Nonlinear friction dynamics on polymer surface under accelerated movement

Directory of Open Access Journals (Sweden)

Yuuki Aita

2017-04-01

Full Text Available Nonlinear phenomena on the soft material surface are one of the most exciting topics of chemical physics. However, only a few reports exist on the friction phenomena under accelerated movement, because friction between two solid surfaces is considered a linear phenomenon in many cases. We aim to investigate how nonlinear accelerated motion affects friction on solid surfaces. In the present study, we evaluate the frictional forces between two polytetrafluoroethylene (PTFE resins using an advanced friction evaluation system. On PTFE surfaces, the normalized delay time δ, which is the time lag in the response of the friction force to the accelerated movement, is observed in the pre-sliding friction process. Under high-velocity conditions, kinetic friction increases with velocity. Based on these experimental results, we propose a two-phase nonlinear model including a pre-sliding process (from the beginning of sliding of a contact probe to the establishment of static friction and a kinetic friction process. The present model consists of several factors including velocity, acceleration, stiffness, viscosity, and vertical force. The findings reflecting the viscoelastic properties of soft material is useful for various fields such as in the fabrication of clothes, cosmetics, automotive materials, and virtual reality systems as well as for understanding friction phenomena on soft material surfaces.

Robust flight control using incremental nonlinear dynamic inversion and angular acceleration prediction

NARCIS (Netherlands)

Sieberling, S.; Chu, Q.P.; Mulder, J.A.

2010-01-01

This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of

Nonlinear acceleration of SN transport calculations

Energy Technology Data Exchange (ETDEWEB)

Fichtl, Erin D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Calef, Matthew T [Los Alamos National Laboratory

2010-12-20

The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.

Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations

NARCIS (Netherlands)

Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der

Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general

Development of a synchrotron radiation beam monitor for the Integrable Optics Test Accelerator

Energy Technology Data Exchange (ETDEWEB)

Scarpelli, Andrea [Univ. of Ferrara (Italy)

2016-01-01

Nonlinear integrable optics applied to beam dynamics may mitigate multi-particle instabilities, but proof of principle experiments have never been carried out. The Integrable Optics Test Accelerator (IOTA) is an electron and proton storage ring currently being built at Fermilab, which addresses tests of nonlinear lattice elements in a real machine in addition to experiments on optical stochastic cooling and on the single-electron wave function. These experiments require an outstanding control over the lattice parameters, achievable with fast and precise beam monitoring systems. This work describes the steps for designing and building a beam monitor for IOTA based on synchrotron radiation, able to measure intensity, position and transverse cross-section beam.

Modeling Nonlinear Change via Latent Change and Latent Acceleration Frameworks: Examining Velocity and Acceleration of Growth Trajectories

Science.gov (United States)

Grimm, Kevin; Zhang, Zhiyong; Hamagami, Fumiaki; Mazzocco, Michele

2013-01-01

We propose the use of the latent change and latent acceleration frameworks for modeling nonlinear growth in structural equation models. Moving to these frameworks allows for the direct identification of "rates of change" and "acceleration" in latent growth curves--information available indirectly through traditional growth…

Nonlinear Krylov acceleration of reacting flow codes

Energy Technology Data Exchange (ETDEWEB)

Kumar, S.; Rawat, R.; Smith, P.; Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)

1996-12-31

We are working on computational simulations of three-dimensional reactive flows in applications encompassing a broad range of chemical engineering problems. Examples of such processes are coal (pulverized and fluidized bed) and gas combustion, petroleum processing (cracking), and metallurgical operations such as smelting. These simulations involve an interplay of various physical and chemical factors such as fluid dynamics with turbulence, convective and radiative heat transfer, multiphase effects such as fluid-particle and particle-particle interactions, and chemical reaction. The governing equations resulting from modeling these processes are highly nonlinear and strongly coupled, thereby rendering their solution by traditional iterative methods (such as nonlinear line Gauss-Seidel methods) very difficult and sometimes impossible. Hence we are exploring the use of nonlinear Krylov techniques (such as CMRES and Bi-CGSTAB) to accelerate and stabilize the existing solver. This strategy allows us to take advantage of the problem-definition capabilities of the existing solver. The overall approach amounts to using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method and its variants as nonlinear preconditioners for the nonlinear Krylov method. We have also adapted a backtracking approach for inexact Newton methods to damp the Newton step in the nonlinear Krylov method. This will be a report on work in progress. Preliminary results with nonlinear GMRES have been very encouraging: in many cases the number of line Gauss-Seidel sweeps has been reduced by about a factor of 5, and increased robustness of the underlying solver has also been observed.

Useful tools for non-linear systems: Several non-linear integral inequalities

Czech Academy of Sciences Publication Activity Database

Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

2013-01-01

Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

Nonlinear acceleration of S_n transport calculations

International Nuclear Information System (INIS)

Fichtl, Erin D.; Warsa, James S.; Calef, Matthew T.

2011-01-01

The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we employ a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application. (author)

Measuring localized nonlinear components in a circular accelerator with a nonlinear tune response matrix

Directory of Open Access Journals (Sweden)

G. Franchetti

2008-09-01

Full Text Available In this paper we present a method for measuring the nonlinear errors in a circular accelerator by taking advantage of the feed-down effect of high order multipoles when the closed orbit is globally deformed. We devise a nonlinear tune response matrix in which the response to a closed orbit deformation is obtained in terms of change of machine tune and correlated with the strength of the local multipoles. A numerical example and a proof of principle experiment to validate the theoretical methods are presented and discussed.

PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena

Science.gov (United States)

Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo

2010-10-01

Back in 1967, Clifford Gardner, John Greene, Martin Kruskal and Robert Miura published a seminal paper in Physical Review Letters which was to become a cornerstone in the theory of integrable systems. In 2006, the authors of this paper received the AMS Steele Prize. In this award the AMS pointed out that `In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.' From this discovery the modern theory of integrability bloomed, leading scientists to a deep understanding of many nonlinear phenomena which is by no means reachable by perturbation methods or other previous tools from linear theories. Nonlinear phenomena appear everywhere in nature, their description and understanding is therefore of great interest both from the theoretical and applicative point of view. If a nonlinear phenomenon can be represented by an integrable system then we have at our disposal a variety of tools to achieve a better mathematical description of the phenomenon. This special issue is largely dedicated to investigations of nonlinear phenomena which are related to the concept of integrability, either involving integrable systems themselves or because they use techniques from the theory of integrability. The idea of this special issue originated during the 18th edition of the Nonlinear Evolution Equations and Dynamical Systems (NEEDS) workshop, held at Isola Rossa, Sardinia, Italy, 16-23 May 2009 (http://needs-conferences.net/2009/). The issue benefits from the occasion offered by the meeting, in particular by its mini-workshops programme, and contains invited review papers and contributed papers. It is worth pointing out that there was an open call for papers and all contributions were peer reviewed

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

Energy Technology Data Exchange (ETDEWEB)

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

2006-09-28

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

Integrability of a system of two nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Zhukhunashvili, V.Z.

1989-01-01

In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants

Lie Algebras for Constructing Nonlinear Integrable Couplings

International Nuclear Information System (INIS)

Zhang Yufeng

2011-01-01

Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti-Johnson (GJ) hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their Hamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations. (general)

Algorithms For Integrating Nonlinear Differential Equations

Science.gov (United States)

Freed, A. D.; Walker, K. P.

1994-01-01

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

IOTA (Integrable Optics Test Accelerator): facility and experimental beam physics program

Science.gov (United States)

Antipov, S.; Broemmelsiek, D.; Bruhwiler, D.; Edstrom, D.; Harms, E.; Lebedev, V.; Leibfritz, J.; Nagaitsev, S.; Park, C. S.; Piekarz, H.; Piot, P.; Prebys, E.; Romanov, A.; Ruan, J.; Sen, T.; Stancari, G.; Thangaraj, C.; Thurman-Keup, R.; Valishev, A.; Shiltsev, V.

2017-03-01

The Integrable Optics Test Accelerator (IOTA) is a storage ring for advanced beam physics research currently being built and commissioned at Fermilab. It will operate with protons and electrons using injectors with momenta of 70 and 150 MeV/c, respectively. The research program includes the study of nonlinear focusing integrable optical beam lattices based on special magnets and electron lenses, beam dynamics of space-charge effects and their compensation, optical stochastic cooling, and several other experiments. In this article, we present the design and main parameters of the facility, outline progress to date and provide the timeline of the construction, commissioning and research. The physical principles, design, and hardware implementation plans for the major IOTA experiments are also discussed.

IOTA (Integrable Optics Test Accelerator): Facility and experimental beam physics program

International Nuclear Information System (INIS)

Antipov, Sergei; Broemmelsiek, Daniel; Bruhwiler, David; Edstrom, Dean; Harms, Elvin

2017-01-01

The Integrable Optics Test Accelerator (IOTA) is a storage ring for advanced beam physics research currently being built and commissioned at Fermilab. It will operate with protons and electrons using injectors with momenta of 70 and 150 MeV/c, respectively. The research program includes the study of nonlinear focusing integrable optical beam lattices based on special magnets and electron lenses, beam dynamics of space-charge effects and their compensation, optical stochastic cooling, and several other experiments. In this article, we present the design and main parameters of the facility, outline progress to date and provide the timeline of the construction, commissioning and research. Finally, the physical principles, design, and hardware implementation plans for the major IOTA experiments are also discussed.

Numerical treatments for solving nonlinear mixed integral equation

Directory of Open Access Journals (Sweden)

M.A. Abdou

2016-12-01

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

Calibration of the Nonlinear Accelerator Model at the Diamond Storage Ring

CERN Document Server

Bartolini, Riccardo; Rowland, James; Martin, Ian; Schmidt, Frank

2010-01-01

The correct implementation of the nonlinear ring model is crucial to achieve the top performance of a synchrotron light source. Several dynamics quantities can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these methods are based on the analysis of turn-by-turn data of excited betatron oscillations. We present the experimental results of the campaign of measurements carried out at the Diamond. A combination of Frequency Map Analysis (FMA) and detuning with momentum measurements has allowed a precise calibration of the nonlinear model capable of reproducing the nonlinear beam dynamics in the storage ring

Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy

Directory of Open Access Journals (Sweden)

Xiuzhi Xing

2014-01-01

Full Text Available Nonlinear integrable couplings of super classical-Boussinesq hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then, its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.

On a new series of integrable nonlinear evolution equations

International Nuclear Information System (INIS)

Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.

1980-10-01

Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)

Fuchs indices and the first integrals of nonlinear differential equations

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2005-01-01

New method of finding the first integrals of nonlinear differential equations in polynomial form is presented. Basic idea of our approach is to use the scaling of solution of nonlinear differential equation and to find the dimensions of arbitrary constants in the Laurent expansion of the general solution. These dimensions allows us to obtain the scalings of members for the first integrals of nonlinear differential equations. Taking the polynomials with unknown coefficients into account we present the algorithm of finding the first integrals of nonlinear differential equations in the polynomial form. Our method is applied to look for the first integrals of eight nonlinear ordinary differential equations of the fourth order. The general solution of one of the fourth order ordinary differential equations is given

Relativistic electron beam acceleration by cascading nonlinear Landau damping of electromagnetic waves in a plasma

International Nuclear Information System (INIS)

Sugaya, R.; Ue, A.; Maehara, T.; Sugawa, M.

1996-01-01

Acceleration and heating of a relativistic electron beam by cascading nonlinear Landau damping involving three or four intense electromagnetic waves in a plasma are studied theoretically based on kinetic wave equations and transport equations derived from relativistic Vlasov endash Maxwell equations. Three or four electromagnetic waves excite successively two or three nonresonant beat-wave-driven relativistic electron plasma waves with a phase velocity near the speed of light [v p =c(1-γ -2 p ) 1/2 , γ p =ω/ω pe ]. Three beat waves interact nonlinearly with the electron beam and accelerate it to a highly relativistic energy γ p m e c 2 more effectively than by the usual nonlinear Landau damping of two electromagnetic waves. It is proved that the electron beam can be accelerated to more highly relativistic energy in the plasma whose electron density decreases temporally with an appropriate rate because of the temporal increase of γ p . copyright 1996 American Institute of Physics

Polynomial solutions of nonlinear integral equations

International Nuclear Information System (INIS)

Dominici, Diego

2009-01-01

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials

Polynomial solutions of nonlinear integral equations

Energy Technology Data Exchange (ETDEWEB)

Dominici, Diego [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443 (United States)], E-mail: dominicd@newpaltz.edu

2009-05-22

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.

Accurate and efficient spin integration for particle accelerators

International Nuclear Information System (INIS)

Abell, Dan T.; Meiser, Dominic; Ranjbar, Vahid H.; Barber, Desmond P.

2015-01-01

Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code GPUSPINTRACK. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.

Accurate and efficient spin integration for particle accelerators

Energy Technology Data Exchange (ETDEWEB)

Abell, Dan T.; Meiser, Dominic [Tech-X Corporation, Boulder, CO (United States); Ranjbar, Vahid H. [Brookhaven National Laboratory, Upton, NY (United States); Barber, Desmond P. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2015-01-15

Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code GPUSPINTRACK. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.

A real nonlinear integrable couplings of continuous soliton hierarchy and its Hamiltonian structure

International Nuclear Information System (INIS)

Yu Fajun

2011-01-01

Some integrable coupling systems of existing papers are linear integrable couplings. In the Letter, beginning with Lax pairs from special non-semisimple matrix Lie algebras, we establish a scheme for constructing real nonlinear integrable couplings of continuous soliton hierarchy. A direct application to the AKNS spectral problem leads to a novel nonlinear integrable couplings, then we consider the Hamiltonian structures of nonlinear integrable couplings of AKNS hierarchy with the component-trace identity. - Highlights: → We establish a scheme to construct real nonlinear integrable couplings. → We obtain a novel nonlinear integrable couplings of AKNS hierarchy. → Hamiltonian structure of nonlinear integrable couplings AKNS hierarchy is presented.

Accurate and efficient spin integration for particle accelerators

Directory of Open Access Journals (Sweden)

Dan T. Abell

2015-02-01

Full Text Available Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.

Evaluation of time integration methods for transient response analysis of nonlinear structures

International Nuclear Information System (INIS)

Park, K.C.

1975-01-01

Recent developments in the evaluation of direct time integration methods for the transient response analysis of nonlinear structures are presented. These developments, which are based on local stability considerations of an integrator, show that the interaction between temporal step size and nonlinearities of structural systems has a pronounced effect on both accuracy and stability of a given time integration method. The resulting evaluation technique is applied to a model nonlinear problem, in order to: 1) demonstrate that it eliminates the present costly process of evaluating time integrator for nonlinear structural systems via extensive numerical experiments; 2) identify the desirable characteristics of time integration methods for nonlinear structural problems; 3) develop improved stiffly-stable methods for application to nonlinear structures. Extension of the methodology for examination of the interaction between a time integrator and the approximate treatment of nonlinearities (such as due to pseudo-force or incremental solution procedures) is also discussed. (Auth.)

Nonlinear Monte Carlo model of superdiffusive shock acceleration with magnetic field amplification

Science.gov (United States)

Bykov, Andrei M.; Ellison, Donald C.; Osipov, Sergei M.

2017-03-01

Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow into the hot downstream thermal plasma with a substantial fraction of energy going into a broad spectrum of superthermal charged particles and magnetic fluctuations. The superthermal particles can penetrate into the shock upstream region producing an extended shock precursor. The cold upstream plasma flow is decelerated by the force provided by the superthermal particle pressure gradient. In high Mach number collisionless shocks, efficient particle acceleration is likely coupled with turbulent magnetic field amplification (MFA) generated by the anisotropic distribution of accelerated particles. This anisotropy is determined by fast particle transport, making the problem strongly nonlinear and multiscale. Here, we present a nonlinear Monte Carlo model of collisionless shock structure with superdiffusive propagation of high-energy Fermi accelerated particles coupled to particle acceleration and MFA, which affords a consistent description of strong shocks. A distinctive feature of the Monte Carlo technique is that it includes the full angular anisotropy of the particle distribution at all precursor positions. The model reveals that the superdiffusive transport of energetic particles (i.e., Lévy-walk propagation) generates a strong quadruple anisotropy in the precursor particle distribution. The resultant pressure anisotropy of the high-energy particles produces a nonresonant mirror-type instability that amplifies compressible wave modes with wavelengths longer than the gyroradii of the highest-energy protons produced by the shock.

Geometric integration for particle accelerators

Science.gov (United States)

Forest, Étienne

2006-05-01

This paper is a very personal view of the field of geometric integration in accelerator physics—a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling—unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.

Geometric integration for particle accelerators

International Nuclear Information System (INIS)

Forest, Etienne

2006-01-01

This paper is a very personal view of the field of geometric integration in accelerator physics-a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling-unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction

Nonlinear Photonics and Novel Optical Phenomena

CERN Document Server

Morandotti, Roberto

2012-01-01

Nonlinear Photonics and Novel Optical Phenomena contains contributed chapters from leading experts in nonlinear optics and photonics, and provides a comprehensive survey of fundamental concepts as well as hot topics in current research on nonlinear optical waves and related novel phenomena. The book covers self-accelerating airy beams, integrated photonics based on high index doped-silica glass, linear and nonlinear spatial beam dynamics in photonic lattices and waveguide arrays, polariton solitons and localized structures in semiconductor microcavities, terahertz waves, and other novel phenomena in different nanophotonic and optical systems.

On the integrability of the generalized Fisher-type nonlinear diffusion equations

International Nuclear Information System (INIS)

Wang Dengshan; Zhang Zhifei

2009-01-01

In this paper, the geometric integrability and Lax integrability of the generalized Fisher-type nonlinear diffusion equations with modified diffusion in (1+1) and (2+1) dimensions are studied by the pseudo-spherical surface geometry method and prolongation technique. It is shown that the (1+1)-dimensional Fisher-type nonlinear diffusion equation is geometrically integrable in the sense of describing a pseudo-spherical surface of constant curvature -1 only for m = 2, and the generalized Fisher-type nonlinear diffusion equations in (1+1) and (2+1) dimensions are Lax integrable only for m = 2. This paper extends the results in Bindu et al 2001 (J. Phys. A: Math. Gen. 34 L689) and further provides the integrability information of (1+1)- and (2+1)-dimensional Fisher-type nonlinear diffusion equations for m = 2

Electron acceleration during the decay of nonlinear Whistler waves in low-beta electron-ion plasma

International Nuclear Information System (INIS)

Umeda, Takayuki; Saito, Shinji; Nariyuki, Yasuhiro

2014-01-01

Relativistic electron acceleration through dissipation of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave in low-beta plasma is investigated by utilizing a one-dimensional fully relativistic electromagnetic particle-in-cell code. The nonlinear (large-amplitude) parent whistler wave decays through the parametric instability which enhances electrostatic ion acoustic waves and electromagnetic whistler waves. These waves satisfy the condition of three-wave coupling. Through the decay instability, the energy of electron bulk velocity supporting the parent wave is converted to the thermal energy perpendicular to the background magnetic field. Increase of the perpendicular temperature triggers the electron temperature anisotropy instability which generates broadband whistler waves and heats electrons in the parallel direction. The broadband whistler waves are inverse-cascaded during the relaxation of the electron temperature anisotropy. In lower-beta conditions, electrons with a pitch angle of about 90° are successively accelerated by inverse-cascaded whistler waves, and selected electrons are accelerated to over a Lorentz factor of 10. The result implies that the nonlinear dissipation of a finite-amplitude and short-wavelength whistler wave plays an important role in producing relativistic nonthermal electrons over a few MeV especially at lower beta plasmas.

Exactly and completely integrable nonlinear dynamical systems

International Nuclear Information System (INIS)

Leznov, A.N.; Savel'ev, M.V.

1987-01-01

The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

Integrable discretization s of derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2002-01-01

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)

Global Format for Conservative Time Integration in Nonlinear Dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2014-01-01

The widely used classic collocation-based time integration procedures like Newmark, Generalized-alpha etc. generally work well within a framework of linear problems, but typically may encounter problems, when used in connection with essentially nonlinear structures. These problems are overcome....... In the present paper a conservative time integration algorithm is developed in a format using only the internal forces and the associated tangent stiffness at the specific time integration points. Thus, the procedure is computationally very similar to a collocation method, consisting of a series of nonlinear...... equivalent static load steps, easily implemented in existing computer codes. The paper considers two aspects: representation of nonlinear internal forces in a form that implies energy conservation, and the option of an algorithmic damping with the purpose of extracting energy from undesirable high...

