been validated with stereo-PIV measurements. A very good agreement is found on time-averaged velocity fields between the two techniques.

  6. Moving vortex phases, dynamical symmetry breaking, and jamming for vortices in honeycomb pinning arrays

    Energy Technology Data Exchange (ETDEWEB)

    Reichhardt, Charles [Los Alamos National Laboratory; Reichhardt, Cynthia [Los Alamos National Laboratory

    2008-01-01

    We show using numerical simulations that vortices in honeycomb pinning arrays can exhibit a remarkable variety of dynamical phases that are distinct from those found for triangular and square pinning arrays. In the honeycomb arrays, it is possible for the interstitial vortices to form dimer or higher n-mer states which have an additional orientational degree of freedom that can lead to the formation of vortex molecular crystals. For filling fractions where dimer states appear, a dynamical symmetry breaking can occur when the dimers flow in one of two possible alignment directions. This leads to transport in the direction transverse to the applied drive. We show that dimerization produces distinct types of moving phases which depend on the direction of the driving force with respect to the pinning lattice symmetry. When the dimers are driven along certain directions, a reorientation of the dimers can produce a jamming phenomenon which results in a strong enhancement in the critical depinning force. The jamming can also cause unusual effects such as an increase in the critical depinning force when the size of the pinning sites is reduced.

  7. Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex

    Science.gov (United States)

    Figliozzi, Patrick; Sule, Nishant; Yan, Zijie; Bao, Ying; Burov, Stanislav; Gray, Stephen K.; Rice, Stuart A.; Vaikuntanathan, Suriyanarayanan; Scherer, Norbert F.

    2017-02-01

    To date investigations of the dynamics of driven colloidal systems have focused on hydrodynamic interactions and often employ optical (laser) tweezers for manipulation. However, the optical fields that provide confinement and drive also result in electrodynamic interactions that are generally neglected. We address this issue with a detailed study of interparticle dynamics in an optical ring vortex trap using 150-nm diameter Ag nanoparticles. We term the resultant electrodynamically interacting nanoparticles a driven optical matter system. We also show that a superior trap is created by using a Au nanoplate mirror in a retroreflection geometry, which increases the electric field intensity, the optical drive force, and spatial confinement. Using nanoparticles versus micron sized colloids significantly reduces the surface hydrodynamic friction allowing us to access small values of optical topological charge and drive force. We quantify a further 50% reduction of hydrodynamic friction when the nanoparticles are driven over the Au nanoplate mirrors versus over a mildly electrostatically repulsive glass surface. Further, we demonstrate through experiments and electrodynamics-Langevin dynamics simulations that the optical drive force and the interparticle interactions are not constant around the ring for linearly polarized light, resulting in a strong position-dependent variation in the nanoparticle velocity. The nonuniformity in the optical drive force is also manifest as an increase in fluctuations of interparticle separation, or effective temperature, as the optical driving force is increased. Finally, we resolve an open issue in the literature on periodic modulation of interparticle separation with comparative measurements of driven 300-nm-diameter polystyrene beads that also clearly reveal the significance of electrodynamic forces and interactions in optically driven colloidal systems. Therefore, the modulations in the optical forces and electrodynamic interactions

  8. Nonlinear dynamics and millikelvin cavity-cooling of levitated nanoparticles

    CERN Document Server

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

    2015-01-01

    Optomechanical systems explore and exploit the coupling between light and the mechanical motion of matter. A nonlinear coupling offers access to rich new physics, in both the quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising of a nanosphere levitated and cooled in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere to millikelvin temperatures for indefinite periods of time in high vacuum. We observe cooling of the linear and non-linear motion, leading to a $10^5$ fold reduction in phonon number $n_p$, attaining final occupancies of $n_p = 100-1000$. This work puts cavity cooling of a levitated object to the quantum ground-state firmly within reach.

  9. Nonlinear dynamics of giant resonances in atomic nuclei

    CERN Document Server

    Vretenar, D; Ring, P; Lalazissis, G A

    1999-01-01

    The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time-series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicate regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.

  10. High Dynamic Performance Nonlinear Source Emulator

    DEFF Research Database (Denmark)

    Nguyen-Duy, Khiem; Knott, Arnold; Andersen, Michael A. E.

    2016-01-01

    As research and development of renewable and clean energy based systems is advancing rapidly, the nonlinear source emulator (NSE) is becoming very essential for testing of maximum power point trackers or downstream converters. Renewable and clean energy sources play important roles in both...... terrestrial and nonterrestrial applications. However, most existing NSEs have only been concerned with simulating energy sources in terrestrial applications, which may not be fast enough for testing of nonterrestrial applications. In this paper, a high-bandwidth NSE is developed that is able to simulate...... change in the input source but also to a load step between nominal and open circuit. Moreover, all of these operation modes have a very fast settling time of only 10 μs, which is hundreds of times faster than that of existing works. This attribute allows for higher speed and a more efficient maximum...

  11. Fast nanoscale addressability of nitrogen-vacancy spins via coupling to a dynamic ferromagnetic vortex

    Science.gov (United States)

    Wolf, M. S.; Badea, R.; Berezovsky, J.

    2016-01-01

    The core of a ferromagnetic vortex domain creates a strong, localized magnetic field, which can be manipulated on nanosecond timescales, providing a platform for addressing and controlling individual nitrogen-vacancy centre spins in diamond at room temperature, with nanometre-scale resolution. Here, we show that the ferromagnetic vortex can be driven into proximity with a nitrogen-vacancy defect using small applied magnetic fields, inducing significant nitrogen-vacancy spin splitting. We also find that the magnetic field gradient produced by the vortex is sufficient to address spins separated by nanometre-length scales. By applying a microwave-frequency magnetic field, we drive both the vortex and the nitrogen-vacancy spins, resulting in enhanced coherent rotation of the spin state. Finally, we demonstrate that by driving the vortex on fast timescales, sequential addressing and coherent manipulation of spins is possible on ∼100 ns timescales. PMID:27296550

  12. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  13. ANALYSIS OF NONLINEAR DYNAMIC STABILITY OF LIQUID-CONVEYING PIPES

    Institute of Scientific and Technical Information of China (English)

    张立翔; 黄文虎

    2002-01-01

    Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson,Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different.

  14. Report of the working group on single-particle nonlinear dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M. (Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division, U.S. Department of Energy (United States))

    1999-04-01

    The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of acclerators. (AIP) [copyright] [ital 1999] [ital American Institute of Physics

  15. Report of the working group on single-particle nonlinear dynamics

    Science.gov (United States)

    Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M.

    1999-04-01

    The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of acclerators. (AIP)

  16. Nonlinear tuning of microresonators for dynamic range enhancement.

    Science.gov (United States)

    Saghafi, M; Dankowicz, H; Lacarbonara, W

    2015-07-08

    This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators.

  17. Nonlinear dynamical system identification using unscented Kalman filter

    Science.gov (United States)

    Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan

    2016-11-01

    Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.

  18. Nonlinear tuning of microresonators for dynamic range enhancement

    Science.gov (United States)

    Saghafi, M.; Dankowicz, H.; Lacarbonara, W.

    2015-01-01

    This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators. PMID:26345078

  19. Nonlinear Analyses of the Dynamic Properties of Hydrostatic Bearing Systems

    Institute of Scientific and Technical Information of China (English)

    LIU Wei(刘伟); WU Xiujiang(吴秀江); V.A. Prokopenko

    2003-01-01

    Nonlinear analyses of hydrostatic bearing systems are necessary to adequately model the fluid-solid interaction. The dynamic properties of linear and nonlinear analytical models of hydrostatic bearings are compared in this paper. The analyses were based on the determination of the aperiodic border of transient processes with external step loads. The results show that the dynamic properties can be most effectively improved by increasing the hydrostatic bearing crosspiece width and additional pocket volume in a bearing can extend the load range for which the transient process is aperiodic, but an additional restrictor and capacitor (RC) chain must be introduced for increasing damping. The nonlinear analyses can also be used to predict typical design parameters for a hydrostatic bearing.

  20. Nonlinear Dynamics, Chaotic and Complex Systems

    Science.gov (United States)

    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. The Interaction Between Dynamics and Chemistry of Ozone in the Set-up Phase of the Northern Hemisphere Polar Vortex

    Science.gov (United States)

    Kawa, S. R.; Bevilacqua, R.; Margitan, J. J.; Douglass, A. R.; Schoeberl, M. R.; Hoppel, K.; Sen, B.; Bhartia, P. K. (Technical Monitor)

    2001-01-01

    The morphology and evolution of the stratospheric ozone (O3) distribution at high latitudes in the Northern Hemisphere (NH) are examined for the late summer and fall seasons of 1999. This time period sets the O3 initial condition for the SOLVE/THESEO field mission performed during winter 1999-2000. In situ and satellite data are used along with a three-dimensional model of chemistry and transport (CTM) to determine the key processes that control the distribution of O3 in the lower-to-middle stratosphere. O3 in the vortex at the beginning of the winter season is found to be nearly constant from 500 to above 800 K with a value at 3 ppmv +/- approx. 10%. Values outside the vortex are up to a factor of 2 higher and increase significantly with potential temperature. The seasonal time series of data from POAM shows that relatively low O3 mixing ratios, which characterize the vortex in late fall, are already present at high latitudes at the end of summer before the vortex circulation sets up. Analysis of the CTM output shows that the minimum O3 and increase in variance in late summer are the result of: 1) stirring of polar concentric O3 gradients by nascent wave-driven transport, and 2) an acceleration of net photochemical loss with decreasing solar illumination. The segregation of low O3 mixing ratios into the vortex as the circulation strengthens through the fall suggests a possible feedback role between O3 chemistry and the vortex formation dynamics. Trajectory calculations from O3 sample points early in the fall, however, show only a weak correlation between initial O3 mixing ratio and potential vorticity later in the season consistent with order-of-magnitude calculations for the relative importance of O3 in the fall radiative balance at high latitudes. The possible connection between O3 chemistry and the dynamics of vortex formation does suggest that these feedbacks and sensitivities need to be better understood in order to make confident predictions of the recovery

  2. Nonlinear dynamics mathematical models for rigid bodies with a liquid

    CERN Document Server

    Lukovsky, Ivan A

    2015-01-01

    This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approaches to fluid-structure interaction problems, the fundamental mathematical background and modeling the dynamics of such complex mechanical systems.