LOO: a low-order nonlinear transport scheme for acceleration of method of characteristics

International Nuclear Information System (INIS)

Li, Lulu; Smith, Kord; Forget, Benoit; Ferrer, Rodolfo

2015-01-01

This paper presents a new physics-based multi-grid nonlinear acceleration method: the low-order operator method, or LOO. LOO uses a coarse space-angle multi-group method of characteristics (MOC) neutron transport calculation to accelerate the fine space-angle MOC calculation. LOO is designed to capture more angular effects than diffusion-based acceleration methods through a transport-based low-order solver. LOO differs from existing transport-based acceleration schemes in that it emphasizes simplified coarse space-angle characteristics and preserves physics in quadrant phase-space. The details of the method, including the restriction step, the low-order iterative solver and the prolongation step are discussed in this work. LOO shows comparable convergence behavior to coarse mesh finite difference on several two-dimensional benchmark problems while not requiring any under-relaxation, making it a robust acceleration scheme. (author)

A new integrability theory for certain nonlinear physical problems

International Nuclear Information System (INIS)

Berger, M.S.

1993-01-01

A new mathematically sound integrability theory for certain nonlinear problems defined by ordinary or partial differential equations is defined. The new theory works in an arbitrary finite number of space dimensions. Moreover, if a system is integrable in the new sense described here, it has a remarkable stability property that distinguishes if from any previously known integrability ideas. The new theory proceeds by establishing a ''global normal form'' for the problem at hand. This normal form holds subject to canonical coordinate transformations, extending such classical ideas by using new nonlinear methods of infinite dimensional functional analysis. The global normal form in question is related to the mathematical theory of singularities of mappings of H. Whitney and R. Thom extended globally and form finite to infinite dimensions. Thus bifurcation phenomena are naturally included in the new integrability theory. Typical examples include the classically nonintegrable Riccati equation, certain non-Euclidean mean field theories, certain parabolic reaction diffusion equations and the hyperbolic nonlinear telegrapher's equation. (Author)

NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

Science.gov (United States)

Caplan, R. M.

2013-04-01

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files. Catalogue identifier: AEOJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOJ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 124453 No. of bytes in distributed program, including test data, etc.: 4728604 Distribution format: tar.gz Programming language: C, CUDA, MATLAB. Computer: PC, MAC. Operating system: Windows, MacOS, Linux. Has the code been vectorized or parallelized?: Yes. Number of processors used: Single CPU, number of GPU processors dependent on chosen GPU card (max is currently 3072 cores on GeForce GTX 690). Supplementary material: Setup guide, Installation guide. RAM: Highly dependent on dimensionality and grid size. For typical medium-large problem size in three dimensions, 4GB is sufficient. Keywords: Nonlinear Schröodinger Equation, GPU, high-order finite difference, Bose-Einstien condensates. Classification: 4.3, 7.7. Nature of problem: Integrate solutions of the time-dependent one-, two-, and three-dimensional cubic nonlinear Schrödinger equation. Solution method: The integrators utilize a fully-explicit fourth-order Runge-Kutta scheme in time

Integral criterion for selecting nonlinear crystals for frequency conversion

International Nuclear Information System (INIS)

Grechin, Sergei G

2009-01-01

An integral criterion, which takes into account all parameters determining the conversion efficiency, is offered for selecting nonlinear crystals for frequency conversion. The angular phase-matching width is shown to be related to the beam walk-off angle. (nonlinear optical phenomena)

PREFACE: Nonlinearity and Geometry: connections with integrability Nonlinearity and Geometry: connections with integrability

Science.gov (United States)

Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.

2009-10-01

Geometric ideas are present in many areas of modern theoretical physics and they are usually associated with the presence of nonlinear phenomena. Integrable nonlinear systems play a prime role both in geometry itself and in nonlinear physics. One can mention general relativity, exact solutions of the Einstein equations, string theory, Yang-Mills theory, instantons, solitons in nonlinear optics and hydrodynamics, vortex dynamics, solvable models of statistical physics, deformation quantization, and many others. Soliton theory now forms a beautiful part of mathematics with very strong physical motivations and numerous applications. Interactions between mathematics and physics associated with integrability issues are very fruitful and stimulating. For instance, spectral theories of linear quantum mechanics turned out to be crucial for studying nonlinear integrable systems. The modern theory of integrable nonlinear partial differential and difference equations, or the `theory of solitons', is deeply rooted in the achievements of outstanding geometers of the end of the 19th and the beginning of the 20th century, such as Luigi Bianchi (1856-1928) and Jean Gaston Darboux (1842-1917). Transformations of surfaces and explicit constructions developed by `old' geometers were often rediscovered or reinterpreted in a modern framework. The great progress of recent years in so-called discrete geometry is certainly due to strong integrable motivations. A very remarkable feature of the results of the classical integrable geometry is the quite natural (although nontrivial) possibility of their discretization. This special issue is dedicated to Jean Gaston Darboux and his pioneering role in the development of the geometric ideas of modern soliton theory. The most famous aspects of his work are probably Darboux transformations and triply orthogonal systems of surfaces, whose role in modern mathematical physics cannot be overestimated. Indeed, Darboux transformations play a central

Nonlinear Fredholm Integral Equation of the Second Kind with Quadrature Methods

Directory of Open Access Journals (Sweden)

M. Jafari Emamzadeh

2010-06-01

Full Text Available In this paper, a numerical method for solving the nonlinear Fredholm integral equation is presented. We intend to approximate the solution of this equation by quadrature methods and by doing so, we solve the nonlinear Fredholm integral equation more accurately. Several examples are given at the end of this paper

Some nonlinear processes relevant to the beat wave accelerator

International Nuclear Information System (INIS)

Bingham, R.; Mori, W.B.

1985-03-01

The beat wave accelerator depends on the generation of a large amplitude plasma wave with a phase velocity close to the velocity of light c. The plasma wave (ωsub(p), ksub(p)) is generated by beating colinear laser beams (ω 1 , k 1 ) and (ω 2 ,k 2 ) with ωsub(p) = ω 1 -ω 2 , ksub(p) = k 1 -k 2 . Since the process involves both large amplitude transverse and longitudinal waves, various nonlinear instabilities associated with either wave may occur. The object of the article is to discuss some of the processes that may compete with the beat wave generation listing their threshold and growth rate. (author)

Adaptive Kronrod-Patterson integration of non-linear finite-element matrices

DEFF Research Database (Denmark)

Janssen, Hans

2010-01-01

inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration...

Nonlinear resonance in Duffing oscillator with fixed and integrative ...

Indian Academy of Sciences (India)

We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter and the strength of the ...

Nonlinear resonance in Duffing oscillator with fixed and integrative ...

Indian Academy of Sciences (India)

2012-03-02

Mar 2, 2012 ... Abstract. We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter α and the ...

Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

International Nuclear Information System (INIS)

Maccari, A.

1997-01-01

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio endash temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a open-quotes universalclose quotes character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. copyright 1997 American Institute of Physics

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.

Nonlinearity and fractional integration in the US dollar/euro exchange rate

Directory of Open Access Journals (Sweden)

Kiran Burcu

2012-01-01

Full Text Available This paper examines the nonlinear behavior and the fractional integration property of the US dollar/euro exchange rate over the period from January 1999 to August 2010 by extending the procedure of Peter M. Robinson (1994 to the case of nonlinearity. First, using the approach developed by Mehmet Caner and Bruce E. Hansen (2001, we investigate the possible presence of nonlinearity in the series through the estimation of a two-regime threshold autoregressive model. After finding nonlinearity, we also allow for disturbances to be fractionally integrated based on the different versions of Robinson (1994 tests. The findings show that the US dollar/euro exchange rate follows a stationary process with a weak evidence for long memory.

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-09-02

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

Partial fourier and parallel MR image reconstruction with integrated gradient nonlinearity correction.

Science.gov (United States)

Tao, Shengzhen; Trzasko, Joshua D; Shu, Yunhong; Weavers, Paul T; Huston, John; Gray, Erin M; Bernstein, Matt A

2016-06-01

To describe how integrated gradient nonlinearity (GNL) correction can be used within noniterative partial Fourier (homodyne) and parallel (SENSE and GRAPPA) MR image reconstruction strategies, and demonstrate that performing GNL correction during, rather than after, these routines mitigates the image blurring and resolution loss caused by postreconstruction image domain based GNL correction. Starting from partial Fourier and parallel magnetic resonance imaging signal models that explicitly account for GNL, noniterative image reconstruction strategies for each accelerated acquisition technique are derived under the same core mathematical assumptions as their standard counterparts. A series of phantom and in vivo experiments on retrospectively undersampled data were performed to investigate the spatial resolution benefit of integrated GNL correction over conventional postreconstruction correction. Phantom and in vivo results demonstrate that the integrated GNL correction reduces the image blurring introduced by the conventional GNL correction, while still correcting GNL-induced coarse-scale geometrical distortion. Images generated from undersampled data using the proposed integrated GNL strategies offer superior depiction of fine image detail, for example, phantom resolution inserts and anatomical tissue boundaries. Noniterative partial Fourier and parallel imaging reconstruction methods with integrated GNL correction reduce the resolution loss that occurs during conventional postreconstruction GNL correction while preserving the computational efficiency of standard reconstruction techniques. Magn Reson Med 75:2534-2544, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Multi-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients

International Nuclear Information System (INIS)

Liao Cui-Cui; Cui Jin-Chao; Liang Jiu-Zhen; Ding Xiao-Hua

2016-01-01

In this paper, we propose a variational integrator for nonlinear Schrödinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrödinger equations with variable coefficients, cubic nonlinear Schrödinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space. (paper)

Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

Energy Technology Data Exchange (ETDEWEB)

Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)

1996-12-31

The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

Application of nonlinear Krylov acceleration to radiative transfer problems

International Nuclear Information System (INIS)

Till, A. T.; Adams, M. L.; Morel, J. E.

2013-01-01

The iterative solution technique used for radiative transfer is normally nested, with outer thermal iterations and inner transport iterations. We implement a nonlinear Krylov acceleration (NKA) method in the PDT code for radiative transfer problems that breaks nesting, resulting in more thermal iterations but significantly fewer total inner transport iterations. Using the metric of total inner transport iterations, we investigate a crooked-pipe-like problem and a pseudo-shock-tube problem. Using only sweep preconditioning, we compare NKA against a typical inner / outer method employing GMRES / Newton and find NKA to be comparable or superior. Finally, we demonstrate the efficacy of applying diffusion-based preconditioning to grey problems in conjunction with NKA. (authors)

Evaluation of polymer based third order nonlinear integrated optics devices

NARCIS (Netherlands)

Driessen, A.; Hoekstra, Hugo; Blom, F.C.; Horst, F.; Horst, F.; Krijnen, Gijsbertus J.M.; van Schoot, J.B.P.; van Schoot, J.B.P.; Lambeck, Paul; Popma, T.J.A.; Diemeer, Mart

Nonlinear polymers are promising materials for high speed active integrated optics devices. In this paper we evaluate the perspectives polymer based nonlinear optical devices can offer. Special attention is directed to the materials aspects. In our experimental work we applied mainly Akzo Nobel DANS

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

Science.gov (United States)

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

CALL FOR PAPERS: Special issue on Current Trends in Integrability and Nonlinear Phenomena Special issue on Current Trends in Integrability and Nonlinear Phenomena

Science.gov (United States)

Gómez-Ullate, D.; Lombardo, S.; Mañas, M.; Mazzocco, M.; Nijhoff, F.; Sommacal, M.

2009-12-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to integrability and nonlinear phenomena. The motivation behind this special issue is to summarize in a single comprehensive publication, the main aspects (past and present), latest developments, different viewpoints and the directions being followed in this multidisciplinary field. We hope that such a special issue could become a particularly valuable reference for the broad scientific community working in integrability and nonlinear phenomena. Editorial policy The Editorial Board has invited D Gómez-Ullate, S Lombardo, M Mañas, M Mazzocco, F Nijhoff and M Sommacal to serve as Guest Editors for the special issue. Their criteria for the acceptance of contributions are as follows. The subject of the paper should relate to the following list of subjects: Integrable systems (including quantum and discrete) and applications Dynamical systems: Hamiltonian systems and dynamics in the complex domain Nonlinear waves, soliton equations and applications Nonlinear ODEs including Painlevé equations and isomonodromic deformations Symmetries and perturbative methods in the classification of integrable PDEs Infinite dimensional Lie algebras and integrable systems Orthogonal polynomials, random matrix theory All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The DEADLINE for contributed papers will be 28 February 2010. This deadline will allow the special issue to appear in October 2010. There is a nominal page limit of 15 printed pages per contribution (invited review papers can be longer). For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and Theoretical

Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

Science.gov (United States)

Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

2009-06-01

In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

Nonlinear Dynamics: Integrability, Chaos and Patterns

International Nuclear Information System (INIS)

Grammaticos, B

2004-01-01

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-locking and b) devil

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

A Nonlinear Observer for Integration of GPS and Inertial Navigation Systems

Directory of Open Access Journals (Sweden)

Bjørnar Vik

2000-10-01

Full Text Available GPS and INS have complementary properties and they are therefore well suited for integration. The integrated solution offers better long term accuracy than a stand-alone INS, and better integrity, availability and continuity than a stand-alone GPS receiver, making it suitable for demanding applications. The integrated filter is nonlinear both in state and measurements, and the extended Kalman-filter has been used with good results, but it has not been proven globally stable, and it is also computationally intensive, especially within a direct integration architecture. In this work a nonlinear observer suitable for direct integration is presented. Global exponent ial stability of the origin of the combined attitude and velocity error systems is proven along with robust stability in the presence of noise and unmodelled dynamics.

Nonlinear free vibration control of beams using acceleration delayed-feedback control

International Nuclear Information System (INIS)

Alhazza, Khaled A; Alajmi, Mohammed; Masoud, Ziyad N

2008-01-01

A single-mode delayed-feedback control strategy is developed to reduce the free vibrations of a flexible beam using a piezoelectric actuator. A nonlinear variational model of the beam based on the von Kàrmàn nonlinear type deformations is considered. Using Galerkin's method, the resulting governing partial differential equations of motion are reduced to a system of nonlinear ordinary differential equations. A linear model using the first mode is derived and is used to characterize the damping produced by the controller as a function of the controller's gain and delay. Three-dimensional figures showing the damping magnitude as a function of the controller gain and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controller gain and delay using both methods are obtained, simulated and compared. To validate the single-mode approximation, numerical simulations are performed using a three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the first-mode vibration

Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonlinear Sliding Surface

OpenAIRE

Yong-Kun Lu

2015-01-01

An adaptive fuzzy integral sliding-mode controller using nonlinear sliding surface is designed for the speed regulator of a field-oriented induction motor drive in this paper. Combining the conventional integral sliding surface with fractional-order integral, a nonlinear sliding surface is proposed for the integral sliding-mode speed control, which can overcome the windup problem and the convergence speed problem. An adaptive fuzzy control term is utilized to approximate the uncertainty. The ...

Existence Results for Some Nonlinear Functional-Integral Equations in Banach Algebra with Applications

Directory of Open Access Journals (Sweden)

Lakshmi Narayan Mishra

2016-04-01

Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.

Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models

NARCIS (Netherlands)

Koopman, S.J.; Lucas, A.; Scharth, M.

2015-01-01

We propose a general likelihood evaluation method for nonlinear non-Gaussian state-space models using the simulation-based method of efficient importance sampling. We minimize the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer

Phase velocity of nonlinear plasma waves in the laser beat-wave accelerator

International Nuclear Information System (INIS)

Spence, W.L.

1985-01-01

The suggested plasma-laser accelerator is an attempt to achieve a very high energy gradient by resonantly exciting a longitudinal wave traveling at close to the speed of light in cold plasma by means of the beat-wave generated by the transverse fields in two laser beams. Previous calculations to all orders in v/sub z/ have been done essentially from the laboratory frame point of view and have treated the plasma wave as having sharply defined phase velocity equal to the speed of light. However a high energy particle beam undergoing acceleration sees the plasma wave from a nearly light-like frame of reference and hence is very sensitive to small deviations in its phase velocity. Here the authors introduce a calculational scheme that includes all orders in v/sub z/ and in the plasma density, and additionally takes into account the influence of plasma nonlinearities on the wave's phase velocity. The main assumption is that the laser frequencies are very large compared to the plasma frequency - under which they are able to in essence formally sum up all orders of forward Raman scattering. They find that the nonlinear plasma wave does not have simply a single phase velocity - it is really a superposition of many - but that the beat-wave which drives it is usefully described by a non-local effective phase velocity function

The Klynac: An integrated klystron and linear accelerator

International Nuclear Information System (INIS)

Potter, James M.; Schwellenbach, David; Meidinger, Alfred

2013-01-01

The Klynac concept integrates an electron gun, a radio frequency (RF) power source, and a coupled-cavity linear accelerator into a single resonant system. The klystron is essentially a conventional klystron structure with an input cavity, some number of intermediate cavities and an output cavity. The accelerator structure is, likewise, a conventional on-axis coupled structure. The uniqueness is the means of coupling the klystron output cavity to the accelerator. The coupler is a resonant coupler rather than an ordinary transmission line. The geometry of such a system need not be coaxial. However, if the klystron and accelerator are coaxial we can eliminate the need for a separate cathode for the accelerator by injecting some of the klystron beam into the accelerator. Such a device can be made cylindrical which is ideal for some applications.

Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation

International Nuclear Information System (INIS)

Zhang, Yu-Juan; Zhao, Dun; Luo, Hong-Gang

2014-01-01

We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton. - Highlights: • We consider a unified model for soliton management by an integrable integro-differential Schrödinger equation. • Using Lax pair, the N-fold Darboux transformation for the equation is presented. • The multi-soliton management is considered. • The synchronized dispersive and nonlinear management is suggested

Nonlinear beam dynamics of accelerators and storage rings. Progress report, June 1985-April 1986

International Nuclear Information System (INIS)

Helleman, R.H.G.

1986-01-01

Research has concentrated on the stability problems and resonances involved in the two-dimensional beam-beam effect. Of course, the results are applicable also to coupled nonlinear two-dimensional (x,y) accelerator lattices. From a nonlinear dynamics point of view this means that we investigated how to extend existing methods that worked satisfactorily for the one-dimensional beam-beam effect to the higher dimensional world of two-dimensional nonlinear lattices. This requires study of four coupled nonlinear lattice equations (for x, y, p/sub x/,p/sub y/), i.e., study of four-dimensional conservative nonlinear maps. Until our investigation this year, such maps had not yet been studied in nonlinear dynamics. One of the main results is the conclusion that the very successful ''residue'' method to determine stability (of whole regions of orbits) for the one-dimensional beam-beam effect cannot, in its present form, be used for the two- or three-dimensional case. The second main result is that we have been successful in demonstrating and unraveling the complete Period Doubling structure of the resonances in these four-dimensional maps (two-dimensional beam-beam effect), including the most minute resonances. This is essential for an understanding of such maps. In addition, it is the ''self-similarity'' of these resonances which inspires, and guides, most of our efforts in redesigning the residue criterion mentioned above

ACCELERATORS: Nonlinear dynamics in Sardinia

International Nuclear Information System (INIS)

Anon.

1985-01-01

In the last few years, two schools devoted to accelerator physics have been set up, one on either side of the Atlantic. The US School on High Energy Particle Accelerators has organized Summer Schools on the physics of particle accelerators, hosted by the major American Laboratories, each year since 1981

ACCELERATORS: Nonlinear dynamics in Sardinia

Energy Technology Data Exchange (ETDEWEB)

Anon.

1985-05-15

In the last few years, two schools devoted to accelerator physics have been set up, one on either side of the Atlantic. The US School on High Energy Particle Accelerators has organized Summer Schools on the physics of particle accelerators, hosted by the major American Laboratories, each year since 1981.

Partially integrable nonlinear equations with one higher symmetry

International Nuclear Information System (INIS)

Mikhailov, A V; Novikov, V S; Wang, J P

2005-01-01

In this letter, we present a family of second order in time nonlinear partial differential equations, which have only one higher symmetry. These equations are not integrable, but have a solution depending on one arbitrary function. (letter to the editor)

Accelerated DNA Methylation Age: Associations with PTSD and Neural Integrity

Science.gov (United States)

Wolf, Erika J.; Logue, Mark W.; Hayes, Jasmeet P.; Sadeh, Naomi; Schichman, Steven A.; Stone, Annjanette; Salat, David H.; Milberg, William; McGlinchey, Regina; Miller, Mark W.