  3. Numerical investigation of bubble nonlinear dynamics characteristics

    Energy Technology Data Exchange (ETDEWEB)

    Shi, Jie, E-mail: shijie@hrbeu.edu.cn; Yang, Desen; Shi, Shengguo; Hu, Bo [Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001 (China); College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China); Zhang, Haoyang; Jiang, Wei [College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China)

    2015-10-28

    The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.

  4. Consensus in Directed Networks of Agents With Nonlinear Dynamics

    NARCIS (Netherlands)

    Yu, Wenwu; Chen, Guanrong; Cao, Ming; Qu, Z.

    2011-01-01

    This technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network. Both local and global consensus are defined and investigated. Techniques for studying the synchronization in such complex networks are exploited to establish various sufficient con

  5. Nonlinear dynamics of near-extremal black holes

    Science.gov (United States)

    Green, Stephen; Gralla, Samuel; Zimmerman, Peter

    2017-01-01

    Near-extremal black holes possess a family of long lived quasinormal modes associated to the near-horizon throat geometry. For long lived modes, nonlinear interactions between the modes can potentially dominate over dissipation. We develop a framework for treating these interactions, and we study their dynamics.

  6. Nonlinear dynamics of incommensurately contacting surfaces : a model study

    NARCIS (Netherlands)

    Consoli, Luca

    2002-01-01

    This PhD thesis is about the nonlinear dynamics of contacting surfaces. More specifically, it deals with the problem of modelling at the microscopic level some of the contributions that lead to the macroscopic effect of dry sliding friction. In chapter 1, we try to give an overview of the physical q

  7. Major open problems in chaos theory and nonlinear dynamics

    CERN Document Server

    Li, Y Charles

    2013-01-01

    Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.

  8. A toolkit for analyzing nonlinear dynamic stochastic models easily

    NARCIS (Netherlands)

    Uhlig, H.F.H.V.S.

    1995-01-01

    Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth

  9. A toolkit for analyzing nonlinear dynamic stochastic models easily

    NARCIS (Netherlands)

    Uhlig, H.F.H.V.S.

    1995-01-01

    Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth

  10. CLASSIFICATION OF BIFURCATIONS FOR NONLINEAR DYNAMICAL PROBLEMS WITH CONSTRAINTS

    Institute of Scientific and Technical Information of China (English)

    吴志强; 陈予恕

    2002-01-01

    Bifurcation of periodic solutions widely existed in nonlinear dynamical systems isa kind of constrained one in intrinsic quality because its amplitude is always non-negative.Classification of the bifurcations with the type of constraint was discussed. All its six typesof transition sets are derived, in which three types are newly found and a method isproposed for analyzing the constrained bifurcation.

  11. Applied Nonlinear Dynamics Analytical, Computational, and Experimental Methods

    CERN Document Server

    Nayfeh, Ali H

    1995-01-01

    A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.

  12. Imaging magnetisation dynamics in nano-contact spin-torque vortex oscillators exhibiting gyrotropic mode splitting

    Science.gov (United States)

    Keatley, Paul Steven; Redjai Sani, Sohrab; Hrkac, Gino; Majid Mohseni, Seyed; Dürrenfeld, Philipp; Åkerman, Johan; Hicken, Robert James

    2017-04-01

    Nano-contact spin-torque vortex oscillators (STVOs) are anticipated to find application as nanoscale sources of microwave emission in future technological applications. Presently the output power and phase stability of individual STVOs are not competitive with existing oscillator technologies. Synchronisation of multiple nano-contact STVOs via magnetisation dynamics has been proposed to enhance the microwave emission. The control of device-to-device variations, such as mode splitting of the microwave emission, is essential if multiple STVOs are to be successfully synchronised. In this work a combination of electrical measurements and time-resolved scanning Kerr microscopy (TRSKM) was used to demonstrate how mode splitting in the microwave emission of STVOs was related to the magnetisation dynamics that are generated. The free-running STVO response to a DC current only was used to identify devices and bias magnetic field configurations for which single and multiple modes of microwave emission were observed. Stroboscopic Kerr images were acquired by injecting a small amplitude RF current to phase lock the free-running STVO response. The images showed that the magnetisation dynamics of a multimode device with moderate splitting could be controlled by the injected RF current so that they exhibit similar spatial character to that of a single mode. Significant splitting was found to result from a complicated equilibrium magnetic state that was observed in Kerr images as irregular spatial characteristics of the magnetisation dynamics. Such dynamics were observed far from the nano-contact and so their presence cannot be detected in electrical measurements. This work demonstrates that TRSKM is a powerful tool for the direct observation of the magnetisation dynamics generated by STVOs that exhibit complicated microwave emission. Characterisation of such dynamics outside the nano-contact perimeter permits a deeper insight into the requirements for optimal phase-locking of

  13. Review of the Study of Nonlinear Atmospheric Dynamics in China (1999-2002)

    Institute of Scientific and Technical Information of China (English)

    刁一娜; 封国林; 刘式达; 刘式适; 罗德海; 黄思训; 陆维松; 丑纪范

    2004-01-01

    Researches on nonlinear atmospheric dynamics in China (1999-2002) are briefly surveyed. This review includes the major achievements in the following branches of nonlinear dynamics: nonlinear stability theory,nonlinear blocking dynamics, 3D spiral structure in the atmosphere, traveling wave solution of the nonlinear evolution equation, numerical predictability in a chaotic system, and global analysis of climate dynamics.Some applications of nonlinear methods such as hierarchy structure of climate and scaling invariance, the spatial-temporal series predictive method, the nonlinear inverse problem, and a new difference scheme with multi-time levels are also introduced.

  14. Nonlinear dynamics of a vectored thrust aircraft

    DEFF Research Database (Denmark)

    Sørensen, C.B; Mosekilde, Erik

    1996-01-01

    With realistic relations for the aerodynamic coefficients, numerical simulations are applied to study the longitudional dynamics of a thrust vectored aircraft. As function of the thrust magnitude and the thrust vectoring angle the equilibrium state exhibits two saddle-node bifurcations and three...

  15. Nonlinear dynamics of a vectored thrust aircraft

    DEFF Research Database (Denmark)

    Sørensen, C.B; Mosekilde, Erik

    1996-01-01

    With realistic relations for the aerodynamic coefficients, numerical simulations are applied to study the longitudional dynamics of a thrust vectored aircraft. As function of the thrust magnitude and the thrust vectoring angle the equilibrium state exhibits two saddle-node bifurcations and three ...

  16. All-optical switching in optically induced nonlinear waveguide couplers

    Energy Technology Data Exchange (ETDEWEB)

    Diebel, Falko, E-mail: falko.diebel@uni-muenster.de; Boguslawski, Martin; Rose, Patrick; Denz, Cornelia [Institut für Angewandte Physik and Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, 48149 Münster (Germany); Leykam, Daniel; Desyatnikov, Anton S. [Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia)

    2014-06-30

    We experimentally demonstrate all-optical vortex switching in nonlinear coupled waveguide arrays optically induced in photorefractive media. Our technique is based on multiplexing of nondiffracting Bessel beams to induce various types of waveguide configurations. Using double- and quadruple-well potentials, we demonstrate precise control over the coupling strength between waveguides, the linear and nonlinear dynamics and symmetry-breaking bifurcations of guided light, and a power-controlled optical vortex switch.

  17. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    WANG Shundin; ZHANG Hua

    2008-01-01

    Using functional derivative technique In quantum field theory,the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations.The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by Introducing the time translation operator.The functional partial differential evolution equations were solved by algebraic dynam-ics.The algebraic dynamics solutions are analytical In Taylor series In terms of both initial functions and time.Based on the exact analytical solutions,a new nu-merical algorithm-algebraic dynamics algorithm was proposed for partial differ-ential evolution equations.The difficulty of and the way out for the algorithm were discussed.The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  18. Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input

    Institute of Scientific and Technical Information of China (English)

    张克勤; 庄开宇; 苏宏业; 褚健; 高红

    2002-01-01

    This paper presents a sliding mode (SM) based identifier to deal wit h the parameter identification problem for a class of parameter uncertain nonlin ear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonline ar system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.

  19. Nonlinear Dynamics and Chaos: Advances and Perspectives

    CERN Document Server

    Thiel, Marco; Romano, M. Carmen; Károlyi, György; Moura, Alessandro

    2010-01-01

    This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos. Each chapter examines a specific research topic and, in addition to reviewing recent results, also discusses future perspectives. The result is an invaluable snapshot of the state of the field by some of its most important researchers. The first contribution in this book, "How did you get into Chaos?", is actually a collection of personal accounts by a number of distinguished scientists on how they entered the field of chaos and dynamical systems, featuring comments and recollections by James Yorke, Harry Swinney, Floris Takens, Peter Grassberger, Edward Ott, Lou Pecora, Itamar Procaccia, Michael Berry, Giulio Casati, Valentin Afraimovich, Robert MacKay, and last but not least, Celso Grebogi, to whom this volume is dedicated.

  20. Nonlinear Dynamics of A Damped Magnetic Oscillator

    CERN Document Server

    Kim, S Y

    1999-01-01

    We consider a damped magnetic oscillator, consisting of a permanent magnet in a periodically oscillating magnetic field. A detailed investigation of the dynamics of this dissipative magnetic system is made by varying the field amplitude $A$. As $A$ is increased, the damped magnetic oscillator, albeit simple looking, exhibits rich dynamical behaviors such as symmetry-breaking pitchfork bifurcations, period-doubling transitions to chaos, symmetry-restoring attractor-merging crises, and saddle-node bifurcations giving rise to new periodic attractors. Besides these familiar behaviors, a cascade of ``resurrections'' (i.e., an infinite sequence of alternating restabilizations and destabilizations) of the stationary points also occurs. It is found that the stationary points restabilize (destabilize) through alternating subcritical (supercritical) period-doubling and pitchfork bifurcations. We also discuss the critical behaviors in the period-doubling cascades.

  1. Process and meaning: nonlinear dynamics and psychology in visual art.

    Science.gov (United States)

    Zausner, Tobi

    2007-01-01

    Creating and viewing visual art are both nonlinear experiences. Creating a work of art is an irreversible process involving increasing levels of complexity and unpredictable events. Viewing art is also creative with collective responses forming autopoietic structures that shape cultural history. Artists work largely from the chaos of the unconscious and visual art contains elements of chaos. Works of art by the author are discussed in reference to nonlinear dynamics. "Travelogues" demonstrates continued emerging interpretations and a deterministic chaos. "Advice to the Imperfect" signifies the resolution of paradox in the nonlinear tension of opposites. "Quanah" shows the nonlinear tension of opposites as an ongoing personal evolution. "The Mother of All Things" depicts seemingly separate phenomena arising from undifferentiated chaos. "Memories" refers to emotional fixations as limit cycles. "Compassionate Heart," "Wind on the Lake," and "Le Mal du Pays" are a series of works in fractal format focusing on the archetype of the mother and child. "Sameness, Depth of Mystery" addresses the illusion of hierarchy and the dynamics of symbols. In "Chasadim" the origin of worlds and the regeneration of individuals emerge through chaos. References to chaos in visual art mirror the nonlinear complexity of life.

  2. Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers

    Directory of Open Access Journals (Sweden)

    Nicolás Peréz Alvarez

    2015-11-01

    Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.

  3. Nearly linear dynamics of nonlinear dispersive waves

    CERN Document Server

    Erdogan, M B; Zharnitsky, V

    2010-01-01

    Dispersive averaging e?ffects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.

  4. Population mixture model for nonlinear telomere dynamics

    Science.gov (United States)

    Itzkovitz, Shalev; Shlush, Liran I.; Gluck, Dan; Skorecki, Karl

    2008-12-01

    Telomeres are DNA repeats protecting chromosomal ends which shorten with each cell division, eventually leading to cessation of cell growth. We present a population mixture model that predicts an exponential decrease in telomere length with time. We analytically solve the dynamics of the telomere length distribution. The model provides an excellent fit to available telomere data and accounts for the previously unexplained observation of telomere elongation following stress and bone marrow transplantation, thereby providing insight into the nature of the telomere clock.

  5. Self-Organized Biological Dynamics and Nonlinear Control

    Science.gov (United States)

    Walleczek, Jan

    2006-04-01

    The frontiers and challenges of biodynamics research Jan Walleczek; Part I. Nonlinear Dynamics in Biology and Response to Stimuli: 1. External signals and internal oscillation dynamics - principal aspects and response of stimulated rhythmic processes Friedemann Kaiser; 2. Nonlinear dynamics in biochemical and biophysical systems: from enzyme kinetics to epilepsy Raima Larter, Robert Worth and Brent Speelman; 3. Fractal mechanisms in neural control: human heartbeat and gait dynamics in health and disease Chung-Kang Peng, Jeffrey M. Hausdorff and Ary L. Goldberger; 4. Self-organising dynamics in human coordination and perception Mingzhou Ding, Yanqing Chen, J. A. Scott Kelso and Betty Tuller; 5. Signal processing in biochemical reaction networks Adam P. Arkin; Part II. Nonlinear Sensitivity of Biological Systems to Electromagnetic Stimuli: 6. Electrical signal detection and noise in systems with long-range coherence Paul C. Gailey; 7. Oscillatory signals in migrating neutrophils: effects of time-varying chemical and electrical fields Howard R. Petty; 8. Enzyme kinetics and nonlinear biochemical amplification in response to static and oscillating magnetic fields Jan Walleczek and Clemens F. Eichwald; 9. Magnetic field sensitivity in the hippocampus Stefan Engström, Suzanne Bawin and W. Ross Adey; Part III. Stochastic Noise-Induced Dynamics and Transport in Biological Systems: 10. Stochastic resonance: looking forward Frank Moss; 11. Stochastic resonance and small-amplitude signal transduction in voltage-gated ion channels Sergey M. Bezrukov and Igor Vodyanoy; 12. Ratchets, rectifiers and demons: the constructive role of noise in free energy and signal transduction R. Dean Astumian; 13. Cellular transduction of periodic and stochastic energy signals by electroconformational coupling Tian Y. Tsong; Part IV. Nonlinear Control of Biological and Other Excitable Systems: 14. Controlling chaos in dynamical systems Kenneth Showalter; 15. Electromagnetic fields and biological

  6. A study on vortex flow control of inlet distortion in the re-engined 727-100 center inlet duct using computational fluid dynamics

    Science.gov (United States)

    Anderson, Bernhard H.; Huang, Pao S.; Paschal, William A.; Cavatorta, Enrico

    1992-01-01

    Computational fluid dynamics was used to investigate the management of inlet distortion by the introduction of discrete vorticity sources at selected locations in the inlet for the purpose of controlling secondary flow. These sources of vorticity were introduced by means of vortex generators. A series of design observations were made concerning the importance of various vortex generator design parameters in minimizing engine face circumferential distortion. The study showed that vortex strength, generator scale, and secondary flow field structure have a complicated and interrelated influence on the engine face distortion, over and above the initial geometry and arrangement of the generators. The installed vortex generator performance was found to be a function of three categories of variables: the inflow conditions, the aerodynamic characteristics associated with the inlet duct, and the design parameters related to the geometry, arrangement, and placement of the vortex generators within the outlet duct itself.

  7. A study on vortex flow control on inlet distortion in the re-engined 727-100 center inlet duct using computational fluid dynamics

    Science.gov (United States)

    Anderson, Bernhard H.; Huang, Pao S.; Paschal, William A.; Cavatorta, Enrico

    1992-01-01

    Computational fluid dynamics was used to investigate the management of inlet distortion by the introduction of discrete vorticity sources at selected locations in the inlet for the purpose of controlling secondary flow. These sources of vorticity were introduced by means of vortex generators. A series of design observations were made concerning the importance of various vortex generator design parameters in minimizing engine face circumferential distortion. The study showed that vortex strength, generator scale, and secondary flow field structure have a complicated and interrelated influence on the engine face distortion, over and above the initial geometry and arrangement of the generators. The installed vortex generator performance was found to be a function of three categories of variables: the inflow conditions, the aerodynamic characteristics associated with the inlet duct, and the design parameters related to the geometry, arrangement, and placement of the vortex generators within the outlet duct itself.

  8. Hub vortex instability and wake dynamics in axial flow wind turbines

    Science.gov (United States)

    Foti, Daniel; Howard, Kevin; Yang, Xiaolei; Guala, Michele; Sotiropoulos, Fotis

    2014-11-01

    The near wake region of an axial flow wind turbine has two distinct shear layers: an outer tip vortex shear layer, which rotates in the same direction as the rotor, and an inner counter-rotating hub vortex shear layer. Recent simulations (Kang et al., J. Fluid Mech. 744, 376 (2014)), corroborated with experiments (Chamorro et al., J. Fluid Mech. 716, 658 (2013)), showed that the hub vortex can undergo spiral vortex breakdown immediately downstream of the turbine. The precessing hub vortex core intercepts and interacts with the tip vortex shear layer causing the large-scale wake meandering motions in the far wake to intensify. These results were obtained for an axial flow hydrokinetic turbine in a turbulent open channel flow. Here we integrate high-resolution LES with experiments to show that a hub vortex instability also occurs in the near wake of a wind turbine in a wind tunnel. We show that the interactions of the hub vortex with the outer flow have significant effects on the wake meandering amplitude and frequency. Our results reinforce the conclusions of Kang et al. (2014) that the hub vortex must be included in wake models to simulate wake interactions at the power plant scale and optimize turbine siting for realistic terrain and wind conditions. This work was supported by DOE (DE-EE0002980, DE-EE0005482 and DE-AC04-94AL85000), the NSF (IIP-1318201), the IREE early career award (UMN) and NSF CAREER: Geophysical Flow Control (CBET-1351303). Computational resources were provided by MSI.