2015-01-01

Background Accumulating evidence suggests that post traumatic stress disorder (PTSD) may accelerate cellular aging and lead to premature morbidity and neurocognitive decline. Methods This study evaluated associations between PTSD and DNA methylation (DNAm) age using recently developed algorithms of cellular age by Horvath (2013) and Hannum et al. (2013). These estimates reflect accelerated aging when they exceed chronological age. We also examined if accelerated cellular age manifested in degraded neural integrity, indexed via diffusion tensor imaging. Results Among 281 male and female veterans of the conflicts in Iraq and Afghanistan, DNAm age was strongly related to chronological age (rs ~.88). Lifetime PTSD severity was associated with Hannum DNAm age estimates residualized for chronological age (β = .13, p= .032). Advanced DNAm age was associated with reduced integrity in the genu of the corpus callosum (β = −.17, p= .009) and indirectly linked to poorer working memory performance via this region (indirect β = − .05, p= .029). Horvath DNAm age estimates were not associated with PTSD or neural integrity. Conclusions Results provide novel support for PTSD-related accelerated aging in DNAm and extend the evidence base of known DNAm age correlates to the domains of neural integrity and cognition. PMID:26447678

Nonlinear Coupling Characteristics Analysis of Integrated System of Electromagnetic Brake and Frictional Brake of Car

Directory of Open Access Journals (Sweden)

Ren He

2015-01-01

Full Text Available Since theoretical guidance is lacking in the design and control of the integrated system of electromagnetic brake and frictional brake, this paper aims to solve this problem and explores the nonlinear coupling characteristics and dynamic characteristics of the integrated system of electromagnetic brake and frictional brake. This paper uses the power bond graph method to establish nonlinear coupling mathematical model of the integrated system of electromagnetic brake and frictional brake and conducts the contrastive analysis on the dynamic characteristics based on this mathematical model. Meanwhile, the accuracy of the nonlinear coupling mathematical model proposed above is verified on the hardware in the loop simulation platform, and nonlinear coupling characteristics of the integrated system are also analyzed through experiments.

Effect of Integral Non-Linearity on Energy Calibration of ...

African Journals Online (AJOL)

The integral non-linearity (INL) of four spectroscopy systems, two integrated (A1 and A2) and two classical (B1 and B2) systems was determined using pulses from a random pulse generator. The effect of INL on the system's energy calibration was also determined. The effect is minimal in the classical system at high ...

Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals

CERN Document Server

Ivancevic, Vladimir G

2008-01-01

Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...

Numerical Solution of Nonlinear Volterra Integral Equations System Using Simpson’s 3/8 Rule

Directory of Open Access Journals (Sweden)

Adem Kılıçman

2012-01-01

Full Text Available The Simpson’s 3/8 rule is used to solve the nonlinear Volterra integral equations system. Using this rule the system is converted to a nonlinear block system and then by solving this nonlinear system we find approximate solution of nonlinear Volterra integral equations system. One of the advantages of the proposed method is its simplicity in application. Further, we investigate the convergence of the proposed method and it is shown that its convergence is of order O(h4. Numerical examples are given to show abilities of the proposed method for solving linear as well as nonlinear systems. Our results show that the proposed method is simple and effective.

Nonlinear spectrum of the ablative Rayleigh-Taylor instability in laser-accelerated planar plasmas

International Nuclear Information System (INIS)

Keskinen, M. J.; Schmitt, A.

2007-01-01

A model for the nonlinear spectrum of the ablative Rayleigh-Taylor instability in laser-accelerated planar plasmas has been developed for a wide range of Froude numbers and scale sizes. It is found that the spectrum can be characterized by an inverse power law with spectral index of approximately 2 in the limit of small-wavenumber spectrum cutoffs and small-scale density gradient scale lengths. Comparison of the model spectrum with recent experimental observations is made with good agreement

Global format for energy-momentum based time integration in nonlinear dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2014-01-01

A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...

GPU-based acceleration of computations in nonlinear finite element deformation analysis.

Science.gov (United States)

Mafi, Ramin; Sirouspour, Shahin

2014-03-01

The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation. Copyright © 2013 John Wiley & Sons, Ltd.

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

Science.gov (United States)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm

KAUST Repository

Desmal, Abdulla

2017-04-03

An efficient electromagnetic inversion scheme for imaging sparse 3-D domains is proposed. The scheme achieves its efficiency and accuracy by integrating two concepts. First, the nonlinear optimization problem is constrained using L₀ or L₁-norm of the solution as the penalty term to alleviate the ill-posedness of the inverse problem. The resulting Tikhonov minimization problem is solved using nonlinear Landweber iterations (NLW). Second, the efficiency of the NLW is significantly increased using a steepest descent algorithm. The algorithm uses a projection operator to enforce the sparsity constraint by thresholding the solution at every iteration. Thresholding level and iteration step are selected carefully to increase the efficiency without sacrificing the convergence of the algorithm. Numerical results demonstrate the efficiency and accuracy of the proposed imaging scheme in reconstructing sparse 3-D dielectric profiles.

Commutator identities on associative algebras and integrability of nonlinear pde's

OpenAIRE

Pogrebkov, A. K.

2007-01-01

It is shown that commutator identities on associative algebras generate solutions of linearized integrable equations. Next, a special kind of the dressing procedure is suggested that in a special class of integral operators enables to associate to such commutator identity both nonlinear equation and its Lax pair. Thus problem of construction of new integrable pde's reduces to construction of commutator identities on associative algebras.

Integrated on-line accelerator modeling at CEBAF

International Nuclear Information System (INIS)

Bowling, B.A.; Shoaee, H.; Van Zeijts, J.; Witherspoon, S.; Watson, W.

1995-01-01

An on-line accelerator modeling facility is currently under development at CEBAF. The model server, which is integrated with the EPICS control system, provides coupled and 2nd-order matrices for the entire accelerator, and forms the foundation for automated model- based control and diagnostic applications. Four types of machine models are provided, including design, golden or certified, live, and scratch or simulated model. Provisions are also made for the use of multiple lattice modeling programs such as DIMAD, PARMELA, and TLIE. Design and implementation details are discussed. 2 refs., 4 figs

Nonlinear Filtering with IMM Algorithm for Ultra-Tight GPS/INS Integration

Directory of Open Access Journals (Sweden)

Dah-Jing Jwo

2013-05-01

Full Text Available Abstract This paper conducts a performance evaluation for the ultra-tight integration of a Global positioning system (GPS and an inertial navigation system (INS, using nonlinear filtering approaches with an interacting multiple model (IMM algorithm. An ultra-tight GPS/INS architecture involves the integration of in-phase and quadrature components from the correlator of a GPS receiver with INS data. An unscented Kalman filter (UKF, which employs a set of sigma points by deterministic sampling, avoids the error caused by linearization as in an extended Kalman filter (EKF. Based on the filter structural adaptation for describing various dynamic behaviours, the IMM nonlinear filtering provides an alternative for designing the adaptive filter in the ultra-tight GPS/INS integration. The use of IMM enables tuning of an appropriate value for the process of noise covariance so as to maintain good estimation accuracy and tracking capability. Two examples are provided to illustrate the effectiveness of the design and demonstrate the effective improvement in navigation estimation accuracy. A performance comparison among various filtering methods for ultra-tight integration of GPS and INS is also presented. The IMM based nonlinear filtering approach demonstrates the effectiveness of the algorithm for improved positioning performance.

Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model

International Nuclear Information System (INIS)

Fujii, Akira; Kluemper, Andreas

1999-01-01

We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation

Nonlinear-Based MEMS Sensors and Active Switches for Gas and Acceleration Applications

KAUST Repository

Younis, Mohammad I.

2016-11-25

In this talk, we demonstrate the realization of smart sensors and actuators through the exploitation of principles of nonlinear dynamics at the micro scale. Specifically, we demonstrate combining sensing and actuation into a single device through what is called smart switches triggered by the detection of a desirable physical quantity. The concept aims to reduce the complexity of systems that rely on controllers and complex algorithms to realize on-demand trigger actions. In the first part of the talk, we discuss the category of switches triggered by the detection of gas. Toward this, electrostatically microbeams resonators are fabricated, then coated with highly absorbent polymers (MOFs), and afterward are exposed to gases. Such devices can be useful for instant alarming of toxic gases. In the second part, we demonstrate switches triggered by shock and acceleration. The concept is demonstrated on a millimeter-scale capacitive sensor. The sensor is tested using acceleration generated from shakers. Such devices can be used for the deployment of airbags in automobiles.

Increase in operation safety of high-current pulsed accelerators by means of nonlinear resistances

International Nuclear Information System (INIS)

Demidov, B.A.; Ivkin, M.V.; Petrov, V.A.; Fanchenko, S.D.

1975-01-01

A circuit for connecting a shaping line through a nonlinear resistor in a high-current pulsed accelerator is proposed and investigated experimentally. For experimental purposes standard resistors are used as nonlinear resistors, they are made in the form of cylinders 100 mm in dia and 60 mm long. The results obtained show that if two resistors are connected in series, the reduction in an initial potential is less than 5% at the logarithmic damping coefficient equal to 1.3. It is also shown that such a method allows elimination of the reverse pumpover of energy to the storage device for untimely actuation of a spark gap that results in the prolongation of the time of potential applying thereby it permits a substantial increase in the reliability of a high-voltage insulation [ru

Design Considerations for Proposed Fermilab Integrable RCS

Energy Technology Data Exchange (ETDEWEB)

Eldred, Jeffrey [Fermilab; Valishev, Alexander

2017-03-02

Integrable optics is an innovation in particle accelerator design that provides strong nonlinear focusing while avoiding parametric resonances. One promising application of integrable optics is to overcome the traditional limits on accelerator intensity imposed by betatron tune-spread and collective instabilities. The efficacy of high-intensity integrable accelerators will be undergo comprehensive testing over the next several years at the Fermilab Integrable Optics Test Accelerator (IOTA) and the University of Maryland Electron Ring (UMER). We propose an integrable Rapid-Cycling Synchrotron (iRCS) as a replacement for the Fermilab Booster to achieve multi-MW beam power for the Fermilab high-energy neutrino program. We provide a overview of the machine parameters and discuss an approach to lattice optimization. Integrable optics requires arcs with integer-pi phase advance followed by drifts with matched beta functions. We provide an example integrable lattice with features of a modern RCS - long dispersion-free drifts, low momentum compaction, superperiodicity, chromaticity correction, separate-function magnets, and bounded beta functions.

Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

International Nuclear Information System (INIS)

Anistratov, Dmitriy Y.

2011-01-01

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

Integrable peakon equations with cubic nonlinearity

International Nuclear Information System (INIS)

Hone, Andrew N W; Wang, J P

2008-01-01

We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are cubic, rather than quadratic. We give a matrix Lax pair for V Novikov's equation, and show how it is related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved quantities are found, as well as a bi-Hamiltonian structure. The latter is used to obtain the Hamiltonian form of the finite-dimensional system for the interaction of N peakons, and the two-body dynamics (N = 2) is explicitly integrated. Finally, all of this is compared with some analogous results for another cubic peakon equation derived by Zhijun Qiao. (fast track communication)

Radio Evolution of Supernova Remnants Including Nonlinear Particle Acceleration: Insights from Hydrodynamic Simulations

Science.gov (United States)

Pavlović, Marko Z.; Urošević, Dejan; Arbutina, Bojan; Orlando, Salvatore; Maxted, Nigel; Filipović, Miroslav D.

2018-01-01

We present a model for the radio evolution of supernova remnants (SNRs) obtained by using three-dimensional hydrodynamic simulations coupled with nonlinear kinetic theory of cosmic-ray (CR) acceleration in SNRs. We model the radio evolution of SNRs on a global level by performing simulations for a wide range of the relevant physical parameters, such as the ambient density, supernova (SN) explosion energy, acceleration efficiency, and magnetic field amplification (MFA) efficiency. We attribute the observed spread of radio surface brightnesses for corresponding SNR diameters to the spread of these parameters. In addition to our simulations of Type Ia SNRs, we also considered SNR radio evolution in denser, nonuniform circumstellar environments modified by the progenitor star wind. These simulations start with the mass of the ejecta substantially higher than in the case of a Type Ia SN and presumably lower shock speed. The magnetic field is understandably seen as very important for the radio evolution of SNRs. In terms of MFA, we include both resonant and nonresonant modes in our large-scale simulations by implementing models obtained from first-principles, particle-in-cell simulations and nonlinear magnetohydrodynamical simulations. We test the quality and reliability of our models on a sample consisting of Galactic and extragalactic SNRs. Our simulations give Σ ‑ D slopes between ‑4 and ‑6 for the full Sedov regime. Recent empirical slopes obtained for the Galactic samples are around ‑5, while those for the extragalactic samples are around ‑4.

The use of induction linacs with nonlinear magnetic drive as high average power accelerators

International Nuclear Information System (INIS)

Birx, D.L.; Cook, E.G.; Hawkins, S.A.; Newton, M.A.; Poor, S.E.; Reginato, L.L.; Schmidt, J.A.; Smith, M.W.

1985-01-01

The marriage of induction linac technology with Nonlinear Magnetic Modulators has produced some unique capabilities. It appears possible to produce electron beams with average currents measured in amperes, at gradients exceeding 1 MeV/m, and with power efficiences approaching 50%. A 2 MeV, 5 kA electron accelerator is under construction at Lawrence Livermore National Laboratory (LLNL) to allow us to demonstrate some of these concepts. Progress on this project is reported here. (orig.)

Integrability and Linear Stability of Nonlinear Waves

Science.gov (United States)

Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo

2018-03-01

It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.

Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics.

Science.gov (United States)

Kieu, K; Schneebeli, L; Norwood, R A; Peyghambarian, N

2012-03-26

We have developed a novel integrated platform for liquid photonics based on liquid core optical fiber (LCOF). The platform is created by fusion splicing liquid core optical fiber to standard single-mode optical fiber making it fully integrated and practical - a major challenge that has greatly hindered progress in liquid-photonic applications. As an example, we report here the realization of ultralow threshold Raman generation using an integrated CS₂ filled LCOF pumped with sub-nanosecond pulses at 532 nm and 1064 nm. The measured energy threshold for the Stokes generation is 1nJ, about three orders of magnitude lower than previously reported values in the literature for hydrogen gas, a popular Raman medium. The integrated LCOF platform opens up new possibilities for ultralow power nonlinear optics such as efficient white light generation for displays, mid-IR generation, slow light generation, parametric amplification, all-optical switching and wavelength conversion using liquids that have orders of magnitude larger optical nonlinearities compared with silica glass.

A Fast GPU-accelerated Mixed-precision Strategy for Fully NonlinearWater Wave Computations

DEFF Research Database (Denmark)

Glimberg, Stefan Lemvig; Engsig-Karup, Allan Peter; Madsen, Morten G.

2011-01-01

We present performance results of a mixed-precision strategy developed to improve a recently developed massively parallel GPU-accelerated tool for fast and scalable simulation of unsteady fully nonlinear free surface water waves over uneven depths (Engsig-Karup et.al. 2011). The underlying wave......-preconditioned defect correction method. The improved strategy improves the performance by exploiting architectural features of modern GPUs for mixed precision computations and is tested in a recently developed generic library for fast prototyping of PDE solvers. The new wave tool is applicable to solve and analyze...

Coupling-governed metamorphoses of the integrable nonlinear Schrödinger system on a triangular-lattice ribbon

Energy Technology Data Exchange (ETDEWEB)

Vakhnenko, Oleksiy O., E-mail: vakhnenko@bitp.kiev.ua

2016-05-27

Highlights: • The integrable nonlinear Schrödinger system on a triangular-lattice ribbon is inclined to metamorphoses. • The system under study is capable to incorporate the effect of external linear potential. • The system criticality against the background parameter reduces the number of independent field variables. • At critical point the system Poisson structure becomes degenerate. • The effect of criticality is elucidated by the system one-soliton solution. - Abstract: The variativity of governing coupling parameters in the integrable nonlinear Schrödinger system on a triangular-lattice ribbon is shown to ensure the important qualitative rearrangements in the system dynamics. There are at least the two types of system crucial modifications stipulated by the two types of governing parameters. Thus the longitudinal coupling parameters regulated mainly by the background values of concomitant field variables are responsible for the bifurcation of primary integrable nonlinear system into the integrable nonlinear system of Ablowitz–Ladik type. As a consequence in a critical point the number of independent field variables is reduced by a half and the system Poisson structure turns out to be degenerate. On the other hand the transverse coupling parameters regulated basically by the choice of their a priori arbitrary dependencies on time are capable to incorporate the effect of external linear potential. As a consequence the primary integrable nonlinear system with appropriately adjusted parametrical driving becomes isomorphic to the system modeling the Bloch oscillations of charged nonlinear carriers in an electrically biased ribbon of triangular lattice. The multi-component structure of basic integrable system alongside with the attractive character of system nonlinearities has predetermined the logic of whole consideration.

An ultra-efficient nonlinear planar integrated platform for optical signal processing and generation

DEFF Research Database (Denmark)

Pu, Minhao; Ottaviano, Luisa; Semenova, Elizaveta

2017-01-01

This paper will discuss the recently developed integrated platform: AlGaAs-oninsulator and its broad range of nonlinear applications. Recent demonstrations of broadband optical signal processing and efficient frequency comb generations in this platform will be reviewed.......This paper will discuss the recently developed integrated platform: AlGaAs-oninsulator and its broad range of nonlinear applications. Recent demonstrations of broadband optical signal processing and efficient frequency comb generations in this platform will be reviewed....

Definition of path integrals and rules for non-linear transformations

International Nuclear Information System (INIS)

Kerler, W.

1978-01-01

Functional integrals are defined as the limit of multidimensional integrals based on fundamental generating distributions. The 'lattice choice' is put into a suitable functional form. The independence of the particular choice and the necessity of this fact are shown. Various forms of the path integrals are derived and discussed. The relation to the traditional ordering problem is pointed out. The mechanism of non-linear transformations of variables is investigated and rules are given. In the case of fields it turns out that the path integrals can also be considered for space translations. (Auth.)

A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

KAUST Repository

Bagci, Hakan

2015-01-07

Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability

A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

KAUST Repository

Bagci, Hakan

2015-01-01

Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability

Integrable systems with quadratic nonlinearity in Fourier space

International Nuclear Information System (INIS)

Marikhin, V.G.

2003-01-01

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

Nonlinear moments method for the isotropic Boltzmann equation and the invariance of collision integral

International Nuclear Information System (INIS)

Ehnder, A.Ya.; Ehnder, I.A.

1999-01-01

A new approach to develop nonlinear moment method to solve the Boltzmann equation is presented. This approach is based on the invariance of collision integral as to the selection of the base functions. The Sonin polynomials with the Maxwell weighting function are selected to serve as the base functions. It is shown that for the arbitrary cross sections of the interaction the matrix elements corresponding to the moments from the nonlinear integral of collisions are bound by simple recurrent bonds enabling to express all nonlinear matrix elements in terms of the linear ones. As a result, high-efficiency numerical pattern to calculate nonlinear matrix elements is obtained. The presented approach offers possibilities both to calculate relaxation processes within high speed range and to some more complex kinetic problems [ru

BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns

Science.gov (United States)

Grammaticos, B.

2004-02-01

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-locking and b) devil

Design of time-pulse coded optoelectronic neuronal elements for nonlinear transformation and integration

Science.gov (United States)

Krasilenko, Vladimir G.; Nikolsky, Alexander I.; Lazarev, Alexander A.; Lazareva, Maria V.

2008-03-01

In the paper the actuality of neurophysiologically motivated neuron arrays with flexibly programmable functions and operations with possibility to select required accuracy and type of nonlinear transformation and learning are shown. We consider neurons design and simulation results of multichannel spatio-time algebraic accumulation - integration of optical signals. Advantages for nonlinear transformation and summation - integration are shown. The offered circuits are simple and can have intellectual properties such as learning and adaptation. The integrator-neuron is based on CMOS current mirrors and comparators. The performance: consumable power - 100...500 μW, signal period- 0.1...1ms, input optical signals power - 0.2...20 μW time delays - less 1μs, the number of optical signals - 2...10, integration time - 10...100 of signal periods, accuracy or integration error - about 1%. Various modifications of the neuron-integrators with improved performance and for different applications are considered in the paper.

Linear and nonlinear tremor acceleration characteristics in patients with Parkinson's disease

International Nuclear Information System (INIS)

Meigal, A Yu; Rissanen, S M; Airaksinen, O; Tarvainen, M P; Georgiadis, S D; Karjalainen, P A; Kankaanpää, M

2012-01-01

The purpose of the study was to evaluate linear and nonlinear tremor characteristics of the hand in patients with Parkinson's disease (PD) and to compare the results with those of healthy old and young control subjects. Furthermore, the aim was to study correlation between tremor characteristics and clinical signs. A variety of nonlinear (sample entropy, cross-sample entropy, recurrence rate, determinism and correlation dimension) and linear (amplitude, spectral peak frequency and total power, and coherence) hand tremor parameters were computed from acceleration measurements for PD patients (n = 30, 68.3 ± 7.8 years), and old (n = 20, 64.2 ± 7.0 years) and young (n = 20, 18.4 ± 1.1 years) control subjects. Nonlinear tremor parameters such as determinism, sample entropy and cross-sample entropy were significantly different between the PD patients and healthy controls. These parameters correlated with the Unified Parkinson's disease rating scale (UPDRS), tremor and finger tapping scores, but not with the rigidity scores. Linear tremor parameters such as the amplitude and the maximum power (power corresponding to peak frequency) also correlated with the clinical findings. No major difference was detected in the tremor characteristics between old and young control subjects. The study revealed that tremor in PD patients is more deterministic and regular when compared to old or young healthy controls. The nonlinear tremor parameters can differentiate patients with PD from healthy control subjects and these parameters may have potential in the assessment of the severity of PD (UPDRS). (paper)

Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation

Directory of Open Access Journals (Sweden)

Berenguer MI

2009-01-01

Full Text Available The authors present a method of numerical approximation of the fixed point of an operator, specifically the integral one associated with a nonlinear Fredholm integral equation, that uses strongly the properties of a classical Schauder basis in the Banach space .

Six-component semi-discrete integrable nonlinear Schrödinger system

Science.gov (United States)

Vakhnenko, Oleksiy O.

2018-01-01

We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.

Correction of nonlinear distortion in high-transverse-emittance ratio-beam production with linear accelerator

Directory of Open Access Journals (Sweden)

Shaoheng Wang

2008-05-01

Full Text Available Derbenev proposed producing a high quality flat beam of high-transverse-emittance ratio (HTER with a linear accelerator. Kim also discussed the round-to-flat transformation of angular-momentum-dominated beam. Fermilab/NICADD Photoinjector Laboratory has performed many experiments on HTER beam production. Experiments and simulations, collectively, showed an S-shaped transverse distribution in the flat beam. In this paper, the source of this emittance deterioration in the transformation is identified as the nonlinear rf cavity focusing force; and a solution is proposed.

On the Possibility of Accelerating Positron on an Electron Wake at SABER

International Nuclear Information System (INIS)

Ischebeck, R.; Joshi, C.; Katsouleas, T.C.; Muggli, P.; Wang, X.

2008-01-01

A new approach for positron acceleration in non-linear plasma wakefields driven by electron beams is presented. Positrons can be produced by colliding an electron beam with a thin foil target embedded in the plasma. Integration of positron production and acceleration in one stage is realized by a single relativistic, intense electron beam. Simulations with the parameters of the proposed SABER facility [1] at SLAC suggest that this concept could be tested there

Integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell

Science.gov (United States)

Vakhnenko, Oleksiy O.

2018-05-01

Developing the idea of increasing the number of structural elements in the unit cell of a quasi-one-dimensional lattice as applied to the semi-discrete integrable systems of nonlinear Schrödinger type, we construct the zero-curvature representation for the general integrable nonlinear system on a lattice with three structural elements in the unit cell. The integrability of the obtained general system permits to find explicitly a number of local conservation laws responsible for the main features of system dynamics and in particular for the so-called natural constraints separating the field variables into the basic and the concomitant ones. Thus, considering the reduction to the semi-discrete integrable system of nonlinear Schrödinger type, we revealed the essentially nontrivial impact of concomitant fields on the Poisson structure and on the whole Hamiltonian formulation of system dynamics caused by the nonzero background values of these fields. On the other hand, the zero-curvature representation of a general nonlinear system serves as an indispensable key to the dressing procedure of system integration based upon the Darboux transformation of the auxiliary linear problem and the implicit Bäcklund transformation of field variables. Due to the symmetries inherent to the six-component semi-discrete integrable nonlinear Schrödinger system with attractive-type nonlinearities, the Darboux-Bäcklund dressing scheme is shown to be simplified considerably, giving rise to the appropriately parameterized multi-component soliton solution consisting of six basic and four concomitant components.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator.

Science.gov (United States)

Botari, Tiago; Leonel, Edson D

2013-01-01

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization.

Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two variables and their applications.

Science.gov (United States)

Xu, Run; Ma, Xiangting

2017-01-01

In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

Science.gov (United States)

Nguyen, Nhan; Ting, Eric

2018-01-01

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

Induction Accelerator Technology Choices for the Integrated Beam Experiment (IBX)

International Nuclear Information System (INIS)

Leitner, M.A.; Celata, C.M.; Lee, E.P.; Logan, B.G.; Sabbi, G.; Waldron, W.L.; Barnard, J.J.

2003-01-01

Over the next three years the research program of the Heavy Ion Fusion Virtual National Laboratory (HIF-VNL), a collaboration among LBNL, LLNL, and PPPL, is focused on separate scientific experiments in the injection, transport and focusing of intense heavy ion beams at currents from 100 mA to 1 A. As a next major step in the HIF-VNL program, we aim for a complete 'source-to-target' experiment, the Integrated Beam Experiment (IBX). By combining the experience gained in the current separate beam experiments IBX would allow the integrated scientific study of the evolution of a single heavy ion beam at high current (∼1 A) through all sections of a possible heavy ion fusion accelerator: the injection, acceleration, compression, and beam focusing.This paper describes the main parameters and technology choices of the planned IBX experiment. IBX will accelerate singly charged potassium or argon ion beams up to 10 MeV final energy and a longitudinal beam compression ratio of 10, resulting in a beam current at target of more than 10 Amperes. Different accelerator cell design options are described in detail: Induction cores incorporating either room temperature pulsed focusing-magnets or superconducting magnets

Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials

International Nuclear Information System (INIS)

Gelebart, Lionel; Mondon-Cancel, Romain

2013-01-01

FFT-based methods are used to solve the problem of a heterogeneous unit-cell submitted to periodic boundary conditions, which is of a great interest in the context of numerical homogenization. Recently (in 2010), Brisard and Zeman proposed simultaneously to use Conjugate Gradient based solvers in order to improve the convergence properties (when compared to the basic scheme, proposed initially in 1994). The purpose of the paper is to extend this idea to the case of non-linear behaviors. The proposed method is based on a Newton-Raphson algorithm and can be applied to various kinds of behaviors (time dependant or independent, with or without internal variables) through a conventional integration procedure as used in finite element codes. It must be pointed out that this approach is fundamentally different from the traditional FFT-based approaches which rely on a fixed-point algorithm (e.g. basic scheme, Eyre and Milton accelerated scheme, Augmented Lagrangian scheme, etc.). The method is compared to the basic scheme on the basis of a simple application (a linear elastic spherical inclusion within a non-linear elastic matrix): a low sensitivity to the reference material and an improved efficiency, for a soft or a stiff inclusion, are observed. At first proposed for a prescribed macroscopic strain, the method is then extended to mixed loadings. (authors)

Two-dimensional nonlinear string-type equations and their exact integration

International Nuclear Information System (INIS)

Leznov, A.N.; Saveliev, M.V.

1982-01-01

On the base of group-theoretical formulation for exactly integrable two-dimensional non-linear dynamical systems associated with a local part of an arbitrary graded Lie algebra we study a string-type subclass of the equations. Explicit expressions have been obtained for their general solutions

Reformulation of nonlinear integral magnetostatic equations for rapid iterative convergence

International Nuclear Information System (INIS)

Bloomberg, D.S.; Castelli, V.

1985-01-01

The integral equations of magnetostatics, conventionally given in terms of the field variables M and H, are reformulated with M and B. Stability criteria and convergence rates of the eigenvectors of the linear iteration matrices are evaluated. The relaxation factor β in the MH approach varies inversely with permeability μ, and nonlinear problems with high permeability converge slowly. In contrast, MB iteration is stable for β 3 , the number of iterations is reduced by two orders of magnitude over the conventional method, and at higher permeabilities the reduction is proportionally greater. The dependence of MB convergence rate on β, degree of saturation, element aspect ratio, and problem size is found numerically. An analytical result for the MB convergence rate for small nonlinear problems is found to be accurate for βless than or equal to1.2. The results are generally valid for two- and three-dimensional integral methods and are independent of the particular discretization procedures used to compute the field matrix

The VINEYARD project: Versatile Integrated Accelerator-based Heterogeneous Data Centers

OpenAIRE

Kachris, Christoforos; Soudris, Dimitrios; Gaydadjiev, Georgi; Nguyen, Huy-Nam

2016-01-01

Emerging applications like cloud computing and big data analytics have created the need for powerful centers hosting hundreds of thousands of servers. Currently, the data centers are based on general purpose processors that provide high flexibility but lacks the energy efficiency of customized accelerators. VINEYARD1 aims to develop novel servers based on programmable hardware accelerators. Furthermore, VINEYARD will develop an integrated framework for allowing end-users to seamlessly utilize...

An approximation method for nonlinear integral equations of Hammerstein type

International Nuclear Information System (INIS)

Chidume, C.E.; Moore, C.

1989-05-01

The solution of a nonlinear integral equation of Hammerstein type in Hilbert spaces is approximated by means of a fixed point iteration method. Explicit error estimates are given and, in some cases, convergence is shown to be at least as fast as a geometric progression. (author). 25 refs

Space-Charge Simulation of Integrable Rapid Cycling Synchrotron

Energy Technology Data Exchange (ETDEWEB)

Eldred, Jeffery [Fermilab; Valishev, Alexander [Fermilab

2017-05-01

Integrable optics is an innovation in particle accelerator design that enables strong nonlinear focusing without generating parametric resonances. We use a Synergia space-charge simulation to investigate the application of integrable optics to a high-intensity hadron ring that could replace the Fermilab Booster. We find that incorporating integrability into the design suppresses the beam halo generated by a mismatched KV beam. Our integrable rapid cycling synchrotron (iRCS) design includes other features of modern ring design such as low momentum compaction factor and harmonically canceling sextupoles. Experimental tests of high-intensity beams in integrable lattices will take place over the next several years at the Fermilab Integrable Optics Test Accelerator (IOTA) and the University of Maryland Electron Ring (UMER).

Comparison of a nonlinear dynamic model of a piping system to test data

International Nuclear Information System (INIS)

Blakely, K.D.; Howard, G.E.; Walton, W.B.; Johnson, B.A.; Chitty, D.E.

1983-01-01

Response of a nonlinear finite element model of the Heissdampfreaktor recirculation piping loop (URL) was compared to measured data, representing the physical benchmarking of a nonlinear model. Analysis-test comparisons of piping response are presented for snapback tests that induced extreme nonlinear behavior of the URL system. Nonlinearities in the system are due to twelve swaybraces (pipe supports) that possessed nonlinear force-deflection characteristics. These nonlinearities distorted system damping estimates made by using the half-power bandwidth method on Fourier transforms of measured accelerations, with the severity of distortion increasing with increasing degree of nonlinearity. Time domain methods, which are not so severely affected by the presence of nonlinearities, were used to compute system damping ratios. Nonlinear dynamic analyses were accurately and efficiently performed using the pseudo-force technique and the finite element program MSC/NASTRAN. Measured damping was incorporated into the model for snapback simulations. Acceleration time histories, acceleration Fourier transforms, and swaybrace force time histories of the nonlinear model, plus several linear models, were compared to test measurements. The nonlinear model predicted three-fourths of the measured peak accelerations to within 50%, half of the accelerations to within 25%, and one-fifth of the accelerations to within 10%. This nonlinear model predicted accelerations (in the time and frequency domains) and swaybrace forces much better than did any of the linear models, demonstrating the increased accuracy resulting from properly simulating nonlinear support behavior. In addition, earthquake response comparisons were made between the experimentally validated nonlinear model and a linear model. Significantly lower element stresses were predicted for the nonlinear model, indicating the potential usefulness of nonlinear simulations in piping design assessments. (orig.)

Iteration and accelerator dynamics

International Nuclear Information System (INIS)

Peggs, S.

1987-10-01

Four examples of iteration in accelerator dynamics are studied in this paper. The first three show how iterations of the simplest maps reproduce most of the significant nonlinear behavior in real accelerators. Each of these examples can be easily reproduced by the reader, at the minimal cost of writing only 20 or 40 lines of code. The fourth example outlines a general way to iteratively solve nonlinear difference equations, analytically or numerically

Analysis of electromagnetic wave interactions on nonlinear scatterers using time domain volume integral equations

KAUST Repository

Ulku, Huseyin Arda

2014-07-06

Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half

New classical r-matrices from integrable non-linear sigma-models

International Nuclear Information System (INIS)

Laartz, J.; Bordemann, M.; Forger, M.; Schaper, U.

1993-01-01

Non-linear sigma models on Riemannian symmetric spaces constitute the most general class of classical non-linear sigma models which are known to be integrable. Using the current algebra structure of these models their canonical structure is analyzed and it is shown that their non-ultralocal fundamental Poisson bracket relation is governed by a field dependent non antisymmetric r-matrix obeying a dynamical Yang Baxter equation. The fundamental Poisson bracket relations and the r-matrix are derived explicitly and a new kind of algebra is found that is supposed to replace the classical Yang Baxter algebra governing the canonical structure of ultralocal models. (Author) 9 refs

Conservative fourth-order time integration of non-linear dynamic systems

DEFF Research Database (Denmark)

Krenk, Steen

2015-01-01

An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...

Achievements in ISICs/SAPP collaborations for electromagnetic modeling of accelerators

International Nuclear Information System (INIS)

Lee Liequan; Ge Lixin; Li Zenghai; Ng, Cho; Schussman, Greg; Ko, Kwok

2005-01-01

SciDAC provides the unique opportunity and the resources for the Electromagnetic System Simulations (ESS) component of High Energy Physics (HEP)'s Accelerator Science and Technology (AST) project to work with researchers in the Integrated Software Infrastructure Centres (ISICs) and Scientific Application Pilot Program (SAPP) to overcome challenging barriers in computer science and applied mathematics in order to perform the large-scale simulations required to support the ongoing R and D efforts on accelerators across the Office of Science. This paper presents the resultant achievements made under SciDAC in important areas of computational science relevant to electromagnetic modelling of accelerators which include nonlinear eigensolvers, shape optimization, adaptive mesh refinement, parallel meshing, and visualization

Analysis of FFAG accelerators and the evolution of circular accelerators

International Nuclear Information System (INIS)

Laslett, J.

1961-01-01

After rapidly comparing circular machines with the linear accelerator and the reasons for the choice of an annular high energy and very high intensity accelerator, recent problems concerning accelerator theory are discussed, with emphasis on their physical character. The FFAG principle. The limit of the energy of FFAG cyclotron. The setting-up and interpreting of mean energy of focusing terms for a spiral FFAG synchrotron. The limiting amplitude stable near the non-linear resonance 2Q z = Q r , as well as the linear coupling resonance of Walkinshaw 2Q z = Q r . The crossed-beam accelerator. The 40 MeV electron model of MURA. Two other parts deal with linear and non-linear methods of injection and extraction using a variable disturbance applied to the magnetic field, as well as to collective effects. The interaction of the beam with the accelerating cavities and the walls. The modification of the phase oscillation equation. The influence of the beams' high frequency fields on the Nielsen longitudinal instability. (author) [fr

Integrated all optical transmodulator circuits with non-linear gain elements and tunable optical fibers

NARCIS (Netherlands)

Kuindersma, P.I.; Leijtens, X.J.M.; Zantvoort, van J.H.C.; Waardt, de H.

2012-01-01

We characterize integrated InP circuits for high speed ‘all-optical’ signal processing. Single chip circuits act as optical transistors. Transmodulation is performed by non-linear gain sections. Integrated tunable filters give signal equalization in time domain.

Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics

CERN Document Server

2016-01-01

This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application...

Suppression of Instabilities Generated by an Anti-Damper with a Nonlinear Magnetic Element in IOTA

Energy Technology Data Exchange (ETDEWEB)

Stern, E. [Fermilab

2018-04-01

The Integrable Optics Test Accelerator (IOTA) storage ring is being constructed at Fermilab as a testbed for new accelerator concepts. One important series of experiments tests the use of a novel nonlinear magnetic insert to damp coherent instabilities. To test the damping power of the element, an instability of desired strength may be intentionally excited with an anti-damper. We report on simulations of beam stabilization using the Synergia modeling framework over ranges of driving and damping strengths.

Painlevйe analysis and integrability of two-coupled non-linear ...

Indian Academy of Sciences (India)

the Painlevйe property. In this case the system is expected to be integrable. In recent years more attention is paid to the study of coupled non-linear oscilla- ... Painlevйe analysis. To be self-contained, in §2 we briefly outline the salient features.

The Lie-Poisson structure of integrable classical non-linear sigma models

International Nuclear Information System (INIS)

Bordemann, M.; Forger, M.; Schaeper, U.; Laartz, J.

1993-01-01

The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into the r-s-matrix formalism for non-ultralocal integrable models first discussed by Maillet. The matrices r and s are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrix c. It is proposed that all these Poisson brackets taken together are representation conditions for a new kind of algebra which, for this class of models, replaces the classical Yang-Baxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed. (orig.)

Study of Piezoelectric Vibration Energy Harvester with non-linear conditioning circuit using an integrated model

Science.gov (United States)

Manzoor, Ali; Rafique, Sajid; Usman Iftikhar, Muhammad; Mahmood Ul Hassan, Khalid; Nasir, Ali

2017-08-01

Piezoelectric vibration energy harvester (PVEH) consists of a cantilever bimorph with piezoelectric layers pasted on its top and bottom, which can harvest power from vibrations and feed to low power wireless sensor nodes through some power conditioning circuit. In this paper, a non-linear conditioning circuit, consisting of a full-bridge rectifier followed by a buck-boost converter, is employed to investigate the issues of electrical side of the energy harvesting system. An integrated mathematical model of complete electromechanical system has been developed. Previously, researchers have studied PVEH with sophisticated piezo-beam models but employed simplistic linear circuits, such as resistor, as electrical load. In contrast, other researchers have worked on more complex non-linear circuits but with over-simplified piezo-beam models. Such models neglect different aspects of the system which result from complex interactions of its electrical and mechanical subsystems. In this work, authors have integrated the distributed parameter-based model of piezo-beam presented in literature with a real world non-linear electrical load. Then, the developed integrated model is employed to analyse the stability of complete energy harvesting system. This work provides a more realistic and useful electromechanical model having realistic non-linear electrical load unlike the simplistic linear circuit elements employed by many researchers.

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

International Nuclear Information System (INIS)

Al Khawaja, U.

2010-01-01

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

Case Study: Accelerating Process Improvement by Integrating the TSP and CMMI

National Research Council Canada - National Science Library

Wall, Daniel S; McHale, James; Pomeroy-Huff, Marsha

2005-01-01

.... This case study describes the process improvement efforts of both NAVAIR divisions and how they integrated the two SEI technologies to accelerate process improvement within their organizations...

Some problems on non-linear semigroups and the blow-up of integral solutions

International Nuclear Information System (INIS)

Pavel, N.H.

1983-07-01

After some introductory remarks, this highly mathematical document considers a unifying approach in the theory of non-linear semigroups. Then a brief survey is given on blow-up of mild solutions from the semilinear case. Finally, the global behavior of solutions to non-linear evolution equations is addressed; it is found that classical results on the behavior of the maximal solution u as t up-arrow tsub(max) hold also for integral solutions

Stability and square integrability of solutions of nonlinear fourth order differential equations

Directory of Open Access Journals (Sweden)

Moussadek Remili

2016-05-01

Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.

An Integrable Discrete Generalized Nonlinear Schrödinger Equation and Its Reductions

International Nuclear Information System (INIS)

Li Hong-Min; Li Yu-Qi; Chen Yong

2014-01-01

An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrödinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrödinger (NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones. (general)

Stationary nonlinear Airy beams

International Nuclear Information System (INIS)

Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.

2011-01-01

We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.