  9. Global investigation of the nonlinear dynamics of carbon nanotubes

    KAUST Repository

    Xu, Tiantian

    2016-11-17

    Understanding the complex nonlinear dynamics of carbon nanotubes (CNTs) is essential to enable utilization of these structures in devices and practical applications. We present in this work an investigation of the global nonlinear dynamics of a slacked CNT when actuated by large electrostatic and electrodynamic excitations. The coexistence of several attractors is observed. The CNT is modeled as an Euler–Bernoulli beam. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses. Critical computational challenges are posed due to the complicated form of the electrostatic force, which describes the interaction between the upper electrode, consisting of the cylindrically shaped CNT, and the lower electrode. Toward this, we approximate the electrostatic force using the Padé expansion. We explore the dynamics near the primary and superharmonic resonances. The nanostructure exhibits several attractors with different characteristics. To achieve deep insight and describe the complexity and richness of the behavior, we analyze the nonlinear response from an attractor-basins point of view. The competition of attractors is highlighted. Compactness and/or fractality of their basins are discussed. Both the effects of varying the excitation frequency and amplitude are examined up to the dynamic pull-in instability.

  10. Boundedness of Formation Configuration for Nonlinear Three-body Dynamics

    Institute of Scientific and Technical Information of China (English)

    LI Peng; SONG Yongduan

    2011-01-01

    The configuration boundedness of the three-body model dynamics is studied for Sun-Earth formation flying missions. The three-body formation flying model is built up with considering the lunar gravitational acceleration and solar radiation pressure. Because traditional linearized dynamics based method has relatively lower accuracy, a modified nonlinear formation configuration analysis method is proposed in this paper. Comparative studies are carried out from three aspects, i.e., natural formation configuration with arbitrary departure time, initialization time and formation configuration boundedness, and specific initialization time for bounded formation configuration. Simulations demonstrate the differences between the two schemes,and indicate that the nonlinear dynamic method reduces the error caused by the model linearization and disturbance approximation, and thus provides higher accuracy for boundedness analysis, which is of value to initial parameters selection for natural three-body formation flying.

  11. On the Nonlinear Evolution of Cosmic Web: Lagrangian Dynamics Revisited

    CERN Document Server

    Wang, Xin

    2014-01-01

    We investigate the nonlinear evolution of cosmic morphologies of the large-scale structure by examining the Lagrangian dynamics of various tensors of a cosmic fluid element, including the velocity gradient tensor, the Hessian matrix of the gravitational potential as well as the deformation tensor. Instead of the eigenvalue representation, the first two tensors, which associate with the "kinematic" and "dynamical" cosmic web classification algorithm respectively, are studied in a more convenient parameter space. These parameters are defined as the rotational invariant coefficients of the characteristic equation of the tensor. In the nonlinear local model (NLM) where the magnetic part of Weyl tensor vanishes, these invariants are fully capable of characterizing the dynamics. Unlike the Zeldovich approximation (ZA), where various morphologies do not change before approaching a one-dimensional singularity, the sheets in NLM are unstable for both overdense and underdense perturbations. While it has long been known...

  12. Selected topics in nonlinear dynamics and theoretical electrical engineering

    Energy Technology Data Exchange (ETDEWEB)

    Kyamakya, Kyandoghere; Chedjou, Jean Camberlain [Kalgenfurt Univ. (Austria); Halang, Wolfgang A.; Li, Zhong [Hagen Fernuniv. (Germany); Mathis, Wolfgang (eds.) [Leibniz Univ. Hannover (Germany). Inst. fuer Theoretische Elektrotechnik

    2013-02-01

    Post proceedings of Joint Conference INDS 2011 and ISTET 2011. Recent advances in nonlinear Dynamics and Synchronization as well as in Theoretical Electrical Engineering. Written by leading experts in the field. This book contains a collection of recent advanced contributions in the field of nonlinear dynamics and synchronization, including selected applications in the area of theoretical electrical engineering. The present book is divided into twenty-one chapters grouped in five parts. The first part focuses on theoretical issues related to chaos and synchronization and their potential applications in mechanics, transportation, communication and security. The second part handles dynamic systems modelling and simulation with special applications to real physical systems and phenomena. The third part discusses some fundamentals of electromagnetics (EM) and addresses the modelling and simulation in some real physical electromagnetic scenarios. The fourth part mainly addresses stability concerns. Finally, the last part assembles some sample applications in the area of optimization, data mining, pattern recognition and image processing.

  13. A Review of the Nonlinear Dynamics of Intraseasonal Oscillations

    Institute of Scientific and Technical Information of China (English)

    ZHAO Qiang; CHEN Jian-Zhou

    2011-01-01

    In recent years, significant progress has been made regarding theories of intraseasonal oscillations (ISOs) (also known as the Madden-Julian oscillation (MJO) in the tropics). This short review introduces the latest advances in ISO theories with an emphasis particularly on theoretical paradigms involving nonlinear dynamics in the following aspects: (1) the basic ideas and limitations of the previous and current theories and hypotheses regarding the MJO, (2) the new multi-scale theory of the MJO based on the intraseasonal planetary equatorial synoptic dynamics (IPESD) framework, and (3) nonlinear dynamics of ISOs in the extratropics based on the resonant triads of Rossby-Haurwitz waves.

  14. Nonlinear instability and dynamic bifurcation of a planeinterface during solidification

    Institute of Scientific and Technical Information of China (English)

    吴金平; 侯安新; 黄定华; 鲍征宇; 高志农; 屈松生

    2001-01-01

    By taking average over the curvature, the temperature and its gradient, the solute con-centration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidifi-cation, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysisof the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equationsshows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition vades with differ-ent thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradientscope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifur-cation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realizedthrough supercritical inverse bifurcation in the rapid solidification area.

  15. Dynamic nonlinear thermal optical effects in coupled ring resonators

    Directory of Open Access Journals (Sweden)

    Chenguang Huang

    2012-09-01

    Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.

  16. Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides

    Institute of Scientific and Technical Information of China (English)

    Zhang Jie-Fang; Jin Mei-Zhen; He Ji-Da; Lou Ji-Hui; Dai Chao-Qing

    2013-01-01

    We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr(o)dinger equation with varying coefficients.And then the dynamics of the first-and the second-order optical rogues are investigated.Finally,the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed.By properly choosing the distributed coefficients,we demonstrate analytically that rogue waves can be restrained or even be annihilated,or emerge periodically and sustain forever.We also figure out the center-of-mass motion of the rogue waves.

  17. Dynamic magnetic hysteresis and nonlinear susceptibility of antiferromagnetic nanoparticles

    Science.gov (United States)

    Kalmykov, Yuri P.; Ouari, Bachir; Titov, Serguey V.

    2016-08-01

    The nonlinear ac stationary response of antiferromagnetic nanoparticles subjected to both external ac and dc fields of arbitrary strength and orientation is investigated using Brown's continuous diffusion model. The nonlinear complex susceptibility and dynamic magnetic hysteresis (DMH) loops of an individual antiferromagnetic nanoparticle are evaluated and compared with the linear regime for extensive ranges of the anisotropy, the ac and dc magnetic fields, damping, and the specific antiferromagnetic parameter. It is shown that the shape and area of the DMH loops of antiferromagnetic particles are substantially altered by applying a dc field that permits tuning of the specific magnetic power loss in the nanoparticles.

  18. Nonlinear Boundary Dynamics and Chiral Symmetry in Holographic QCD

    CERN Document Server

    Albrecht, Dylan; Wilcox, Ronald J

    2011-01-01

    In the hard-wall model of holographic QCD we find that nonlinear boundary dynamics are required in order to maintain the correct pattern of explicit and spontaneous chiral symmetry breaking beyond leading order in the pion fields. With the help of a field redefinition, we demonstrate that the requisite nonlinear boundary conditions are consistent with the Sturm-Liouville structure required for the Kaluza-Klein decomposition of bulk fields. Observables insensitive to the chiral limit receive only small corrections in the improved description, and classical calculations in the hard-wall model remain surprisingly accurate.

  19. Stress-enhanced Gelation: A Dynamic Nonlinearity of Elasticity

    Science.gov (United States)

    Yao, Norman Y.; Broedersz, Chase P.; Depken, Martin; Becker, Daniel J.; Pollak, Martin R.; MacKintosh, Frederick C.; Weitz, David A.

    2013-01-01

    A hallmark of biopolymer networks is their sensitivity to stress, reflected by pronounced nonlinear elastic stiffening. Here, we demonstrate a distinct dynamical nonlinearity in biopolymer networks consisting of F-actin cross-linked by α-actinin-4. Applied stress delays the onset of relaxation and flow, markedly enhancing gelation and extending the regime of solid-like behavior to much lower frequencies. We show that this macroscopic network response can be accounted for at the single molecule level by the increased binding affinity of the cross-linker under load, characteristic of catch-bond-like behavior. PMID:23383843

  20. Nonlinear dynamics of electromagnetic pulses in cold relativistic plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Bonatto, A.; Pakter, R.; Rizzato, F.B. [Universidade Federal do Rio Grande do Sul, Instituto de Fisica, Rio Grande do Sul (Brazil)

    2004-07-01

    The propagation of intense electromagnetic pulses in plasmas is a subject of current interest particularly for particle acceleration and laser fusion.In the present analysis we study the self consistent propagation of nonlinear electromagnetic pulses in a one dimensional relativistic electron-ion plasma, from the perspective of nonlinear dynamics. We show how a series of Hamiltonian bifurcations give rise to the electric fields which are of relevance in the subject of particle acceleration. Connections between these bifurcated solutions and results of earlier analysis are made. (authors)

  1. Building better oscillators using nonlinear dynamics and pattern formation

    Indian Academy of Sciences (India)

    M C Cross; Eyal Kenig; John-Mark A Allen

    2015-03-01

    Frequency and time references play an essential role in modern technology and in living systems. The precision of self-sustained oscillations is limited by the effects of noise, which becomes evermore important as the sizes of the devices become smaller. In this paper, we review our recent theoretical results on using nonlinear dynamics and pattern formation to reduce the effects of noise and improve the frequency precision of oscillators, with particular reference to ongoing experiments on oscillators based on nanomechanical resonators. We discuss using resonator nonlinearity, novel oscillator architectures and the synchronization of arrays of oscillators, to improve the frequency precision.