Nonlinear dynamics in integrated coupled DFB lasers with ultra-short delay.

Science.gov (United States)

Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi

2014-03-10

We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.

Report of the working group on single-particle nonlinear dynamics

International Nuclear Information System (INIS)

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.

1999-01-01

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 accelerators. (AIP) copyright 1999 American Institute of Physics

Integrability and soliton in a classical one dimensional site dependent biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity

International Nuclear Information System (INIS)

Kavitha, L.; Daniel, M.

2002-07-01

The integrability of one dimensional classical continuum inhomogeneous biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity on the soliton of an underlying completely integrable spin model are studied. The dynamics of the spin system is expressed in terms of a higher order generalized nonlinear Schroedinger equation through a differential geometric approach which becomes integrable for a particular choice of the biquadratic exchange interaction and for linear inhomogeneity. The effect of nonlinear inhomogeneity on the spin soliton is studied by carrying out a multiple scale perturbation analysis. (author)

Preliminary accelerator plans for maximizing the integrated LHC luminosity

CERN Document Server

Benedikt, Michael; Ruggiero, F; Ostojic, R; Scandale, Walter; Shaposhnikova, Elena; Wenninger, J

2006-01-01

A working group on "Proton Accelerators for the Future" (PAF) has been created in May 2005 by the CERN direction to elaborate a baseline scenario of the possible development and upgrade of the present Proton Accelerator Complex. This report is the result of the investigation conducted until the end of 2005, in close connection with the working group on "Physics Opportunities with Future Proton Accelerators" (POFPA) and is consistent with their recommendations. Focused on the goal of maximizing the integrated luminosity for the LHC experiments, a scenario of evolution is proposed, subject to further refinement using the future experience of commissioning and running-in the collider and its injector complex. The actions to be taken in terms of consolidation, R & D and improvement are outlined. The benefits for other types of physics are mentioned and will be investigated in more detail in the future.

Nonlinear dynamics aspects of modern storage rings

International Nuclear Information System (INIS)

Helleman, R.H.G.; Kheifets, S.A.

1986-01-01

The authors try to address the following two questions: a. Why should accelerator physicists to be interested in the recent, sometimes abstract, developments in Nonlinear Dynamics, a field which will recently was mainly studied by mathematicians, theoretical physicists and astronomers? That such an interest to some extent already exists is apparent from the fact that many accelerator physicists attended this School and several analogous meetings in the past. b. Why should researchers from nonlinear dynamics be interested in modern Storage Rings which are largely designed and built by experimental physicists and engineers? At the moment few 'nonlinear scientists' work on storage rings (or in the field of accelerator physics). It is a hopeful sign that many (more) attended this School

Integral sliding mode-based formation control of multiple unertain robots via nonlinear disturbane observer

Directory of Open Access Journals (Sweden)

Dianwei Qian

2016-11-01

Full Text Available This article proposes a control scheme for formation of maneuvers of a team of mobile robots. The control scheme integrates the integral sliding mode control method with the nonlinear disturbance observer technique. The leader–follower formation dynamics suffer from uncertainties originated from the individual robots. The uncertainties challenge the formation control of such robots. Assuming that the uncertainties are unknown but bounded, an nonlinear disturbance observer-based observer is utilized to approximate them. The observer outputs feed on an integral sliding mode control-based controller. The controller and observer are integrated into the control scheme to realize formation maneuvers despite uncertainties. The formation stability is analyzed by means of the Lyapunov’s theorem. In the sense of Lyapunov, not only the convergence of the approximation errors is guaranteed but also such a control scheme can asymptotically stabilize the formation system. Compared to the results by the sole integral sliding mode control, some simulations are presented to demonstrate the feasibility and performance of the control scheme.

Integrability of the Einstein-nonlinear SU(2) σ-model in a nontrivial topological sector

Energy Technology Data Exchange (ETDEWEB)

Paliathanasis, Andronikos [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Durban University of Technology, Institute of Systems Science, Durban (South Africa); Taves, Tim [Centro de Estudios Cientificos (CECS), Valdivia (Chile); Leach, P.G.L. [Durban University of Technology, Department of Mathematics and Institute of Systems Science, Research and Postgraduate Support, Durban (South Africa); University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

2017-12-15

The integrability of the Λ-Einstein-nonlinear SU(2)σ-model with nonvanishing cosmological charge is studied. We apply the method of singularity analysis of differential equations and we show that the equations for the gravitational field are integrable. The first few terms of the solution are presented. (orig.)

Experimental analysis of nonlinear oscillations in the undergraduate physics laboratory

International Nuclear Information System (INIS)

Moreno, R; Page, A; Riera, J; Hueso, J L

2014-01-01

In this paper, we present a simple experiment to introduce the nonlinear behaviour of oscillating systems in the undergraduate physics laboratory. The transverse oscillations of a spring allow reproduction of three totally different scenarios: linear oscillations, nonlinear oscillations reducible to linear for small displacements, and intrinsically nonlinear oscillations. The chosen approach consists of measuring the displacements using video photogrammetry and computing the velocities and the accelerations by means of a numerical differentiation algorithm. In this way, one can directly check the differential equation of the motion without having to integrate it, or perform an experimental study of the potential energy in each of the analysed scenarios. This experiment allows first year students to reflect on the consequences and the limits of the linearity assumption for small displacements that is so often made in technical studies. (paper)

The use of the J* integral for non-linear fracture mechanics

International Nuclear Information System (INIS)

Hellen, T.K.

1976-09-01

The Griffith energy balance criterion, first postulated over 50 years ago, is still the basis of linear elastic fracture mechanics. From this, accurate numerical methods for establishing stress intensity factors and energy release rates have been developed. One such method involves path independent contour integrals about the crack tip. An improved contour integral, designated J* is discussed, and shown to have distinct advantages over others in non-linear strain situations. A number of examples are shown including fractures in thermo-plastic and creep situations. (author)

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

Science.gov (United States)

Mobayen, Saleh

2018-06-01

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear Analysis and Intelligent Control of Integrated Vehicle Dynamics

Directory of Open Access Journals (Sweden)

C. Huang

2014-01-01

Full Text Available With increasing and more stringent requirements for advanced vehicle integration, including vehicle dynamics and control, traditional control and optimization strategies may not qualify for many applications. This is because, among other factors, they do not consider the nonlinear characteristics of practical systems. Moreover, the vehicle wheel model has some inadequacies regarding the sideslip angle, road adhesion coefficient, vertical load, and velocity. In this paper, an adaptive neural wheel network is introduced, and the interaction between the lateral and vertical dynamics of the vehicle is analyzed. By means of nonlinear analyses such as the use of a bifurcation diagram and the Lyapunov exponent, the vehicle is shown to exhibit complicated motions with increasing forward speed. Furthermore, electric power steering (EPS and active suspension system (ASS, which are based on intelligent control, are used to reduce the nonlinear effect, and a negotiation algorithm is designed to manage the interdependences and conflicts among handling stability, driving smoothness, and safety. Further, a rapid control prototype was built using the hardware-in-the-loop simulation platform dSPACE and used to conduct a real vehicle test. The results of the test were consistent with those of the simulation, thereby validating the proposed control.

LEGO: A modular accelerator design code

International Nuclear Information System (INIS)

Cai, Y.; Donald, M.; Irwin, J.; Yan, Y.

1997-08-01

An object-oriented accelerator design code has been designed and implemented in a simple and modular fashion. It contains all major features of its predecessors: TRACY and DESPOT. All physics of single-particle dynamics is implemented based on the Hamiltonian in the local frame of the component. Components can be moved arbitrarily in the three dimensional space. Several symplectic integrators are used to approximate the integration of the Hamiltonian. A differential algebra class is introduced to extract a Taylor map up to arbitrary order. Analysis of optics is done in the same way both for the linear and nonlinear case. Currently, the code is used to design and simulate the lattices of the PEP-II. It will also be used for the commissioning

Nonlinear transport of dynamic system phase space

International Nuclear Information System (INIS)

Xie Xi; Xia Jiawen

1993-01-01

The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example

Beam manipulation techniques, nonlinear beam dynamics, and space charge effect in high energy high power accelerators

Energy Technology Data Exchange (ETDEWEB)

Lee, S. Y. [Indiana Univ., Bloomington, IN (United States)

2014-04-07

We had carried out a design of an ultimate storage ring with beam emittance less than 10 picometer for the feasibility of coherent light source at X-ray wavelength. The accelerator has an inherent small dynamic aperture. We study method to improve the dynamic aperture and collective instability for an ultimate storage ring. Beam measurement and accelerator modeling are an integral part of accelerator physics. We develop the independent component analysis (ICA) and the orbit response matrix method for improving accelerator reliability and performance. In collaboration with scientists in National Laboratories, we also carry out experimental and theoretical studies on beam dynamics. Our proposed research topics are relevant to nuclear and particle physics using high brightness particle and photon beams.

Beam Stability and Nonlinear Dynamics. Proceedings

International Nuclear Information System (INIS)

Parsa, Z.

1997-01-01

These proceedings represent papers presented at the Beam Stability and Nonlinear Dynamics symposium held in Santa Barbara in December 1996. The symposium was sponsored by the National Science Foundation as part of the United States long term accelerator research. The focus of this symposium was on nonlinear dynamics and beam stability. The topics included single-particle and many-particle dynamics, and stability in large circular accelerators such as the Large Hadron Collider(LHC). Other subjects covered were spin dynamics, nonlinear aberration correction, collective effects in the LHC, sawtooth instability and Landau damping in the presence of strong nonlinearity. There were presentations concerning plasma physics including the effect of beam echo. There are 17 papers altogether in these proceedings and 8 of them have been abstracted for the Energy Science and Technology database

Nonlinear dynamic analysis using Petrov-Galerkin natural element method

International Nuclear Information System (INIS)

Lee, Hong Woo; Cho, Jin Rae

2004-01-01

According to our previous study, it is confirmed that the Petrov-Galerkin Natural Element Method (PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin Natural Element Method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem

Nonlinear system identification of smart structures under high impact loads

International Nuclear Information System (INIS)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-01-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure–MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure–MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes. (paper)

Nonlinear system identification of smart structures under high impact loads

Science.gov (United States)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-05-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.

Science.gov (United States)

Chowdury, A; Kedziora, D J; Ankiewicz, A; Akhmediev, N

2014-09-01

We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.

Bayesian integration and non-linear feedback control in a full-body motor task.

Science.gov (United States)

Stevenson, Ian H; Fernandes, Hugo L; Vilares, Iris; Wei, Kunlin; Körding, Konrad P

2009-12-01

A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots) on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter) is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller). We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.

Bayesian integration and non-linear feedback control in a full-body motor task.

Directory of Open Access Journals (Sweden)

Ian H Stevenson

2009-12-01

Full Text Available A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller. We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.

Present accelerated expansion of the universe from new Weyl-integrable gravity approach

Energy Technology Data Exchange (ETDEWEB)

Aguila, Ricardo; Madriz Aguilar, Jose Edgar; Moreno, Claudia [Universidad de Guadalajara (UdG), Departamento de Matematicas, Centro Universitario de Ciencias Exactas e ingenierias (CUCEI), Guadalajara, Jalisco (Mexico); Bellini, Mauricio [Universidad Nacional de Mar del Plata (UNMdP), Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Mar del Plata (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), La Plata (Argentina)

2014-11-15

We investigate if a recently introduced formulation of general relativity on a Weyl-integrable geometry contains cosmological solutions exhibiting acceleration in the present cosmic expansion. We derive the general conditions to have acceleration in the expansion of the universe and obtain a particular solution for the Weyl scalar field describing a cosmological model for the present time in concordance with the data combination Planck + WP + BAO + SN. (orig.)

Nonlinear integral equations for the sausage model

Science.gov (United States)

Ahn, Changrim; Balog, Janos; Ravanini, Francesco

2017-08-01

The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.

Single particle dynamics in circular accelerators

International Nuclear Information System (INIS)

Ruth, R.D.

1986-10-01

The purpose of this paper is to introduce the reader to the theory associated with the transverse dynamics of single particle, in circular accelerators. The discussion begins with a review of Hamiltonian dynamics and canonical transformations. The case of a single particle in a circular accelerator is considered with a discussion of non-linear terms and chromaticity. The canonical perturbation theory is presented and nonlinear resonances are considered. Finally, the concept of renormalization and residue criterion are examined. (FI)

On the integration of an ODE involving the derivative of a Preisach nonlinearity

International Nuclear Information System (INIS)

Flynn, D; Rasskazov, O

2005-01-01

We offer an algorithm for numerical integration of an ODE with a Preisach nonlinearity under the derivative on the left-hand side. Despite the exotic form, equations of that kind are important in applied disciplines, for example in terrestrial hydrology

Accelerating functional verification of an integrated circuit

Science.gov (United States)

Deindl, Michael; Ruedinger, Jeffrey Joseph; Zoellin, Christian G.

2015-10-27

Illustrative embodiments include a method, system, and computer program product for accelerating functional verification in simulation testing of an integrated circuit (IC). Using a processor and a memory, a serial operation is replaced with a direct register access operation, wherein the serial operation is configured to perform bit shifting operation using a register in a simulation of the IC. The serial operation is blocked from manipulating the register in the simulation of the IC. Using the register in the simulation of the IC, the direct register access operation is performed in place of the serial operation.

Non-integrability of the Huang--Li nonlinear financial model

OpenAIRE

Szumiński, Wojciech

2017-01-01

In this paper we consider Huang--Li nonlinear financial system recently studied in the literature. It has the form of three first order differential equations \\[ \\dot x=z+(y-a)x,\\quad \\dot y=1-b y-x^2,\\quad \\dot z=-x-c z, \\] where $(a,b,c)$ are real positive parameters. We show that this system is not integrable in the class of functions meromorphic in variables $(x,y,z)$. We give an analytic proof of this fact analysing properties the of differential Galois group of variational equations alo...

CAS CERN Accelerator School: Advanced accelerator physics. Proceedings. Vol. 2

International Nuclear Information System (INIS)

Turner, S.

1987-01-01

This advanced course on general accelerator physics is the second of the biennial series given by the CERN Accelerator School and follows on from the first basic course given at Gif-sur-Yvette, Paris, in 1984. Stress is placed on the mathematical tools of Hamiltonian mechanics and the Vlasov and Fokker-Planck equations, which are widely used in accelerator theory. The main topics treated in this present work include: nonlinear resonances, chromaticity, motion in longitudinal phase space, growth and control of longitudinal and transverse beam emittance, space-charge effects and polarization. The seminar programme treats some specific accelerator techniques, devices, projects and future possibilities. (orig.)

Comment on the consistency of truncated nonlinear integral equation based theories of freezing

International Nuclear Information System (INIS)

Cerjan, C.; Bagchi, B.; Rice, S.A.

1985-01-01

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions

The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

International Nuclear Information System (INIS)

Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

2007-05-01

The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

Some integral formulations occurring in accelerator physics

International Nuclear Information System (INIS)

Miano, G.; Verolino, L.; Vaccaro, V.G.

1995-10-01

In this paper a powerful and robust analytical-numerical approach to study the electromagnetic interaction between a bunch of particles and the discontinuities of the vacuum chamber of a particle accelerator is discussed. In particular the diffraction of the electromagnetic field created by a bunch of a bunch of charges travelling through an iris and a drift tube is considered. Choosing in both cases a spectral transform of the current density distribution on the scatterer as unknowns, an effective numerical model is obtained. These unknowns have to satisfy a system of dual integral equations. A general procedure to transform this system into only one Fredholm integral equation of the second kind (in the case of the iris) or to a system of linear algebraic equations by means of a Neumann series (in the case of the drift tube) is described. These models allow to compute the longitudinal coupling impedance with a good accuracy either in the low frequency limit or in the high frequency limit

Some integral formulations occurring in accelerator physics

Energy Technology Data Exchange (ETDEWEB)

Miano, G; Verolino, L [Naples Univ. (Italy). Dip. di Ingegneria Elettronica; [INFN, Naples (Italy); Vaccaro, V G [Naples Univ. (Italy). Dip. di Scienze Fisiche; [INFN, Naples (Italy)

1995-10-01

In this paper a powerful and robust analytical-numerical approach to study the electromagnetic interaction between a bunch of particles and the discontinuities of the vacuum chamber of a particle accelerator is discussed. In particular the diffraction of the electromagnetic field created by a bunch of a bunch of charges travelling through an iris and a drift tube is considered. Choosing in both cases a spectral transform of the current density distribution on the scatterer as unknowns, an effective numerical model is obtained. These unknowns have to satisfy a system of dual integral equations. A general procedure to transform this system into only one Fredholm integral equation of the second kind (in the case of the iris) or to a system of linear algebraic equations by means of a Neumann series (in the case of the drift tube) is described. These models allow to compute the longitudinal coupling impedance with a good accuracy either in the low frequency limit or in the high frequency limit.

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

Science.gov (United States)

Shivakumar, J.; Ashok, M. H.; Khadakbhavi, Vishwanath; Pujari, Sanjay; Nandurkar, Santosh

2018-02-01

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

Estimation of non-linear continuous time models for the heat exchange dynamics of building integrated photovoltaic modules

DEFF Research Database (Denmark)

Jimenez, M.J.; Madsen, Henrik; Bloem, J.J.

2008-01-01

This paper focuses on a method for linear or non-linear continuous time modelling of physical systems using discrete time data. This approach facilitates a more appropriate modelling of more realistic non-linear systems. Particularly concerning advanced building components, convective and radiati...... that a description of the non-linear heat transfer is essential. The resulting model is a non-linear first order stochastic differential equation for the heat transfer of the PV component....... heat interchanges are non-linear effects and represent significant contributions in a variety of components such as photovoltaic integrated facades or roofs and those using these effects as passive cooling strategies, etc. Since models are approximations of the physical system and data is encumbered...

Time history nonlinear earthquake response analysis considering materials and geometrical nonlinearity

International Nuclear Information System (INIS)

Kobayashi, T.; Yoshikawa, K.; Takaoka, E.; Nakazawa, M.; Shikama, Y.

2002-01-01

A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat uplift, were considered. The 'Lattice Model' for the soil-structure interaction model was employed. An earthquake record on soil surface at the site was used as control motion, and deconvoluted to the input motion of the analysis model at GL-52 m with 300 Gal of maximum acceleration. The following two analyses were considered: (A) time history nonlinear, (B) equivalent linear, and the advantage of time history nonlinear earthquake response analysis method is discussed

An accurate technique for the solution of the nonlinear point kinetics equations

International Nuclear Information System (INIS)

Picca, Paolo; Ganapol, Barry D.; Furfaro, Roberto

2011-01-01

A novel methodology for the solution of non-linear point kinetic (PK) equations is proposed. The technique is based on a piecewise constant approximation of PK system of ODEs and explicitly accounts for reactivity feedback effects, through an iterative cycle. High accuracy is reached by introducing a sub-mesh for the numerical evaluation of integrals involved and by correcting the source term to include the non-linear effect on a finer time scale. The use of extrapolation techniques for convergence acceleration is also explored. Results for adiabatic feedback model are reported and compared with other benchmarks in literature. The convergence trend makes the algorithm particularly attractive for applications, including in multi-point kinetics and quasi-static frameworks. (author)

Accelerating execution of the integrated TIGER series Monte Carlo radiation transport codes

Science.gov (United States)

Smith, L. M.; Hochstedler, R. D.

1997-02-01

Execution of the integrated TIGER series (ITS) of coupled electron/photon Monte Carlo radiation transport codes has been accelerated by modifying the FORTRAN source code for more efficient computation. Each member code of ITS was benchmarked and profiled with a specific test case that directed the acceleration effort toward the most computationally intensive subroutines. Techniques for accelerating these subroutines included replacing linear search algorithms with binary versions, replacing the pseudo-random number generator, reducing program memory allocation, and proofing the input files for geometrical redundancies. All techniques produced identical or statistically similar results to the original code. Final benchmark timing of the accelerated code resulted in speed-up factors of 2.00 for TIGER (the one-dimensional slab geometry code), 1.74 for CYLTRAN (the two-dimensional cylindrical geometry code), and 1.90 for ACCEPT (the arbitrary three-dimensional geometry code).

Accelerating execution of the integrated TIGER series Monte Carlo radiation transport codes

International Nuclear Information System (INIS)

Smith, L.M.; Hochstedler, R.D.