  2. NONLINEAR DYNAMICS OF A CRACKED ROTOR IN A MANEUVERING AIRCRAFT

    Institute of Scientific and Technical Information of China (English)

    LIN Fu-sheng 林富生; MENG Guang 孟光; Eric Hahn

    2004-01-01

    The nonlinear dynamics of a cracked rotor system in an aircraft maneuvering with constant velocity or acceleration was investigated. The influence of the aircraft climbing angle on the cracked rotor system response is of particular interest and the results show that the climbing angle can markedly affect the parameter range for bifurcation, for quasi-periodic response and for chaotic response as well as for system stability. Aircraft acceleration is also shown to significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for on-line rotor crack fault diagnosis.

  3. Nonlinear analysis and dynamic structure in the energy market

    Science.gov (United States)

    Aghababa, Hajar

    This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non

  4. Nonlinear dynamics of rotating shallow water methods and advances

    CERN Document Server

    Zeitlin, Vladimir

    2007-01-01

    The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wa

  5. Adaptive steady-state stabilization for nonlinear dynamical systems

    Science.gov (United States)

    Braun, David J.

    2008-07-01

    By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.

  6. Nonlinear dynamics of a flexible portal frame under support excitation

    Science.gov (United States)

    de Paula, Aline Souza; Balthazar, José Manoel; Felix, Jorge Luis Palacios

    2012-11-01

    This paper presents a nonlinear dynamic analysis of a flexible portal frame subjected to support excitation, which is provided by an electro-dynamical shaker. The problem is reduced to a mathematical model of four degrees of freedom and the equations of motion are derived via Lagrangian formulation. The main goal of this study is to investigate the dynamic interactions between a flexible portal frame and a non-ideal support excitation. The numerical analysis shows a complex behavior of the system, which can be observed by phase spaces, Poincaŕ sections and bifurcation diagrams..

  7. Global dynamics for steep nonlinearities in two dimensions

    Science.gov (United States)

    Gedeon, Tomáš; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe

    2017-01-01

    This paper discusses a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. We study switching models of regulatory networks. To each switching network we associate a Morse graph, a computable object that describes a Morse decomposition of the dynamics. In this paper we show that all smooth perturbations of the switching system share the same Morse graph and we compute explicit bounds on the size of the allowable perturbation. This shows that computationally tractable switching systems can be used to characterize dynamics of smooth systems with steep nonlinearities.

  8. Dynamics of Venus' Southern hemisphere and South Polar Vortex from VIRTIS data obtained during the Venus Expres Mission

    Science.gov (United States)

    Hueso, R.; Garate-Lopez, I.; Sanchez-Lavega, A.

    2011-12-01

    The VIRTIS instrument onboard Venus Express observes Venus in two channels (visible and infrared) obtaining spectra and multi-wavelength images of the planet. The images have been used to trace the motions of the atmosphere at different layers of clouds [1-3]. We review the VIRTIS cloud image data and wind results obtained by different groups [1-3] and we present new results concerning the morphology and evolution of the South Polar Vortex at the upper and lower cloud levels with data covering the first 900 days of the mission. We present wind measurements of the South hemisphere obtained by cloud tracking individual cloud features and higher-resolution wind results of the polar region covering the evolution of the South polar vortex. The later were obtained by an image correlation algorithm run under human supervision to validate the data. We present day-side data of the upper clouds obtained at 380 and 980 nm sensitive to altitudes of 66-70 km, night-side data in the near infrared at 1.74 microns of the lower cloud (45-50 km) and day and night-side data obtained in the thermal infrared (wavelengths of 3.8 and 5.1 microns) which covers the dynamical evolution of Venus South Polar vortex at the cloud tops (66-70 km). We explore the different dynamics associated to the varying morphology of the vortex, its dynamical structure at different altitudes, the variability of the global wind data of the southern hemisphere and the interrelation of the polar vortex dynamics with the wind dynamics at subpolar and mid-latitudes. Acknowledgements: Work funded by Spanish MICIIN AYA2009-10701 with FEDER support and Grupos Gobierno Vasco IT-464-07. References [1] A. Sánchez-Lavega et al., Geophys. Res. Lett. 35, L13204, (2008). [2] D. Luz et al., Science, 332, 577-580 (2011). [3] R. Hueso, et al., Icarus doi:10.1016/j.icarus.2011.04.020 (2011)

  9. Optical Vortex Solitons in Parametric Wave Mixing

    CERN Document Server

    Alexander, T J; Buryak, A V; Sammut, R A; Alexander, Tristram J.; Kivshar, Yuri S.; Buryak, Alexander V.; Sammut, Rowland A.

    2000-01-01

    We analyze two-component spatial optical vortex solitons supported by degenerate three- or four-wave mixing in a nonlinear bulk medium. We study two distinct cases of such solitons, namely, parametric vortex solitons due to phase-matched second-harmonic generation in a optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a `halo-vortex', consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a harmonic field that guides a bright localized ring-like mode of a fundamental frequency field.

  10. Dynamic structural correlation via nonlinear programming techniques

    Science.gov (United States)

    Ting, T.; Ojalvo, I. U.

    1988-01-01

    A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.

  11. Steady vortex force theory and slender-wing flow diagnosis

    Institute of Scientific and Technical Information of China (English)

    Y.T.Yang; R.K.Zhang; Y.R.An; J.Z.Wu

    2007-01-01

    The concept vortex force in aerodynamics is sys-tematically examined based on a new steady vortex-force theory (Wu et al., Vorticity and vortex dynamics, Springer, 2006) which expresses the aerodynamic force (and moment) by the volume and boundary integrals of the Lamb vector.In this paper, the underlying physics of this theory is explo-red, including the general role of the Lamb vector in non-linear aerodynamics, its initial formation, and its relevance to the total-pressure non-uniformity. As a typical example, the theory is applied to the flow over a slender delta wing at a large angle of attack. The highly localized flow structures with high Lamb-vector peaks are identified in terms of their net contribution to various constituents of the total aerody-namic force. This vortex-force diagnosis sheds new light on the flow control and configuration optimization.

  12. Applications of chaos and nonlinear dynamics in engineering - Vol 1

    CERN Document Server

    Rondoni, Lamberto; Banerjee, Santo

    2011-01-01

    Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role.   This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘r...

  13. Applications of chaos and nonlinear dynamics in science and engineering

    CERN Document Server

    Rondoni, Lamberto; Mitra, Mala

    Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever the quantitative modeling and analysis of complex, nonlinear phenomena are required, chaos theory and its methods can play a key role.    This second volume concentrates on reviewing further relevant, contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such as the spread of epidemics; electronic circuits; chaos control in mechanical devices; secure communication; and digital watermarking. Featuring contributions from active and leading research groups, this collection is ideal both as a reference work and as a ‘recipe book’ full of tried and tested, successf...

  14. A Girsanov particle filter in nonlinear engineering dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Saha, Nilanjan [Structures Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore-560012 (India); Roy, D. [Structures Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore-560012 (India)], E-mail: royd@civil.iisc.ernet.in

    2009-02-02

    In this Letter, we propose a novel variant of the particle filter (PF) for state and parameter estimations of nonlinear engineering dynamical systems, modelled through stochastic differential equations (SDEs). The aim is to address a possible loss of accuracy in the estimates due to the discretization errors, which are inevitable during numerical integration of the SDEs. In particular, we adopt an explicit local linearization of the governing nonlinear SDEs and the resulting linearization errors in the estimates are corrected using Girsanov transformation of measures. Indeed, the linearization scheme via transformation of measures provides a weak framework for computing moments and this fits in well with any stochastic filtering strategy wherein estimates are themselves statistical moments. We presently implement the strategy using a bootstrap PF and numerically illustrate its performance for state and parameter estimations of the Duffing oscillator with linear and nonlinear measurement equations.

  15. Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers

    DEFF Research Database (Denmark)

    Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.

    of nonlinear beam reshaping occurring on a short time scale before the establishment of a steady state regime. In experiment, a 532nm laser beam can be injected into a single hole of an infiltrated PCF cladding structure, and the temporal dynamics of the nonlinear response is measured by monitoring......Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio......-sensing as well as active devices for all-optical switching at low (mW) laser powers. Commercially available PCFs infiltrated with liquids also provide a versatile and compact tool for exploration of the fundamentals of nonlinear beam propagation in periodic photonic structures. To explore the full scientific...

  16. Nonlinear systems techniques for dynamical analysis and control

    CERN Document Server

    Lefeber, Erjen; Arteaga, Ines

    2017-01-01

    This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...