1997-01-01

Execution of the integrated TIGER series (ITS) of coupled electron/photon Monte Carlo radiation transport codes has been accelerated by modifying the FORTRAN source code for more efficient computation. Each member code of ITS was benchmarked and profiled with a specific test case that directed the acceleration effort toward the most computationally intensive subroutines. Techniques for accelerating these subroutines included replacing linear search algorithms with binary versions, replacing the pseudo-random number generator, reducing program memory allocation, and proofing the input files for geometrical redundancies. All techniques produced identical or statistically similar results to the original code. Final benchmark timing of the accelerated code resulted in speed-up factors of 2.00 for TIGER (the one-dimensional slab geometry code), 1.74 for CYLTRAN (the two-dimensional cylindrical geometry code), and 1.90 for ACCEPT (the arbitrary three-dimensional geometry code)

Nonlinear Control of Hydraulic Manipulator for Decommissioning Nuclear Reactor

Energy Technology Data Exchange (ETDEWEB)

Kim, Myoung-Ho; Lee, Sung-Uk; Kim, Chang-Hoi; Choi, Byung-Seon; Moon, Jei-Kwon [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2016-10-15

Robot technique is need to decommission nuclear reactor because of high radiation environment. Especially, Manipulator systems are useful for dismantling complex structure in a nuclear facility. In addition, Hydraulic system is applied to handle heavy duty object. Since hydraulic system can demonstrate high power. The manipulator with hydraulic power is already developed. To solve this problem, various nonlinear control method includes acceleration control. But, it is difficult because acceleration value is highly noisy. In this paper, the nonlinear control algorithm without acceleration control is studied. To verify, the hydraulic manipulator model had been developed. Furthermore, the numerical simulation is carried out. The nonlinear control without acceleration parameter method is developed for hydraulic manipulator. To verify control algorithm, the manipulator is modeled by MBD and the hydraulic servo system is also derived. In addition, the numerical simulation is also carried out. Especially, PID gain is determined though TDC algorithm. In the result of numerical simulation, tracking performance is good without acceleration control. Thus, the PID though TDC with SMC is good for hydraulic manipulator control.

Nonlinear Control of Hydraulic Manipulator for Decommissioning Nuclear Reactor

International Nuclear Information System (INIS)

Kim, Myoung-Ho; Lee, Sung-Uk; Kim, Chang-Hoi; Choi, Byung-Seon; Moon, Jei-Kwon

2016-01-01

Robot technique is need to decommission nuclear reactor because of high radiation environment. Especially, Manipulator systems are useful for dismantling complex structure in a nuclear facility. In addition, Hydraulic system is applied to handle heavy duty object. Since hydraulic system can demonstrate high power. The manipulator with hydraulic power is already developed. To solve this problem, various nonlinear control method includes acceleration control. But, it is difficult because acceleration value is highly noisy. In this paper, the nonlinear control algorithm without acceleration control is studied. To verify, the hydraulic manipulator model had been developed. Furthermore, the numerical simulation is carried out. The nonlinear control without acceleration parameter method is developed for hydraulic manipulator. To verify control algorithm, the manipulator is modeled by MBD and the hydraulic servo system is also derived. In addition, the numerical simulation is also carried out. Especially, PID gain is determined though TDC algorithm. In the result of numerical simulation, tracking performance is good without acceleration control. Thus, the PID though TDC with SMC is good for hydraulic manipulator control

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

International Nuclear Information System (INIS)

Prykarpatsky, Yarema A.; Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.; Samoylenko, Valeriy H.

2010-12-01

A gradient-holonomic approach for the Lax type integrability analysis of differential-discrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied and the related gradient identity is stated. The integrability of a discrete nonlinear Schroedinger type dynamical system is treated in detail. The integrability of a generalized Riemann type discrete hydrodynamical system is discussed. (author)

Detecting chaos in particle accelerators through the frequency map analysis method.

Science.gov (United States)

Papaphilippou, Yannis

2014-06-01

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

Science.gov (United States)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

Acceleration of Blender Cycles Path-Tracing Engine Using Intel Many Integrated Core Architecture

OpenAIRE

Jaroš , Milan; Říha , Lubomír; Strakoš , Petr; Karásek , Tomáš; Vašatová , Alena; Jarošová , Marta; Kozubek , Tomáš

2015-01-01

Part 2: Algorithms; International audience; This paper describes the acceleration of the most computationally intensive kernels of the Blender rendering engine, Blender Cycles, using Intel Many Integrated Core architecture (MIC). The proposed parallelization, which uses OpenMP technology, also improves the performance of the rendering engine when running on multi-core CPUs and multi-socket servers. Although the GPU acceleration is already implemented in Cycles, its functionality is limited. O...

Curvature-driven acceleration: a utopia or a reality?

International Nuclear Information System (INIS)

Das, Sudipta; Banerjee, Narayan; Dadhich, Naresh

2006-01-01

The present work shows that a combination of nonlinear contributions from the Ricci curvature in Einstein field equations can drive a late time acceleration of expansion of the universe. The transit from the decelerated to the accelerated phase of expansion takes place smoothly without having to resort to a study of asymptotic behaviour. This result emphasizes the need for thorough and critical examination of models with nonlinear contribution from the curvature

Curvature-driven acceleration: a utopia or a reality?

Energy Technology Data Exchange (ETDEWEB)

Das, Sudipta [Relativity and Cosmology Research Centre, Department of Physics, Jadavpur University, Calcutta-700 032 (India); Banerjee, Narayan [Relativity and Cosmology Research Centre, Department of Physics, Jadavpur University, Calcutta-700 032 (India); Dadhich, Naresh [Inter University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007 (India)

2006-06-21

The present work shows that a combination of nonlinear contributions from the Ricci curvature in Einstein field equations can drive a late time acceleration of expansion of the universe. The transit from the decelerated to the accelerated phase of expansion takes place smoothly without having to resort to a study of asymptotic behaviour. This result emphasizes the need for thorough and critical examination of models with nonlinear contribution from the curvature.

Generating multi-GeV electron bunches using single stage laser wakefield acceleration in a 3D nonlinear regime

Directory of Open Access Journals (Sweden)

W. Lu

2007-06-01

Full Text Available The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for laser wakefield acceleration (LWFA in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels. We demonstrate our results by presenting a sample particle-in-cell (PIC simulation of a 30   fs, 200 TW laser interacting with a 0.75 cm long plasma with density 1.5×10^{18}  cm^{-3} to produce an ultrashort (10 fs monoenergetic bunch of self-injected electrons at 1.5 GeV with 0.3 nC of charge. For future higher-energy accelerator applications, we propose a parameter space, which is distinct from that described by Gordienko and Pukhov [Phys. Plasmas 12, 043109 (2005PHPAEN1070-664X10.1063/1.1884126] in that it involves lower plasma densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high.

The importance of non-linearities in modern proton synchrotrons

International Nuclear Information System (INIS)

Wilson, E.J.N.

1977-01-01

The paper outlines the physics and mathematics of non-linear field errors in the quide fields of accelerators, with particular reference to large accelerators such as the SPS. These non-linearities give rise to closed orbital distortions and non-linear resonances or stopbands. Both of these effects are briefly discussed and the use of resonances for slow beam extraction is also described. Another problem considered is that of chromaticity of the particle beam. The use of sextupoles to correct chromaticity and the Landau damping of beam instabilities using octupoles are also discussed. In the final section the application of Hamiltonian mechanics to non-linearities is demonstrated. The author concludes that the effect of non-linearities on particle dynamics may place a more severe limit on intensity and storage time in large rings than any other effect in transverse phase space. (B.D.)

Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent

International Nuclear Information System (INIS)

Zhikov, Vasilii V; Pastukhova, Svetlana E

2008-01-01

Elliptic equations of p(x)-Laplacian type are investigated. There is a well-known logarithmic condition on the modulus of continuity of the nonlinearity exponent p(x), which ensures that a Laplacian with variable order of nonlinearity inherits many properties of the usual p-Laplacian of constant order. One of these is the so-called improved integrability of the gradient of the solution. It is proved in this paper that this property holds also under a slightly more general condition on the exponent p(x), although then the improvement of integrability is logarithmic rather than power-like. The method put forward is based on a new generalization of Gehring's lemma, which relies upon the reverse Hoelder inequality 'with increased support and exponent on the right-hand side'. A counterexample is constructed that reveals the extent to which the condition on the modulus of continuity obtained is sharp. Bibliography: 28 titles.

Nonlinear Science

CERN Document Server

Yoshida, Zensho

2010-01-01

This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl

Higher order criterion for the nonexistence of formal first integral for nonlinear systems

Directory of Open Access Journals (Sweden)

Zhiguo Xu

2017-11-01

Full Text Available The main purpose of this article is to find a criterion for the nonexistence of formal first integrals for nonlinear systems under general resonance. An algorithm illustrates an application to a class of generalized Lokta-Volterra systems. Our result generalize the classical Poincare's nonintegrability theorem and the existing results in the literature.

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

International Nuclear Information System (INIS)

Sui, Jinxue; Yang, Li; Hu, Yunan

2016-01-01

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

An Integration Testing Facility for the CERN Accelerator Controls System

CERN Document Server

Stapley, N; Bau, J C; Deghaye, S; Dehavay, C; Sliwinski, W; Sobczak, M

2009-01-01

A major effort has been invested in the design, development, and deployment of the LHC Control System. This large control system is made up of a set of core components and dependencies, which although tested individually, are often not able to be tested together on a system capable of representing the complete control system environment, including hardware. Furthermore this control system is being adapted and applied to CERN's whole accelerator complex, and in particular for the forthcoming renovation of the PS accelerators. To ensure quality is maintained as the system evolves, and toimprove defect prevention, the Controls Group launched a project to provide a dedicated facility for continuous, automated, integration testing of its core components to incorporate into its production process. We describe the project, initial lessons from its application, status, and future directions.

Stripline kicker for integrable optics test accelerator

Energy Technology Data Exchange (ETDEWEB)

Antipov, Sergey A.; Didenko, Alexander; Lebedev, Valeri; Valishev, Alexander

2016-06-30

We present a design of a stripline kicker for Integrable Optics Test Accelerator (IOTA). For its experimental program IOTA needs two full-aperture kickers, capable to create an arbitrary controllable kick in 2D. For that reason their strengths are variable in a wide range of amplitudes up to 16 mrad, and the pulse length 100 ns is less than a revolution period for electrons. In addition, the kicker should have a physical aperture of 40 mm for a proposed operation with proton beam, and an outer size of 70 mm to fit inside existing quadrupole magnets to save space in the ring. Computer simulations using CST Microwave Studio show high field uniformity and wave impedance close to 50 {\\Omega}.

Integral reinforcement learning for continuous-time input-affine nonlinear systems with simultaneous invariant explorations.

Science.gov (United States)

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

2015-05-01

This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods.

Nonlinear Waves in Complex Systems

DEFF Research Database (Denmark)

2007-01-01

The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...

Excitation of Accelerating Plasma Waves by Counter-propagating Laser Beams

International Nuclear Information System (INIS)

Gennady Shvets; Nathaniel J. Fisch; Alexander Pukhov

2001-01-01

Generation of accelerating plasma waves using two counter-propagating laser beams is considered. Colliding-beam accelerator requires two laser pulses: the long pump and the short timing beam. We emphasize the similarities and differences between the conventional laser wakefield accelerator and the colliding-beam accelerator (CBA). The highly nonlinear nature of the wake excitation is explained using both nonlinear optics and plasma physics concepts. Two regimes of CBA are considered: (i) the short-pulse regime, where the timing beam is shorter than the plasma period, and (ii) the parametric excitation regime, where the timing beam is longer than the plasma period. Possible future experiments are also outlined

Self-accelerating universe in Galileon cosmology

International Nuclear Information System (INIS)

Silva, Fabio P.; Koyama, Kazuya

2009-01-01

We present a cosmological model with a solution that self-accelerates at late times without signs of ghost instabilities on small scales. The model is a natural extension of the Brans-Dicke (BD) theory including a nonlinear derivative interaction, which appears in a theory with the Galilean shift symmetry. The existence of the self-accelerating universe requires a negative BD parameter but, thanks to the nonlinear term, small fluctuations around the solution are stable on small scales. General relativity is recovered at early times and on small scales by this nonlinear interaction via the Vainshtein mechanism. At late time, gravity is strongly modified and the background cosmology shows a phantomlike behavior and the growth rate of structure formation is enhanced. Thus this model leaves distinct signatures in cosmological observations and it can be distinguished from standard LCDM cosmology.

A new 3-D integral code for computation of accelerator magnets

International Nuclear Information System (INIS)

Turner, L.R.; Kettunen, L.

1991-01-01

For computing accelerator magnets, integral codes have several advantages over finite element codes; far-field boundaries are treated automatically, and computed field in the bore region satisfy Maxwell's equations exactly. A new integral code employing edge elements rather than nodal elements has overcome the difficulties associated with earlier integral codes. By the use of field integrals (potential differences) as solution variables, the number of unknowns is reduced to one less than the number of nodes. Two examples, a hollow iron sphere and the dipole magnet of Advanced Photon Source injector synchrotron, show the capability of the code. The CPU time requirements are comparable to those of three-dimensional (3-D) finite-element codes. Experiments show that in practice it can realize much of the potential CPU time saving that parallel processing makes possible. 8 refs., 4 figs., 1 tab

Nonlinear silicon photonics

Science.gov (United States)

Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.

2017-09-01

Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.

Nonlinear interaction of charged particles with strong laser pulses in a gaseous media

Directory of Open Access Journals (Sweden)

H. K. Avetissian

2007-07-01

Full Text Available The charged particles nonlinear dynamics in the field of a strong electromagnetic wave pulse of finite duration and certain form of the envelope, in the refractive medium with a constant and variable refraction indexes, is investigated by means of numerical integration of the classical relativistic equations of motion. The particle energy dependence on the pulse intensity manifests the nonlinear threshold phenomenon of a particle reflection and capture by actual laser pulses in dielectric-gaseous media that takes place for a plane electromagnetic wave in the induced Cherenkov process. Laser acceleration of the particles in the result of the reflection from the pulse envelope and in the capture regime with the variable refraction index along the pulse propagation direction is investigated.

Plasma based charged-particle accelerators

International Nuclear Information System (INIS)

Bingham, R; Mendonca, J T; Shukla, P K

2004-01-01

Studies of charged-particle acceleration processes remain one of the most important areas of research in laboratory, space and astrophysical plasmas. In this paper, we present the underlying physics and the present status of high gradient and high energy plasma accelerators. We will focus on the acceleration of charged particles to relativistic energies by plasma waves that are created by intense laser and particle beams. The generation of relativistic plasma waves by intense lasers or electron beams in plasmas is important in the quest for producing ultra-high acceleration gradients for accelerators. With the development of compact short pulse high brightness lasers and electron positron beams, new areas of studies for laser/particle beam-matter interactions is opening up. A number of methods are being pursued vigorously to achieve ultra-high acceleration gradients. These include the plasma beat wave accelerator mechanism, which uses conventional long pulse (∼100 ps) modest intensity lasers (I ∼ 10 14 -10 16 W cm -2 ), the laser wakefield accelerator (LWFA), which uses the new breed of compact high brightness lasers ( 10 18 W cm -2 , the self-modulated LWFA concept, which combines elements of stimulated Raman forward scattering, and electron acceleration by nonlinear plasma waves excited by relativistic electron and positron bunches. In the ultra-high intensity regime, laser/particle beam-plasma interactions are highly nonlinear and relativistic, leading to new phenomena such as the plasma wakefield excitation for particle acceleration, relativistic self-focusing and guiding of laser beams, high-harmonic generation, acceleration of electrons, positrons, protons and photons. Fields greater than 1 GV cm -1 have been generated with particles being accelerated to 200 MeV over a distance of millimetre. Plasma wakefields driven by positron beams at the Stanford Linear Accelerator Center facility have accelerated the tail of the positron beam. In the near future

Nonlinear dynamics of autonomous vehicles with limits on acceleration

Science.gov (United States)

Davis, L. C.

2014-07-01

The stability of autonomous vehicle platoons with limits on acceleration and deceleration is determined. If the leading-vehicle acceleration remains within the limits, all vehicles in the platoon remain within the limits when the relative-velocity feedback coefficient is equal to the headway time constant [k=1/h]. Furthermore, if the sensitivity α>1/h, no collisions occur. String stability for small perturbations is assumed and the initial condition is taken as the equilibrium state. Other values of k and α that give stability with no collisions are found from simulations. For vehicles with non-negligible mechanical response, simulations indicate that the acceleration-feedback-control gain might have to be dynamically adjusted to obtain optimal performance as the response time changes with engine speed. Stability is demonstrated for some perturbations that cause initial acceleration or deceleration greater than the limits, yet do not cause collisions.

Monitoring of Non-Linear Ground Movement in an Open Pit Iron Mine Based on an Integration of Advanced DInSAR Techniques Using TerraSAR-X Data

Directory of Open Access Journals (Sweden)

José Claudio Mura

2016-05-01

Full Text Available This work presents an investigation to determine ground deformation based on an integration of DInSAR Time-Series (DTS and Persistent Scatterer Interferometry (PSI techniques aiming at detecting high rates of linear and non-linear ground movement. The combined techniques were applied in an open pit iron mine located in Carajás Mineral Province (Brazilian Amazon region, using a set of 33 TerraSAR-X-1 images acquired from March 2012 to April 2013 when, due to a different deformation behavior during the dry and wet seasons in the Amazon region, a non-linear deformation was detected. The DTS analysis was performed on a stack of multi-look unwrapped interferograms using an extension of the SVD (Singular Value Decomposition, where a set of additional weighted constraints on the acceleration of the displacement was incorporated to control the smoothness of the time-series solutions, whose objective was to correct the atmospheric phase artifacts. The height errors and the deformation history provided by the DTS technique were used as previous information to perform the PSI analysis. This procedure improved the capability of the PSI technique to detect non-linear movement as well as to increase the numbers of point density of the final results. The results of the combined techniques are presented and compared with total station/prisms and ground-based radar (GBR measurements.

A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system

International Nuclear Information System (INIS)

Zhao, Hai-qiong; Yuan, Jinyun

2016-01-01

A new integrable semi-discrete version is proposed for the multi-component coherently coupled nonlinear Schrödinger equation. The integrability of the semi-discrete system is confirmed by existence of Lax pair and infinite number of conservation laws. With the aid of gauge transformations, explicit formulas for N -fold Darboux transformations are derived whereby some physically important solutions of the system are presented. Furthermore, the theory of the semi-discrete system including Lax pair, Darboux transformations, exact solutions and infinite number of conservation laws are shown for their continuous counterparts in the continuous limit. (paper)

Acceleration of the AFEN method by two-node nonlinear iteration

Energy Technology Data Exchange (ETDEWEB)

Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1999-12-31

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

Acceleration of the AFEN method by two-node nonlinear iteration

Energy Technology Data Exchange (ETDEWEB)

Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1998-12-31

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

GPU-based, parallel-line, omni-directional integration of measured acceleration field to obtain the 3D pressure distribution

Science.gov (United States)

Wang, Jin; Zhang, Cao; Katz, Joseph

2016-11-01

A PIV based method to reconstruct the volumetric pressure field by direct integration of the 3D material acceleration directions has been developed. Extending the 2D virtual-boundary omni-directional method (Omni2D, Liu & Katz, 2013), the new 3D parallel-line omni-directional method (Omni3D) integrates the material acceleration along parallel lines aligned in multiple directions. Their angles are set by a spherical virtual grid. The integration is parallelized on a Tesla K40c GPU, which reduced the computing time from three hours to one minute for a single realization. To validate its performance, this method is utilized to calculate the 3D pressure fields in isotropic turbulence and channel flow using the JHU DNS Databases (http://turbulence.pha.jhu.edu). Both integration of the DNS acceleration as well as acceleration from synthetic 3D particles are tested. Results are compared to other method, e.g. solution to the Pressure Poisson Equation (e.g. PPE, Ghaemi et al., 2012) with Bernoulli based Dirichlet boundary conditions, and the Omni2D method. The error in Omni3D prediction is uniformly low, and its sensitivity to acceleration errors is local. It agrees with the PPE/Bernoulli prediction away from the Dirichlet boundary. The Omni3D method is also applied to experimental data obtained using tomographic PIV, and results are correlated with deformation of a compliant wall. ONR.