  17. Nonlinear dynamics of nanoelectromechanical cantilevers based on nanowire piezoresistive detection

    Directory of Open Access Journals (Sweden)

    Baguet S.

    2012-07-01

    Full Text Available The nonlinear dynamics of in-plane nanoelectromechanical cantilevers based on silicon nanowire piezoresistive detection is investigated using a comprehensive analytical model that remains valid up to large displacements in the case of electrostatic actuation. This multiphysics model takes into account geometric, inertial and electrostatic nonlinearities as well as the fringing field effects which are significant for thin resonators. The bistability as well as multistability limits are considered in order to provide close-form expressions of the critical amplitudes. Third order nonlinearity cancellation is analytically inspected and set via an optimal DC drive voltage which permits the actuation of the NEMS beyond its critical amplitude. It may result on a large enhancement of the sensor performances by driving optimally the nanocantilever at very large amplitude, while suppressing the hysteresis.

  18. Non-linear dynamic response of a wind turbine blade

    Science.gov (United States)

    Chopra, I.; Dugundji, J.

    1979-01-01

    The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.

  19. Design of advanced materials for linear and nonlinear dynamics

    DEFF Research Database (Denmark)

    Frandsen, Niels Morten Marslev

    The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... design is accurate and somewhat simple analysis tools, as well as a fundamental understanding of the physical phenomena responsible for the relevant effects. The emphasis of this work lies primarily in the investigation of various advanced material models, developing the necessary analytical tools...... to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple...

  20. Nonlinear Dynamical Modeling and Forecast of ENSO Variability

    Science.gov (United States)

    Feigin, Alexander; Mukhin, Dmitry; Gavrilov, Andrey; Seleznev, Aleksey; Loskutov, Evgeny

    2017-04-01

    New methodology of empirical modeling and forecast of nonlinear dynamical system variability [1] is applied to study of ENSO climate system. The methodology is based on two approaches: (i) nonlinear decomposition of data [2], that provides low-dimensional embedding for further modeling, and (ii) construction of empirical model in the form of low dimensional random dynamical ("stochastic") system [3]. Three monthly data sets are used for ENSO modeling and forecast: global sea surface temperature anomalies, troposphere zonal wind speed, and thermocline depth; all data sets are limited by 30 S, 30 N and have horizontal resolution 10x10 . We compare results of optimal data decomposition as well as prognostic skill of the constructed models for different combinations of involved data sets. We also present comparative analysis of ENSO indices forecasts fulfilled by our models and by IRI/CPC ENSO Predictions Plume. [1] A. Gavrilov, D. Mukhin, E. Loskutov, A. Feigin, 2016: Construction of Optimally Reduced Empirical Model by Spatially Distributed Climate Data. 2016 AGU Fall Meeting, Abstract NG31A-1824. [2] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

  1. A data driven nonlinear stochastic model for blood glucose dynamics.

    Science.gov (United States)

    Zhang, Yan; Holt, Tim A; Khovanova, Natalia

    2016-03-01

    The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.

  2. Flight Dynamic Simulation with Nonlinear Aeroelastic Interaction using the ROM-ROM Procedure Project

    Data.gov (United States)

    National Aeronautics and Space Administration — ZONA Technology, Inc. proposes to develop an integrated flight dynamics simulation capability with nonlinear aeroelastic interactions by combining a flight dynamics...

  3. Nonlinear dynamic behaviors of ball bearing rotor system

    Institute of Scientific and Technical Information of China (English)

    WANG Li-qin; CUI Li; ZHENG De-zhi; GU Le

    2009-01-01

    Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing. Five-DOF dynamic equations of rotor supported by ball bearings were estimated. The Newmark-β method and Newton-Laphson method were used to solve the equations. The dynamic characteristics of rotor system were studied through the time response, the phase portrait, the Poincar? maps and the bifurcation diagrams. The results show that the system goes through the quasiperiodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions. The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases; the initial contact angle of ball bearing affects dynamic behaviors of the system obviously. The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.

  4. On time-space of nonlinear phenomena with Gompertzian dynamics.

    Science.gov (United States)

    Waliszewski, Przemyslaw; Konarski, Jerzy

    2005-04-01

    This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.

  5. Effects of noise on the phase dynamics of nonlinear oscillators

    Science.gov (United States)

    Daffertshofer, A.

    1998-07-01

    Various properties of human rhythmic movements have been successfully modeled using nonlinear oscillators. However, despite some extensions towards stochastical differential equations, these models do not comprise different statistical features that can be explained by nondynamical statistics. For instance, one observes certain lag one serial correlation functions for consecutive periods during periodic motion. This work aims at an extension of dynamical descriptions in terms of stochastically forced nonlinear oscillators such as ξ¨+ω20ξ=n(ξ,ξ˙)+q(ξ,ξ˙)Ψ(t), where the nonlinear function n(ξ,ξ˙) generates a limit cycle and Ψ(t) denotes colored noise that is multiplied via q(ξ,ξ˙). Nonlinear self-excited systems have been frequently investigated, particularly emphasizing stability properties and amplitude evolution. Thus, one can focus on the effects of noise on the frequency or phase dynamics that can be analyzed by use of time-dependent Fokker-Planck equations. It can be shown that noise multiplied via polynoms of arbitrary finite order cannot generate the desired period correlation but predominantly results in phase diffusion. The system is extended in terms of forced oscillators in order to find a minimal model producing the required error correction.

  6. Nonlinear dynamics in eccentric Taylor-Couette-Poiseuille flow

    Science.gov (United States)

    Pier, Benoît; Caulfield, C. P.

    2015-11-01

    The flow in the gap between two parallel but eccentric cylinders and driven by an axial pressure gradient and inner cylinder rotation is characterized by two geometrical parameters (radius ratio and eccentricity) and two dynamic parameters (axial and azimuthal Reynolds numbers). Such a theoretical configuration is a model for the flow between drill string and wellbore in the hydrocarbon drilling industry. The linear convective and absolute instability properties have been systematically derived in a recent study [Leclercq, Pier & Scott, J. Fluid Mech. 2013 and 2014]. Here we address the nonlinear dynamics resulting after saturation of exponentially growing small-amplitude perturbations. By using direct numerical simulations, a range of finite-amplitude states are found and characterized: nonlinear traveling waves (an eccentric counterpart of Taylor vortices, associated with constant hydrodynamic loading on the inner cylinder), modulated nonlinear waves (with time-periodic torque and flow rate) and more irregular states. In the nonlinear regime, the hydrodynamic forces are found to depart significantly from those prevailing for the base flow, even in situations of weak linear instability.

  7. Nonlinear Alfvén wave dynamics in plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Sarkar, Anwesa; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Schamel, Hans [Theoretical Physics, University of Bayreuth, D-95440 Bayreuth (Germany)

    2015-07-15

    Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.

  8. The coupled nonlinear dynamics of a lift system

    Science.gov (United States)

    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.

  9. The coupled nonlinear dynamics of a lift system

    Energy Technology Data Exchange (ETDEWEB)

    Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)

    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.

  10. APPLICATION OF MODIFIED CONVERSION METHOD TO A NONLINEAR DYNAMICAL SYSTEM

    Directory of Open Access Journals (Sweden)

    G.I. Melnikov

    2015-01-01

    Full Text Available The paper deals with a mathematical model of dynamical system with single degree of freedom, presented in the form of ordinary differential equations with nonlinear parts in the form of polynomials with constant and periodic coefficients. A modified method for the study of self-oscillations of nonlinear mechanical systems is presented. A refined method of transformation and integration of the equation, based on Poincare-Dulac normalization method has been developed. Refinement of the method lies in consideration of higher order nonlinear terms by Chebyshev economization technique that improves the accuracy of the calculations. Approximation of the higher order remainder terms by homogeneous forms of lower orders is performed; in the present case, it is done by cubic forms. An application of the modified method for the Van-der-Pol equation is considered as an example; the expressions for the amplitude and the phase of the oscillations are obtained in an analytical form. The comparison of the solution of the Van-der-Pol equation obtained by the developed method and the exact solution is performed. The error of the solution obtained by the modified method equals to 1%, which shows applicability of the developed method for analysis of self-oscillations of nonlinear dynamic systems with constant and periodic parameters.

  11. Nonlinear Alfvén wave dynamics in plasmas

    Science.gov (United States)

    Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans

    2015-07-01

    Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.

  12. Vortex cores and vortex motion in superconductors with anisotropic Fermi surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Galvis, J.A. [Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales Nicolás Cabrera, Condensed Matter Physics Center (IFIMAC), Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid (Spain); Departamento de Ciencias Naturales, Facultad de ingeniería y Ciencias Básicas, Universidad Central, Bogotá (Colombia); National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310 (United States); Herrera, E.; Guillamón, I.; Vieira, S. [Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales Nicolás Cabrera, Condensed Matter Physics Center (IFIMAC), Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid (Spain); Unidad Asociada de Altos Campos Magnéticos y Bajas Temperaturas, UAM, CSIC, Madrid (Spain); Suderow, H., E-mail: hermann.suderow@uam.es [Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales Nicolás Cabrera, Condensed Matter Physics Center (IFIMAC), Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid (Spain); Unidad Asociada de Altos Campos Magnéticos y Bajas Temperaturas, UAM, CSIC, Madrid (Spain)

    2017-02-15

    Highlights: • The observation of vortex cores is reviewed, with emphasis in new experiments. • Vortex cores are follow superconducting gap and Fermi surface shapes. • The vortex core shape influences vortex dynamics. - Abstract: Explaning static and dynamic properties of the vortex lattice in anisotropic superconductors requires a careful characterization of vortex cores. The vortex core contains Andreev bound states whose spatial extension depends on the anisotropy of the electronic band-structure and superconducting gap. This might have an impact on the anisotropy of the superconducting properties and on vortex dynamics. Here we briefly summarize basic concepts to understand anisotropic vortex cores and review vortex core imaging experiments. We further discuss moving vortex lattices and the influence of vortex core shape in vortex motion. We find vortex motion in highly tilted magnetic fields. We associate vortex motion to the vortex entry barrier and the screening currents at the surface. We find preferential vortex motion along the main axis of the vortex lattice. After travelling integers of the intervortex distance, we find that vortices move more slowly due to the washboard potential of the vortex lattice.