Integration of Geometrical and Material Nonlinear Energy Sink with Piezoelectric Material Energy Harvester

Directory of Open Access Journals (Sweden)

Ye-Wei Zhang

2017-01-01

Full Text Available This paper presents a novel design by integrating geometrical and material nonlinear energy sink (NES with a piezoelectric-based vibration energy harvester under shock excitation, which can realize vibration control and energy harvesting. The nonlinear spring and hysteresis behavior of the NES could reflect geometrical and material nonlinearity, respectively. Two configurations of the piezoelectric device, including the piezoelectric element embedded between the NES mass and the single-degree-of-freedom system or ground, are utilised to examine the energy dissipated by damper and hysteresis behavior of NES and the energy harvested by the piezoelectric element. Similar numerical research methods of Runge-Kutta algorithm are used to investigate the two configurations. The energy transaction measure (ETM is adopted to examine the instantaneous energy transaction between the primary and the NES-piezoelectricity system. And it demonstrates that the dissipated and harvested energy transaction is transferred from the primary system to the NES-piezoelectricity system and the instantaneous transaction of mechanical energy occupies a major part of the energy of transaction. Both figurations could realize vibration control efficiently.

Integration of Attributes from Non-Linear Characterization of Cardiovascular Time-Series for Prediction of Defibrillation Outcomes.

Directory of Open Access Journals (Sweden)

Sharad Shandilya

Full Text Available The timing of defibrillation is mostly at arbitrary intervals during cardio-pulmonary resuscitation (CPR, rather than during intervals when the out-of-hospital cardiac arrest (OOH-CA patient is physiologically primed for successful countershock. Interruptions to CPR may negatively impact defibrillation success. Multiple defibrillations can be associated with decreased post-resuscitation myocardial function. We hypothesize that a more complete picture of the cardiovascular system can be gained through non-linear dynamics and integration of multiple physiologic measures from biomedical signals.Retrospective analysis of 153 anonymized OOH-CA patients who received at least one defibrillation for ventricular fibrillation (VF was undertaken. A machine learning model, termed Multiple Domain Integrative (MDI model, was developed to predict defibrillation success. We explore the rationale for non-linear dynamics and statistically validate heuristics involved in feature extraction for model development. Performance of MDI is then compared to the amplitude spectrum area (AMSA technique.358 defibrillations were evaluated (218 unsuccessful and 140 successful. Non-linear properties (Lyapunov exponent > 0 of the ECG signals indicate a chaotic nature and validate the use of novel non-linear dynamic methods for feature extraction. Classification using MDI yielded ROC-AUC of 83.2% and accuracy of 78.8%, for the model built with ECG data only. Utilizing 10-fold cross-validation, at 80% specificity level, MDI (74% sensitivity outperformed AMSA (53.6% sensitivity. At 90% specificity level, MDI had 68.4% sensitivity while AMSA had 43.3% sensitivity. Integrating available end-tidal carbon dioxide features into MDI, for the available 48 defibrillations, boosted ROC-AUC to 93.8% and accuracy to 83.3% at 80% sensitivity.At clinically relevant sensitivity thresholds, the MDI provides improved performance as compared to AMSA, yielding fewer unsuccessful defibrillations

Coherent Synchrotron Radiation A Simulation Code Based on the Non-Linear Extension of the Operator Splitting Method

CERN Document Server

Dattoli, Giuseppe

2005-01-01

The coherent synchrotron radiation (CSR) is one of the main problems limiting the performance of high intensity electron accelerators. A code devoted to the analysis of this type of problems should be fast and reliable: conditions that are usually hardly achieved at the same time. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problem in accelerators. The extension of these method to the non-linear case is ideally suited to treat CSR instability problems. We report on the development of a numerical code, based on the solution of the Vlasov equation, with the inclusion of non-linear contribution due to wake field effects. The proposed solution method exploits an algebraic technique, using exponential operators implemented numerically in C++. We show that the integration procedure is capable of reproducing the onset of an instability and effects associated with bunching mechanisms leading to the growth of the instability itself. In addition, parametric studies a...

Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems

International Nuclear Information System (INIS)

Alabau-Boussouira, Fatiha

2005-01-01

This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy

LEGO - A Class Library for Accelerator Design and Simulation

International Nuclear Information System (INIS)

Cai, Yunhai

1998-01-01

An object-oriented class library of accelerator design and simulation is designed and implemented in a simple and modular fashion. All physics of single-particle dynamics is implemented based on the Hamiltonian in the local frame of the component. Symplectic integrators are used to approximate the integration of the Hamiltonian. A differential algebra class is introduced to extract a Taylor map up to arbitrary order. Analysis of optics is done in the same way both for the linear and non-linear cases. Recently, Monte Carlo simulation of synchrotron radiation has been added into the library. The code is used to design and simulate the lattices of the PEP-II and SPEAR3. And it is also used for the commissioning of the PEP-II. Some examples of how to use the library will be given

High Power Amplifiers Chain nonlinearity influence on the accelerating beam stability in free electron laser (FLASH)

CERN Document Server

Cichalewski, w

2010-01-01

The high power amplifiers transfer characteristics nonlinearities can have a negative influence on the overall system performance. This is also true for the TESLA superconducting cavities accelerating field parameters control systems. This Low Level Radio Frequency control systems uses microwave high power amplifiers (like 10 MW klystrons) as actuators in the mentioned feedback loops. The amplitude compression and phase deviations phenomena introduced to the control signals can reduce the feedback performance and cause electron beam energy instabilities. The transfer characteristics deviations in the Free Electron Laser in Hamburg experiment have been investigated. The outcome of this study together with the description of the developed linearization method based on the digital predistortion approach have been described in this paper. Additionally, the results from the linearization tool performance tests in the FLASH's RF systems have been placed.

Long-range corrected density functional theory with accelerated Hartree-Fock exchange integration using a two-Gaussian operator [LC-ωPBE(2Gau)].

Science.gov (United States)

Song, Jong-Won; Hirao, Kimihiko

2015-10-14

Since the advent of hybrid functional in 1993, it has become a main quantum chemical tool for the calculation of energies and properties of molecular systems. Following the introduction of long-range corrected hybrid scheme for density functional theory a decade later, the applicability of the hybrid functional has been further amplified due to the resulting increased performance on orbital energy, excitation energy, non-linear optical property, barrier height, and so on. Nevertheless, the high cost associated with the evaluation of Hartree-Fock (HF) exchange integrals remains a bottleneck for the broader and more active applications of hybrid functionals to large molecular and periodic systems. Here, we propose a very simple yet efficient method for the computation of long-range corrected hybrid scheme. It uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. As a result, the two-Gaussian HF operator, which mimics the shape of the error function operator, reduces computational time dramatically (e.g., about 14 times acceleration in C diamond calculation using periodic boundary condition) and enables lower scaling with system size, while maintaining the improved features of the long-range corrected density functional theory.

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)

Nonlinear dynamics of electromagnetic pulses in cold relativistic plasmas

International Nuclear Information System (INIS)

Bonatto, A.; Pakter, R.; Rizzato, F.B.

2004-01-01

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)

A modeling GUI for accelerator physics of the storage ring at SSRF

International Nuclear Information System (INIS)

Chen Guangling; Tian Shunqiang; Liu Guimin; Jiang Bocheng

2009-01-01

In this paper, we report a MATLAB-based GUI tool, bodgui, which integrates functions of lattice editor, linear match, and nonlinear optimization, and visualized tracking functions for beam optics design. A user can switch his/her design procedures one to another. Flexibilities are provided for adjusting or optimizing the lattice settings in commissioning or operation of the accelerators. The algorithm of the linear match and nonlinear optimization, and the GUI windows including the main functions and running status, are presented. The SSRF storage ring was employed as a test lattice. Several optics modes designed and optimized by the GUI tools were used for commissioning the storage ring. Functions of bodgui tool are machine-independent, and it can be well applied to modern light sources being built in other parts of the world. (authors)

Nonlinear cyclotron-resonance accelerations by a generalized EM wave

International Nuclear Information System (INIS)

Akimoto, K.; Hojo, H.

2004-01-01

Particle accelerations by a one-dimensional, electromagnetic, dispersive pulse in an external magnetic field are investigated. It is found that the well-known cyclotron resonance may be classified into three regimes as the length and/or the amplitude of the pulse are varied. Namely, as the pulse amplitude increases, the transit-time cyclotron-resonance acceleration (CRA) evolves to phase trapping, and reflect particles. The amplitude and wave dispersion as well as the pulse length strongly affect those accelerations. The interesting phenomena of quantization of resonance velocities in between the two regimes are also investigated. This new mechanism may lead to wave amplification at some discrete frequencies other than the cyclotron frequency. (authors)

Single-particle dynamics in a nonlinear accelerator lattice: attaining a large tune spread with octupoles in IOTA

Science.gov (United States)

Antipov, S. A.; Nagaitsev, S.; Valishev, A.

2017-04-01

Fermilab is constructing the Integrable Optics Test Accelerator (IOTA) as the centerpiece of the Accelerator R&D Program towards high-intensity circular machines. One of the factors limiting the beam intensity in present circular accelerators is collective instabilities, which can be suppressed by a spread of betatron frequencies (tunes) through the Landau damping mechanism or by an external damper, if the instability is slow enough. The spread is usually created by octupole magnets, which introduce the tune dependence on the amplitude and, in some cases, by a chromatic spread (tune dependence on particle's momentum). The introduction of octupoles usually has both beneficial (improved Landau damping) and harmful properties, such as a resonant behavior and a reduction of the dynamic aperture. One of the research goals at the IOTA ring is to achieve a large betatron tune spread, while retaining a large dynamic aperture, using conventional octupole magnets in a special but realistic accelerator configuration. The configuration, although not integrable by design, approximates an autonomous 2D Hamiltonian system. In this paper, we present results of computer simulations of an electron beam in the IOTA by particle tracking and the Frequency Map Analysis. The results show that the ring's octupole magnets can be configured to provide a betatron tune shift of 0.08 (for particles at large amplitudes) with the dynamical aperture of over 20 beam sigma for a 150-MeV electron beam. The influence of the synchrotron motion, lattice errors, and magnet imperfections is insignificant for the parameters and levels of tolerances set by the design of the ring. The described octupole insert could be beneficial for enhancing Landau damping in high intensity machines.

On a method for constructing the Lax pairs for nonlinear integrable equations

International Nuclear Information System (INIS)

Habibullin, I T; Poptsova, M N; Khakimova, A R

2016-01-01

We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found immediately, coinciding with the linearization of the considered nonlinear equation. The second one is obtained as an invariant manifold to the linearized equation. A surprisingly simple relation between the second operator of the Lax pair and the recursion operator is discussed: the recursion operator can immediately be found from the Lax pair. Examples considered in the article are convincing evidence that the found Lax pairs differ from the classical ones. The examples also show that the suggested objects are true Lax pairs which allow the construction of infinite series of conservation laws and hierarchies of higher symmetries. In the case of the hyperbolic type partial differential equation our algorithm is slightly modified; in order to construct the Lax pairs from the invariant manifolds we use the cutting off conditions for the corresponding infinite Laplace sequence. The efficiency of the method is illustrated by application to some equations given in the Svinolupov–Sokolov classification list for which the Lax pairs and the recursion operators have not been found earlier. (paper)

A Precision-Positioning Method for a High-Acceleration Low-Load Mechanism Based on Optimal Spatial and Temporal Distribution of Inertial Energy

Directory of Open Access Journals (Sweden)

Xin Chen

2015-09-01

Full Text Available High-speed and precision positioning are fundamental requirements for high-acceleration low-load mechanisms in integrated circuit (IC packaging equipment. In this paper, we derive the transient nonlinear dynamicresponse equations of high-acceleration mechanisms, which reveal that stiffness, frequency, damping, and driving frequency are the primary factors. Therefore, we propose a new structural optimization and velocity-planning method for the precision positioning of a high-acceleration mechanism based on optimal spatial and temporal distribution of inertial energy. For structural optimization, we first reviewed the commonly flexible multibody dynamic optimization using equivalent static loads method (ESLM, and then we selected the modified ESLM for optimal spatial distribution of inertial energy; hence, not only the stiffness but also the inertia and frequency of the real modal shapes are considered. For velocity planning, we developed a new velocity-planning method based on nonlinear dynamic-response optimization with varying motion conditions. Our method was verified on a high-acceleration die bonder. The amplitude of residual vibration could be decreased by more than 20% via structural optimization and the positioning time could be reduced by more than 40% via asymmetric variable velocity planning. This method provides an effective theoretical support for the precision positioning of high-acceleration low-load mechanisms.

Effect of strong-focusing field distortions on particle motion in a linear accelerator

International Nuclear Information System (INIS)

Bondarev, B.I.; Durkin, A.P.; Solov'ev, L.Yu.

1979-01-01

The increased sensitivity of quadrupole focusing channel used in the highenergetic part of the linear accelerator makes it necessary to pay serious attention to the effect of various distortions of focusing fields on the transverse motion of the beam. The distortions may cause the inadmissible losses of particles in the accelerator. To achieve this aim the main equation of disturbed motion of particles in the linear accelerator, obtained by analogy with the cyclic accelerator theory is presented. The investigation of the solutions of this equation has permitted to obtain the analytical formulas for the estimation of the beam size increase under the effect of focusing field distortions of various types, such as structural non-linearity, gradient errors, random non-linearity, channel axis deformation. While studying the effect of structural non-linearity considered are the resonance effects and obtained are the relations describing the maximum beam size increase in the channel of the linear accelerator in the presence and in the absence of the resonance

Optimal Constant-Stress Accelerated Degradation Test Plans Using Nonlinear Generalized Wiener Process

Directory of Open Access Journals (Sweden)

Zhen Chen

2016-01-01

Full Text Available Accelerated degradation test (ADT has been widely used to assess highly reliable products’ lifetime. To conduct an ADT, an appropriate degradation model and test plan should be determined in advance. Although many historical studies have proposed quite a few models, there is still room for improvement. Hence we propose a Nonlinear Generalized Wiener Process (NGWP model with consideration of the effects of stress level, product-to-product variability, and measurement errors for a higher estimation accuracy and a wider range of use. Then under the constraints of sample size, test duration, and test cost, the plans of constant-stress ADT (CSADT with multiple stress levels based on the NGWP are designed by minimizing the asymptotic variance of the reliability estimation of the products under normal operation conditions. An optimization algorithm is developed to determine the optimal stress levels, the number of units allocated to each level, inspection frequency, and measurement times simultaneously. In addition, a comparison based on degradation data of LEDs is made to show better goodness-of-fit of the NGWP than that of other models. Finally, optimal two-level and three-level CSADT plans under various constraints and a detailed sensitivity analysis are demonstrated through examples in this paper.

Methods of stability analysis in nonlinear mechanics

International Nuclear Information System (INIS)

Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.

1989-01-01

We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs

Spinor Field Nonlinearity and Space-Time Geometry

Science.gov (United States)

Saha, Bijan

2018-03-01

Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time

The use of a path independent integral in non-linear fracture mechanics

International Nuclear Information System (INIS)

Hellen, T.K.

1977-01-01

A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. Numerical examples are presented comparing the J and J* integrals for a number of cracked plates under thermal, plastic and creep environments. To demonstrate the accuracy for a simple thermo-elastic case, a centre cracked plate subject to a symmetric quadratic gradient is included. Here, the J integral is shown to be path dependent whereas good independence is seen for the J* integral. The case of an elastic-plastic plate is invetigated to demonstrate path independence for both integrals in non-linear elasticity, and the effects of unloading are discussed. An alternative method for obtaining the change of potential energy over a small crack extension is briefly mentioned and compared to the J and J* results in this case. An axisymmetric bar with an internal penny-shaped crack subjected to tension is discussed under elastic-plastic materials behavior

Radiation pressure acceleration of ultrathin foils

Energy Technology Data Exchange (ETDEWEB)

Macchi, Andrea; Veghini, Silvia; Pegoraro, Francesco [Department of Physics ' E. Fermi' , Largo B Pontecorvo 3, 56127 Pisa (Italy); Liseykina, Tatyana V, E-mail: macchi@df.unipi.i [Max Planck Institute for Nuclear Physics, Heidelberg (Germany)

2010-04-15

The acceleration of sub-wavelength, solid-density plasma foils by the ultraintense radiation pressure of circularly polarized laser pulses is investigated analytically and with simulations. An improved 'Light Sail' or accelerating mirror model, accounting for nonlinear self-induced transparency effects, is used for estimating the optimal thickness for acceleration. The model predictions are in good agreement with one-dimensional simulations. These latter are analyzed in detail to unfold the dynamics and self-organization of electrons and ions during the acceleration. Two-dimensional simulations are also performed to address the effects of target bending and of laser intensity inhomogeneity.

Modeling nonlinearities in MEMS oscillators.

Science.gov (United States)

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Integrated Vibration and Acceleration Testing to Reduce Payload Mass, Cost and Mission Risk, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — We propose to develop a capability to provide integrated acceleration, vibration, and shock testing using a state-of-the-art centrifuge, allowing for the test of...

Single-particle dynamics in a nonlinear accelerator lattice: attaining a large tune spread with octupoles in IOTA

International Nuclear Information System (INIS)

Antipov, S.A.; Nagaitsev, S.; Valishev, A.

2017-01-01

Fermilab is constructing the Integrable Optics Test Accelerator (IOTA) as the centerpiece of the Accelerator R and D Program towards high-intensity circular machines. One of the factors limiting the beam intensity in present circular accelerators is collective instabilities, which can be suppressed by a spread of betatron frequencies (tunes) through the Landau damping mechanism or by an external damper, if the instability is slow enough. The spread is usually created by octupole magnets, which introduce the tune dependence on the amplitude and, in some cases, by a chromatic spread (tune dependence on particle's momentum). The introduction of octupoles usually has both beneficial (improved Landau damping) and harmful properties, such as a resonant behavior and a reduction of the dynamic aperture. One of the research goals at the IOTA ring is to achieve a large betatron tune spread, while retaining a large dynamic aperture, using conventional octupole magnets in a special but realistic accelerator configuration. The configuration, although not integrable by design, approximates an autonomous 2D Hamiltonian system. In this paper, we present results of computer simulations of an electron beam in the IOTA by particle tracking and the Frequency Map Analysis. The results show that the ring's octupole magnets can be configured to provide a betatron tune shift of 0.08 (for particles at large amplitudes) with the dynamical aperture of over 20 beam sigma for a 150-MeV electron beam. The influence of the synchrotron motion, lattice errors, and magnet imperfections is insignificant for the parameters and levels of tolerances set by the design of the ring. The described octupole insert could be beneficial for enhancing Landau damping in high intensity machines.

Gallium nitride on gallium oxide substrate for integrated nonlinear optics

KAUST Repository

Awan, Kashif M.; Dolgaleva, Ksenia; Mumthaz Muhammed, Mufasila; Roqan, Iman S.

2017-01-01

Gallium Nitride (GaN), being a direct bandgap semiconductor with a wide bandgap and high thermal stability, is attractive for optoelectronic and electronic applications. Furthermore, due to its high optical nonlinearity — the characteristic of all 111-V semiconductors — GaN is also expected to be a suitable candidate for integrated nonlinear photonic circuits for a plethora of apphcations, ranging from on-chip wavelength conversion to quantum computing. Although GaN devices are in commercial production, it still suffers from lack of a suitable substrate material to reduce structural defects like high densities of threading dislocations (TDs), stacking faults, and grain boundaries. These defects significandy deteriorate the optical quality of the epi-grown GaN layer, since they act as non-radiative recombination centers. Recent studies have shown that GaN grown on (−201) β-Gallium Oxide (Ga2O3) has superior optical quality due to a better lattice matching as compared to GaN grown on Sapphire (Al2O3) [1-3]. In this work, we report on the fabrication of GaN waveguides on GaiOj substrate and their optical characterization to assess their feasibihty for efficient four-wave mixing (FWM).

Gallium nitride on gallium oxide substrate for integrated nonlinear optics

KAUST Repository

Awan, Kashif M.

2017-11-22

Gallium Nitride (GaN), being a direct bandgap semiconductor with a wide bandgap and high thermal stability, is attractive for optoelectronic and electronic applications. Furthermore, due to its high optical nonlinearity — the characteristic of all 111-V semiconductors — GaN is also expected to be a suitable candidate for integrated nonlinear photonic circuits for a plethora of apphcations, ranging from on-chip wavelength conversion to quantum computing. Although GaN devices are in commercial production, it still suffers from lack of a suitable substrate material to reduce structural defects like high densities of threading dislocations (TDs), stacking faults, and grain boundaries. These defects significandy deteriorate the optical quality of the epi-grown GaN layer, since they act as non-radiative recombination centers. Recent studies have shown that GaN grown on (−201) β-Gallium Oxide (Ga2O3) has superior optical quality due to a better lattice matching as compared to GaN grown on Sapphire (Al2O3) [1-3]. In this work, we report on the fabrication of GaN waveguides on GaiOj substrate and their optical characterization to assess their feasibihty for efficient four-wave mixing (FWM).