  13. Without bounds a scientific canvas of nonlinearity and complex dynamics

    CERN Document Server

    Ryazantsev, Yuri; Starov, Victor; Huang, Guo-Xiang; Chetverikov, Alexander; Arena, Paolo; Nepomnyashchy, Alex; Ferrus, Alberto; Morozov, Eugene

    2013-01-01

    Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.

  14. Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

    Directory of Open Access Journals (Sweden)

    Taher S. Hassan

    2016-01-01

    Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t,  i=1,…,n-1,   with  x0=x,  ϕβ(u≔uβsgn⁡u, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

  15. A nonlinear dynamics for the scalar field in Randers spacetime

    Science.gov (United States)

    Silva, J. E. G.; Maluf, R. V.; Almeida, C. A. S.

    2017-03-01

    We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.

  16. A nonlinear dynamics for the scalar field in Randers spacetime

    Directory of Open Access Journals (Sweden)

    J.E.G. Silva

    2017-03-01

    Full Text Available We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.

  17. Genealogical tree of Russian schools on Nonlinear Dynamics

    CERN Document Server

    Prants, S V

    2015-01-01

    One of the most prominent feature of research in Russia and the former Soviet Union is so-called scientific schools. It is a collaboration of researchers with a common scientific background working, as a rule, together in a specific city or even at an institution. The genealogical tree of scientific schools on nonlinear dynamics in Russia and the former Soviet Union is grown. We use these terminology in a broad sense including theory of dynamical systems and chaos and its applications in nonlinear physics. In most cases we connect two persons if one was an advisor of the Doctoral thesis of another one. It is an analogue of the Candidate of Science thesis in Russia. If the person had no official advisor or we don't know exactly who was an advisor, we fix that person who was known to be an informal teacher and has influenced on him/her very much.

  18. Nonlinear dynamical behavior of shallow cylindrical reticulated shells

    Institute of Scientific and Technical Information of China (English)

    WANG Xin-zhi; LIANG Cong-xing; HAN Ming-jun; YEH Kai-yuan; WANG Gang

    2007-01-01

    By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the separating variable function, the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support. The tensile force is solved out from the compatible equations, a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin. The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function. The existence of the chaotic motion of the single-layer shallow cylinmapping.

  19. A Study on the Dynamic Mechanism of the Formation of Mesoscale Vortex in Col Field

    Institute of Scientific and Technical Information of China (English)

    JIANG Yongqiang; WANG Yuan; HUANG Hong

    2012-01-01

    The mesoscale vortex associated with a mesoscale low-level jet (mLLJ) usually causes heavy rainfall in the col field.The col field is defined as a region between two highs and two lows,with the isobaric surface similar to a col.Using a two-dimensional shallow water model,the meso-β scale vortex couplets (MβVCs)induced by eight types of mesoscale wind perturbations in an ideal col field were numerically simulated.With the sizes of ~100 km,the MβVCs induced by northerly perturbation (NP) and southerly perturbation (SP)moved toward the col point.The sizes of MβVCs induced by southwesterly perturbation (SWP),southeasterly perturbation (SEP),northwesterly perturbation (NWP),and northeasterly perturbation (NEP) were relatively small for the perturbations moving toward dilatation axis.The MβVC induced by easterly perturbation (EP) and westerly perturbation (WP) could not develop because they quickly moved away from the col point,before the circulation could form.The size of the circulation was determined by the distance between the vortex and the col point.The closer to the col point the vortex was,the larger the size of vortex.The comparisons of maximum vorticity and vorticity root mean square error (RMSE) of the NP,the SWP,and the WP show that the maximum vorticity and the vorticity RMSE of the NP decreased slower than other perturbations.Therefore,the weak environment of the col field favors the maintenance of vorticity and the formation of vortex.When a mesoscalc vortex forms near the col point or moves toward the col point,it may maintain a quasi-stationary state in the stable col field.

  20. Nonlinear modeling of neural population dynamics for hippocampal prostheses

    OpenAIRE

    Song, Dong; Chan, Rosa H.M.; Vasilis Z Marmarelis; Hampson, Robert E.; Deadwyler, Sam A.; Berger, Theodore W.

    2009-01-01

    Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input–output transformation of spike trains. In this approach, a MIMO model comprises a series of physio...

  1. Numerical Analysis of the Dynamics of Nonlinear Solids and Structures

    Science.gov (United States)

    2008-08-01

    of the conservation/ dissipation properties in time for the elastoplastic case 64 11.6. Concluding remarks 70 References 71 li...development of stable time-stepping algorithms for nonlinear dynamics. The focus was on inelastic solids, including finite strain elastoplastic and...set of plas- tic/ damage evolution equations (usually of a unilaterally constrained character due to the presence of the so-called yield/ damage

  2. Estimating dynamic equilibrium economies: linear versus nonlinear likelihood

    OpenAIRE

    2004-01-01

    This paper compares two methods for undertaking likelihood-based inference in dynamic equilibrium economies: a sequential Monte Carlo filter proposed by Fernández-Villaverde and Rubio-Ramírez (2004) and the Kalman filter. The sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. The authors report two main results...

  3. Analyzing the Dynamics of Nonlinear Multivariate Time Series Models

    Institute of Scientific and Technical Information of China (English)

    DenghuaZhong; ZhengfengZhang; DonghaiLiu; StefanMittnik

    2004-01-01

    This paper analyzes the dynamics of nonlinear multivariate time series models that is represented by generalized impulse response functions and asymmetric functions. We illustrate the measures of shock persistences and asymmetric effects of shocks derived from the generalized impulse response functions and asymmetric function in bivariate smooth transition regression models. The empirical work investigates a bivariate smooth transition model of US GDP and the unemployment rate.

  4. Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics

    Science.gov (United States)

    Low, B. C.

    2015-01-01

    Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics: Eulerian and Lagrangian descriptions of three dimensional (3D) MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clarifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global constraint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low- β limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results in sheet dissipation, resistive heating and topological changes in the field notwithstanding the small resistivity. Strong Faraday induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun's corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit

  5. Analysis of Nonlinear Structural Dynamics and Resonance in Trees

    Directory of Open Access Journals (Sweden)

    H. Doumiri Ganji

    2012-01-01

    Full Text Available Wind and gravity both impact trees in storms, but wind loads greatly exceed gravity loads in most situations. Complex behavior of trees in windstorms is gradually turning into a controversial concern among ecological engineers. To better understand the effects of nonlinear behavior of trees, the dynamic forces on tree structures during periods of high winds have been examined as a mass-spring system. In fact, the simulated dynamic forces created by strong winds are studied in order to determine the responses of the trees to such dynamic loads. Many of such nonlinear differential equations are complicated to solve. Therefore, this paper focuses on an accurate and simple solution, Differential Transformation Method (DTM, to solve the derived equation. In this regard, the concept of differential transformation is briefly introduced. The approximate solution to this equation is calculated in the form of a series with easily computable terms. Then, the method has been employed to achieve an acceptable solution to the presented nonlinear differential equation. To verify the accuracy of the proposed method, the obtained results from DTM are compared with those from the numerical solution. The results reveal that this method gives successive approximations of high accuracy solution.

  6. Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics

    Institute of Scientific and Technical Information of China (English)

    Xin Yu; Na Duan

    2009-01-01

    This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.

  7. Predicting catastrophes in nonlinear dynamical systems by compressive sensing.

    Science.gov (United States)

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

    2011-04-15

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

  8. Predicting catastrophes in nonlinear dynamical systems by compressive sensing

    CERN Document Server

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

    2011-01-01

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

  9. Contributions of plasma physics to chaos and nonlinear dynamics

    Science.gov (United States)

    Escande, D. F.

    2016-11-01

    This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016

  10. Dynamics in a nonlinear Keynesian good market model

    Energy Technology Data Exchange (ETDEWEB)

    Naimzada, Ahmad, E-mail: ahmad.naimzada@unimib.it [Department of Economics, Quantitative Methods and Management, University of Milano-Bicocca, U7 Building, Via Bicocca degli Arcimboldi 8, 20126 Milano (Italy); Pireddu, Marina, E-mail: marina.pireddu@unimib.it [Department of Mathematics and Applications, University of Milano-Bicocca, U5 Building, Via Cozzi 55, 20125 Milano (Italy)

    2014-03-15

    In this paper, we show how a rich variety of dynamical behaviors can emerge in the standard Keynesian income-expenditure model when a nonlinearity is introduced, both in the cases with and without endogenous government spending. A specific sigmoidal functional form is used for the adjustment mechanism of income with respect to the excess demand, in order to bound the income variation. With the aid of analytical and numerical tools, we investigate the stability conditions, bifurcations, as well as periodic and chaotic dynamics. Globally, we study multistability phenomena, i.e., the coexistence of different kinds of attractors.

  11. Vortex dynamics in superconducting MgB2 and prospects for applications.

    Science.gov (United States)

    Bugoslavsky, Y; Perkins, G K; Qi, X; Cohen, L F; Caplin, A D

    2001-03-29

    The recently discovered superconductor magnesium diboride, MgB2, has a transition temperature, Tc, approaching 40 K, placing it intermediate between the families of low- and high-temperature superconductors. In practical applications, superconductors are permeated by quantized vortices of magnetic flux. When a supercurrent flows, there is dissipation of energy unless these vortices are 'pinned' in some way, and so inhibited from moving under the influence of the Lorentz force. Such vortex motion ultimately determines the critical current density, Jc, which the superconductor can support. Vortex behaviour has proved to be more complicated in high-temperature superconductors than in low-temperature superconductors and, although this has stimulated extensive theoretical and experimental research, it has also impeded applications. Here we describe the vortex behaviour in MgB2, as reflected in Jc and in the vortex creep rate, S, the latter being a measure of how fast the 'persistent' supercurrents decay. Our results show that naturally occurring grain boundaries are highly transparent to supercurrents, a desirable property which contrasts with the behaviour of the high-temperature superconductors. On the other hand, we observe a steep, practically deleterious decline in Jc with increasing magnetic field, which is likely to reflect the high degree of crystalline perfection in our samples, and hence a low vortex pinning energy.

  12. Vortex dynamics and surface pressure fluctuations on a normal flat plate

    Science.gov (United States)

    Hemmati, Arman; Wood, David H.; Martinuzzi, Robert J.; Ferrari, Simon W.; Hu, Yaoping

    2016-11-01

    The effect of vortex formation and interactions on surface pressure fluctuations is examined in the wake of a normal flat plate by analyzing Direct Numerical Simulations at Re =1200. A novel local maximum score-based 3D method is used to track vortex development in the region close to the plate where the major contributions to the surface pressure are generated. Three distinct vortex shedding regimes are identified by changes in the lift and drag fluctuations. The instances of maximum drag coincide with impingement of newly formed vortices on the plate. This results in large and concentrated areas of rotational and strain contributions to generation of pressure fluctuations. Streamwise vortex straining and chordwise stretching are correlated with the large ratios of streamwise to chordwise normal stresses and regions of significant rotational contribution to the pressure. In contrast at the minimum drag, the vorticity field close to the plate is disorganized, and vortex roll-up occurs farther downstream. This leads to a uniform distribution of pressure. This study was supported by Alberta Innovates Technology Futures (AITF) and Natural Sciences and Engineering Research Council of Canada (NSERC).

  13. Study of nonlinear processes of a large experimental thermoacoustic-Stirling heat engine by using computational fluid dynamics

    Science.gov (United States)

    Yu, G. Y.; Luo, E. C.; Dai, W.; Hu, J. Y.

    2007-10-01

    This article focuses on using computational fluid dynamics (CFD) method to study several important nonlinear phenomenon and processes of a large experimental thermoacoustic-Stirling heat engine. First, the simulated physical model was introduced, and the suitable numerical scheme and algorithm for the time-dependent compressible thermoacoustic system was determined through extensive numerical tests. Then, the simulation results of the entire evolution process of self-excited thermoacoustic oscillation and the acoustical characteristics of pressure and velocity waves were presented and analyzed. Especially, the onset temperature and the saturation process of dynamic pressure were captured by the CFD simulation. In addition, another important nonlinear phenomenon accompanying the acoustic wave, which is the steady mass flow through the traveling-wave loop inside the thermoacoustic engine, was studied. To suppress the steady mass flow numerically, a fan model was adopted in the simulation. Finally, the multidimensional effects of vortex formation in the thermal buffer tube and other components were displayed numerically. Most importantly, a substantial comparison between the simulation and experiments was made, which demonstrated well the validity and powerfulness of the CFD simulation for characterizing several complicated nonlinear phenomenon involved in the self-excited thermoacoustic heat engine.

  14. Experimental Study On The Mixing Induced By Inertia-gravity Wave Breaking On The Dynamical Barrier of A Vortex

    Science.gov (United States)

    Moulin, F.; Flor, J.

    We present the results of an experimental investigation on the material transport across the shear zone of a cyclonic vortex induced by the breaking of inertia-gravity waves. As has been suggested by McIntyre (1995) this could be a possible mechamism of ozone transport across the dynamical barrier of the polar vortex. The experiments were conducted in a 1 meter size tank containing a rotating stratified fluid. Barotropic vortices were generated by siphoning off fluid with a long perforated tube and per- turbed by planar internal waves generated by the vertical oscillation of a horizontal circular cylinder. As predicted by theorical results based on the WKB approximation, the waves opposing the vortex velocity field were trapped in the outer edge of the vor- tex. In some cases, the increase of wave energy in this region was strong enough to lead to 3-dimensional breaking of the wave pattern. Experimental visualization tech- niques were used to determine the class of instability responsible for this breaking and to measure the induced mixing. A simple model to predict the efficiency of the mixing process will be presented.

  15. Nonlinear dynamic susceptibilities of interacting and noninteracting magnetic nanoparticles

    CERN Document Server

    Joensson, P; García-Palacios, J L; Svedlindh, P

    2000-01-01

    The linear and cubic dynamic susceptibilities of solid dispersions of nanosized maghemite gamma-Fe sub 2 O sub 3 particles have been measured for three samples with a volume concentration of magnetic particles ranging from 0.3% to 17%, in order to study the effect of dipole-dipole interactions. Significant differences between the dynamic response of the samples are observed. While the linear and cubic dynamic susceptibilities of the most dilute sample compare reasonably well with the corresponding expressions proposed by Raikher and Stepanov for noninteracting particles, the nonlinear dynamic response of the most concentrated sample exhibits at low temperatures similar features as observed in a Ag(11 at% Mn) spin glass.

  16. Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model

    CERN Document Server

    Nesterov, Alexander I; Berman, Gennady P; Mavromatos, Nick E

    2016-01-01

    We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.

  17. Nonlinear dynamics of dipoles in microtubules: Pseudospin model.

    Science.gov (United States)

    Nesterov, Alexander I; Ramírez, Mónica F; Berman, Gennady P; Mavromatos, Nick E

    2016-06-01

    We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frame of the classical pseudospin model. We derive the system of nonlinear dynamical partial differential equations of motion for interacting dipoles and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to achieve a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.

  18. Optical Nonlinearities and Ultrafast Carrier Dynamics in Semiconductor Quantum Dots

    Energy Technology Data Exchange (ETDEWEB)

    Klimov, V.; McBranch, D.; Schwarz, C.

    1998-08-10

    Low-dimensional semiconductors have attracted great interest due to the potential for tailoring their linear and nonlinear optical properties over a wide-range. Semiconductor nanocrystals (NC's) represent a class of quasi-zero-dimensional objects or quantum dots. Due to quantum cordhement and a large surface-to-volume ratio, the linear and nonlinear optical properties, and the carrier dynamics in NC's are significantly different horn those in bulk materials. napping at surface states can lead to a fast depopulation of quantized states, accompanied by charge separation and generation of local fields which significantly modifies the nonlinear optical response in NC's. 3D carrier confinement also has a drastic effect on the energy relaxation dynamics. In strongly confined NC's, the energy-level spacing can greatly exceed typical phonon energies. This has been expected to significantly inhibit phonon-related mechanisms for energy losses, an effect referred to as a phonon bottleneck. It has been suggested recently that the phonon bottleneck in 3D-confined systems can be removed due to enhanced role of Auger-type interactions. In this paper we report femtosecond (fs) studies of ultrafast optical nonlinearities, and energy relaxation and trap ping dynamics in three types of quantum-dot systems: semiconductor NC/glass composites made by high temperature precipitation, ion-implanted NC's, and colloidal NC'S. Comparison of ultrafast data for different samples allows us to separate effects being intrinsic to quantum dots from those related to lattice imperfections and interface properties.

  19. Investigation of Nonlinear Pupil Dynamics by Recurrence Quantification Analysis

    Directory of Open Access Journals (Sweden)

    L. Mesin

    2013-01-01

    Full Text Available Pupil is controlled by the autonomous nervous system (ANS. It shows complex movements and changes of size even in conditions of constant stimulation. The possibility of extracting information on ANS by processing data recorded during a short experiment using a low cost system for pupil investigation is studied. Moreover, the significance of nonlinear information contained in the pupillogram is investigated. We examined 13 healthy subjects in different stationary conditions, considering habitual dental occlusion (HDO as a weak stimulation of the ANS with respect to the maintenance of the rest position (RP of the jaw. Images of pupil captured by infrared cameras were processed to estimate position and size on each frame. From such time series, we extracted linear indexes (e.g., average size, average displacement, and spectral parameters and nonlinear information using recurrence quantification analysis (RQA. Data were classified using multilayer perceptrons and support vector machines trained using different sets of input indexes: the best performance in classification was obtained including nonlinear indexes in the input features. These results indicate that RQA nonlinear indexes provide additional information on pupil dynamics with respect to linear descriptors, allowing the discrimination of even a slight stimulation of the ANS. Their use in the investigation of pathology is suggested.

  20. Linear and nonlinear dynamic systems in financial time series prediction

    Directory of Open Access Journals (Sweden)

    Salim Lahmiri

    2012-10-01

    Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.