Nonlinear theory of transverse-multimode plasma accelerators

International Nuclear Information System (INIS)

Kuzelev, M.V.; Panin, V.A.; Plotnikov, A.P.

1991-01-01

The excitation of the higher transverse modes in a plasma-filled waveguide by a high-power electron beam is considered. General nonlinear equations are obtained which treat the excitation of the higher transverse plasma waves by a high-current relativistic beam. Results are presented of the numerical solutions of these equations. In the case of ultrarelativistic beams analytical expressions are found for the maximum amplitudes of the excited modes and the Q of the amplification. Numerical estimates are presented for realistic parameters

MgB_{2} nonlinear properties investigated under localized high rf magnetic field excitation

Directory of Open Access Journals (Sweden)

Tamin Tai

2012-12-01

Full Text Available The high transition temperature and low surface resistance of MgB_{2} attracts interest in its potential application in superconducting radio frequency accelerating cavities. However, compared to traditional Nb cavities, the viability of MgB_{2} at high rf fields is still open to question. Our approach is to study the nonlinear electrodynamics of the material under localized rf magnetic fields. Because of the presence of the small superconducting gap in the π band, the nonlinear response of MgB_{2} at low temperature is potentially complicated compared to a single-gap s-wave superconductor such as Nb. Understanding the mechanisms of nonlinearity coming from the two-band structure of MgB_{2}, as well as extrinsic sources of nonlinearity, is an urgent requirement. A localized and strong rf magnetic field, created by a magnetic write head, is integrated into our nonlinear-Meissner-effect scanning microwave microscope [T. Tai et al., IEEE Trans. Appl. Supercond. 21, 2615 (2011ITASE91051-822310.1109/TASC.2010.2096531]. MgB_{2} films with thickness 50 nm, fabricated by a hybrid physical-chemical vapor deposition technique on dielectric substrates, are measured at a fixed location and show a strongly temperature-dependent third harmonic response. We propose that several possible mechanisms are responsible for this nonlinear response.

Wave transmission in nonlinear lattices

International Nuclear Information System (INIS)

Hennig, D.; Tsironis, G.P.

1999-01-01

The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Hamiltonian systems in accelerator physics

International Nuclear Information System (INIS)

Laslett, L.J.

1985-06-01

General features of the design of annular particle accelerators or storage rings are outlined and the Hamiltonian character of individual-ion motion is indicated. Examples of phase plots are presented, for the motion in one spatial degree of freedom, of an ion subject to a periodic nonlinear focusing force. A canonical transformation describing coupled nonlinear motion also is given, and alternative types of graphical display are suggested for the investigation of long-term stability in such cases. 7 figs

Acceleration of Feynman loop integrals in high-energy physics on many core GPUs

International Nuclear Information System (INIS)

Yuasa, F; Ishikawa, T; Hamaguchi, N; Koike, T; Nakasato, N

2013-01-01

The current and future colliders in high-energy physics require theorists to carry out a large scale computation for a precise comparison between experimental results and theoretical ones. In a perturbative approach several methods to evaluate Feynman loop integrals which appear in the theoretical calculation of cross-sections are well established in the one-loop level, however, more studies are necessary for higher-order levels. Direct Computation Method (DCM) is developed to evaluate multi-loop integrals. DCM is based on a combination of multidimensional numerical integration and extrapolation on a sequence of integrals. It is a fully numerical method and is applicable to a wide class of integrals with various physics parameters. The computation time depends on physics parameters and the topology of loop diagrams and it becomes longer for the two-loop integrals. In this paper we present our approach to the acceleration of the two-loop integrals by DCM on multiple GPU boards

Code comparison for accelerator design and analysis

International Nuclear Information System (INIS)

Parsa, Z.

1988-01-01

We present a comparison between results obtained from standard accelerator physics codes used for the design and analysis of synchrotrons and storage rings, with programs SYNCH, MAD, HARMON, PATRICIA, PATPET, BETA, DIMAD, MARYLIE and RACE-TRACK. In our analysis we have considered 5 (various size) lattices with large and small angles including AGS Booster (10/degree/ bend), RHIC (2.24/degree/), SXLS, XLS (XUV ring with 45/degree/ bend) and X-RAY rings. The differences in the integration methods used and the treatment of the fringe fields in these codes could lead to different results. The inclusion of nonlinear (e.g., dipole) terms may be necessary in these calculations specially for a small ring. 12 refs., 6 figs., 10 tabs

Does the Internet Accelerate the Integration of Domestic Markets? Evidence from China

Institute of Scientific and Technical Information of China (English)

Lijuan Xie; Wenwei Ai; Hao Zhang

2016-01-01

This paper employs a hybrid methodology that combines case study and econometric research to examine the impact of the Internet on domestic market integration.There is not much research on this issue in the literature.From the multi-case analysis,this paper firstly obtains two main indications which are clear yet contrary to each other about how the Internet influences the market integration process.To be specific,although the Internet has both the ability and the potential to promote market integration,it is not always effective and could even harm this process due to several constraints.Using a provincial-level panel dataset from 2007 to 2013 in China,this paper empirically investigates whether the Intemet plays a positive role in the market integration process.Contradictory to common expectations,we do not find any empirical evidence that the Internet accelerates the integration of domestic markets.Thus,when compared with taking advantage of Internet tools,manmade obstacles to market integration that exist in current trading systems and business models deserve more attention.

Semiconductor acceleration sensor

Science.gov (United States)

Ueyanagi, Katsumichi; Kobayashi, Mitsuo; Goto, Tomoaki

1996-09-01

This paper reports a practical semiconductor acceleration sensor especially suited for automotive air bag systems. The acceleration sensor includes four beams arranged in a swastika structure. Two piezoresistors are formed on each beam. These eight piezoresistors constitute a Wheatstone bridge. The swastika structure of the sensing elements, an upper glass plate and a lower glass plate exhibit the squeeze film effect which enhances air dumping, by which the constituent silicon is prevented from breakdown. The present acceleration sensor has the following features. The acceleration force component perpendicular to the sensing direction can be cancelled. The cross-axis sensitivity is less than 3 percent. And, the erroneous offset caused by the differences between the thermal expansion coefficients of the constituent materials can be canceled. The high aspect ratio configuration realized by plasma etching facilitates reducing the dimensions and improving the sensitivity of the acceleration sensor. The present acceleration sensor is 3.9 mm by 3.9 mm in area and 1.2 mm in thickness. The present acceleration sensor can measure from -50 to +50 G with sensitivity of 0.275 mV/G and with non-linearity of less than 1 percent. The acceleration sensor withstands shock of 3000 G.

AlGaAs-On-Insulator nonlinear photonics

DEFF Research Database (Denmark)

Pu, Minhao; Ottaviano, Luisa; Semenova, Elizaveta

We present an AlGaAs-on-insulator platform for integrated nonlinear photonics. We demonstrate the highest reported conversion efficiency and ultra-broadband four-wave mixing for an integrated platform around 1550nm......We present an AlGaAs-on-insulator platform for integrated nonlinear photonics. We demonstrate the highest reported conversion efficiency and ultra-broadband four-wave mixing for an integrated platform around 1550nm...

Particle acceleration inside PWN: Simulation and observational constraints with INTEGRAL

International Nuclear Information System (INIS)

Forot, M.

2006-12-01

The context of this thesis is to gain new constraints on the different particle accelerators that occur in the complex environment of neutron stars: in the pulsar magnetosphere, in the striped wind or wave outside the light cylinder, in the jets and equatorial wind, and at the wind terminal shock. An important tool to constrain both the magnetic field and primary particle energies is to image the synchrotron ageing of the population, but it requires a careful modelling of the magnetic field evolution in the wind flow. The current models and understanding of these different accelerators, the acceleration processes and open questions have been reviewed in the first part of the thesis. The instrumental part of this work involves the IBIS imager, on board the INTEGRAL satellite, that provides images with 12' resolution from 17 keV to MeV where the SPI spectrometer takes over up, to 10 MeV, but with a reduced 2 degrees resolution. A new method for using the double-layer IBIS imager as a Compton telescope with coded mask aperture. Its performance has been measured. The Compton scattering information and the achieved sensitivity also open a new window for polarimetry in gamma rays. A method has been developed to extract the linear polarization properties and to check the instrument response for fake polarimetric signals in the various backgrounds and projection effects

Integration of Transients in Axisymmetrical Cavities for Accelerators: Formulation and applications to BNL Photocathode Gun

International Nuclear Information System (INIS)

Parsa, Z.; Serafini, L.

1992-04-01

This note provides a sketch of the formalism used for the Integration of Transients in Axisymmetrical Cavities for Accelerators, (ITACA). Application to study the BNL Photocathode Gun via the code ITACA is also included

Classical mechanics and electromagnetism in accelerator physics

CERN Document Server

Stupakov, Gennady

2018-01-01

This self-contained textbook with exercises discusses a broad range of selected topics from classical mechanics and electromagnetic theory that inform key issues related to modern accelerators. Part I presents fundamentals of the Lagrangian and Hamiltonian formalism for mechanical systems, canonical transformations, action-angle variables, and then linear and nonlinear oscillators. The Hamiltonian for a circular accelerator is used to evaluate the equations of motion, the action, and betatron oscillations in an accelerator. From this base, we explore the impact of field errors and nonlinear resonances. This part ends with the concept of the distribution function and an introduction to the kinetic equation to describe large ensembles of charged particles and to supplement the previous single-particle analysis of beam dynamics. Part II focuses on classical electromagnetism and begins with an analysis of the electromagnetic field from relativistic beams, both in vacuum and in a resistive pipe. Plane electromagne...

Three-dimensional sparse electromagnetic imaging accelerated by projected steepest descent

KAUST Repository

Desmal, Abdulla

2016-11-02

An efficient and accurate scheme for solving the nonlinear electromagnetic inverse scattering problem on three-dimensional sparse investigation domains is proposed. The minimization problem is constructed in such a way that the data misfit between measurements and scattered fields (which are expressed as a nonlinear function of the contrast) is constrained by the contrast\\'s first norm. The resulting minimization problem is solved using nonlinear Landweber iterations accelerated using a steepest descent algorithm. A projection operator is applied at every iteration to enforce the sparsity constraint by thresholding the result of that iteration. Steepest descent algorithm ensures accelerated and convergent solution by utilizing larger iteration steps selected based on a necessary B-condition.

Calibration of the nonlinear ring model at the Diamond Light Source

Directory of Open Access Journals (Sweden)

R. Bartolini

2011-05-01

Full Text Available Nonlinear beam dynamics plays a crucial role in defining the performance of a storage ring. The beam lifetime, the injection efficiency, and the dynamic and momentum apertures available to the beam are optimized during the design phase by a proper optimization of the linear lattice and of the distribution of sextupole families. The correct implementation of the design model, especially the nonlinear part, is a nontrivial accelerator physics task. Several parameters of the nonlinear dynamics can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these parameters are extracted from the analysis of turn-by-turn data after the excitation of betatron oscillations of the particles in the ring. We present the experimental results of the campaign of measurements carried out at the Diamond storage ring to characterize the nonlinear beam dynamics. A combination of frequency map analysis with the detuning with momentum measurements has allowed for a precise calibration of the nonlinear model that can accurately reproduce the nonlinear beam dynamics in Diamond.

Electromagnetic nonlinear gyrokinetics with polarization drift

International Nuclear Information System (INIS)

Duthoit, F.-X.; Hahm, T. S.; Wang, Lu

2014-01-01

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete

Electron cyclotron harmonic wave acceleration

Science.gov (United States)

Karimabadi, H.; Menyuk, C. R.; Sprangle, P.; Vlahos, L.

1987-01-01

A nonlinear analysis of particle acceleration in a finite bandwidth, obliquely propagating electromagnetic cyclotron wave is presented. It has been suggested by Sprangle and Vlahos in 1983 that the narrow bandwidth cyclotron radiation emitted by the unstable electron distribution inside a flaring solar loop can accelerate electrons outside the loop by the interaction of a monochromatic wave propagating along the ambient magnetic field with the ambient electrons. It is shown here that electrons gyrating and streaming along a uniform, static magnetic field can be accelerated by interacting with the fundamental or second harmonic of a monochromatic, obliquely propagating cyclotron wave. It is also shown that the acceleration is virtually unchanged when a wave with finite bandwidth is considered. This acceleration mechanism can explain the observed high-energy electrons in type III bursts.

Electron cyclotron harmonic wave acceleration

International Nuclear Information System (INIS)

Karimabadi, H.; Menyuk, C.R.; Sprangle, P.; Vlahos, L.; Salonika Univ., Greece)

1987-01-01

A nonlinear analysis of particle acceleration in a finite bandwidth, obliquely propagating electromagnetic cyclotron wave is presented. It has been suggested by Sprangle and Vlahos in 1983 that the narrow bandwidth cyclotron radiation emitted by the unstable electron distribution inside a flaring solar loop can accelerate electrons outside the loop by the interaction of a monochromatic wave propagating along the ambient magnetic field with the ambient electrons. It is shown here that electrons gyrating and streaming along a uniform, static magnetic field can be accelerated by interacting with the fundamental or second harmonic of a monochromatic, obliquely propagating cyclotron wave. It is also shown that the acceleration is virtually unchanged when a wave with finite bandwidth is considered. This acceleration mechanism can explain the observed high-energy electrons in type III bursts. 31 references

A family of integrable differential–difference equations, its bi-Hamiltonian structure and binary nonlinearization of the Lax pairs and adjoint Lax pairs

International Nuclear Information System (INIS)

Xu Xixiang

2012-01-01

Highlights: ► We deduce a family of integrable differential–difference equations. ► We present a discrete Hamiltonian operator involving two arbitrary real parameters. ► We establish the bi-Hamiltonian structure for obtained integrable family. ► Liouvolle integrability of the obtained family is demonstrated. ► Every equation in obtained family is factored through the binary nonlinearization. - Abstract: A family of integrable differential–difference equations is derived by the method of Lax pairs. A discrete Hamiltonian operator involving two arbitrary real parameters is introduced. When the parameters are suitably selected, a pair of discrete Hamiltonian operators is presented. Bi-Hamiltonian structure of obtained family is established by discrete trace identity. Then, Liouville integrability for the obtained family is proved. Ultimately, through the binary nonlinearization of the Lax pairs and adjoint Lax pairs, every differential–difference equation in obtained family is factored by an integrable symplectic map and a finite-dimensional integrable system in Liouville sense.

Finding a nonlinear lattice with improved integrability using Lie transform perturbation theory

International Nuclear Information System (INIS)

Sonnad, Kiran G.; Cary, John R.

2004-01-01

A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case

The development and validation of a numerical integration method for non-linear viscoelastic modeling

Science.gov (United States)

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

The use of a path independent integral in non-linear fracture mechanics

International Nuclear Information System (INIS)

Hellen, T.K.

1977-01-01

The use of the Rice J-intergral to assess conditions at a crack tip in an elastic or non-linear elastic body is well known. The integral equals the energy release rate and is path independent for any contour surrounding the crack tip provided no other singularities are encompassed. The path independence propertiy breaks down, however, in more general situations such as in three dimensional stress systems, plasticity unloading, thermal or creep states. Hence the required crack tip characteristics represented by the value of the integral round a contour whose radius about the tip tends to zero, is not reproduced along contours away from the tip. Consequently, an alternative integral, designated J*, has been proposed which equals J for elastic cases and in the other cases cited above remains path independent. A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. (Auth. )

Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

Science.gov (United States)

Lu, Jianfeng; Zhou, Zhennan

2018-02-01

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

Accelerator physics and modeling: Proceedings

International Nuclear Information System (INIS)

Parsa, Z.

1991-01-01

This report contains papers on the following topics: Physics of high brightness beams; radio frequency beam conditioner for fast-wave free-electron generators of coherent radiation; wake-field and space-charge effects on high brightness beams. Calculations and measured results for BNL-ATF; non-linear orbit theory and accelerator design; general problems of modeling for accelerators; development and application of dispersive soft ferrite models for time-domain simulation; and bunch lengthening in the SLC damping rings

SINS/CNS Nonlinear Integrated Navigation Algorithm for Hypersonic Vehicle

Directory of Open Access Journals (Sweden)

Yong-jun Yu

2015-01-01

Full Text Available Celestial Navigation System (CNS has characteristics of accurate orientation and strong autonomy and has been widely used in Hypersonic Vehicle. Since the CNS location and orientation mainly depend upon the inertial reference that contains errors caused by gyro drifts and other error factors, traditional Strap-down Inertial Navigation System (SINS/CNS positioning algorithm setting the position error between SINS and CNS as measurement is not effective. The model of altitude azimuth, platform error angles, and horizontal position is designed, and the SINS/CNS tightly integrated algorithm is designed, in which CNS altitude azimuth is set as measurement information. GPF (Gaussian particle filter is introduced to solve the problem of nonlinear filtering. The results of simulation show that the precision of SINS/CNS algorithm which reaches 130 m using three stars is improved effectively.

f (T) Non-linear Massive Gravity and the Cosmic Acceleration

International Nuclear Information System (INIS)

Wu You; Chen Zu-Cheng; Wei Hao; Wang Jia-Xin

2015-01-01

Inspired by the f (R) non-linear massive gravity, we propose a new kind of modified gravity model, namely f (T) non-linear massive gravity, by adding the dRGT mass term reformulated in the vierbein formalism, to the f (T) theory. We then investigate the cosmological evolution of f (T) massive gravity, and constrain it by using the latest observational data. We find that it slightly favors a crossing of the phantom divide line from the quintessence-like phase (w_d_e > −1) to the phantom-like one (w_d_e < −1) as redshift decreases. (paper)

Asymptotic integration of some nonlinear differential equations with fractional time derivative

International Nuclear Information System (INIS)

Baleanu, Dumitru; Agarwal, Ravi P; Mustafa, Octavian G; Cosulschi, Mirel

2011-01-01

We establish that, under some simple integral conditions regarding the nonlinearity, the (1 + α)-order fractional differential equation 0 D α t (x') + f(t, x) = 0, t > 0, has a solution x element of C([0,+∞),R) intersection C 1 ((0,+∞),R), with lim t→0 [t 1-α x'(t)] element of R, which can be expanded asymptotically as a + bt α + O(t α-1 ) when t → +∞ for given real numbers a, b. Our arguments are based on fixed point theory. Here, 0 D α t designates the Riemann-Liouville derivative of order α in (0, 1).

Response of Non-Linear Systems to Renewal Impulses by Path Integration

DEFF Research Database (Denmark)

Nielsen, Søren R.K.; Iwankiewicz, R.

The cell-to-cell mapping (path integration) technique has been devised for MDOF non-linear and non-hysteretic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (an Erlang process). Since the renewal...... point process has not independent increments the state vector of the system, consisting of the generalized displacements and velocities, is not a Markov process. Initially it is shown how the indicated systems can be converted to an equivalent Poisson driven system at the expense of introducing...... additional discrete-valued state variables for which the stochastic equations are also formulated....

Integrable parameter regimes and stationary states of nonlinearly coupled electromagnetic and ion-acoustic waves

International Nuclear Information System (INIS)

Rao, N.N.

1998-01-01

A systematic analysis of the stationary propagation of nonlinearly coupled electromagnetic and ion-acoustic waves in an unmagnetized plasma via the ponderomotive force is carried out. For small but finite amplitudes, the governing equations have a Hamiltonian structure, but with a kinetic energy term that is not positive definite. The Hamiltonian is similar to the well-known Hacute enon endash Heiles Hamiltonian of nonlinear dynamics, and is completely integrable in three regimes of the allowed parameter space. The corresponding second invariants of motion are also explicitly obtained. The integrable parameter regimes correspond to supersonic values of the Mach number, which characterizes the propagation speed of the coupled waves. On the other hand, in the sub- as well as near-sonic regimes, the coupled mode equations admit different types of exact analytical solutions, which represent nonlinear localized eigenstates of the electromagnetic field trapped in the density cavity due to the ponderomotive potential. While the density cavity has always a single-dip structure, for larger amplitudes it can support higher-order modes having a larger number of nodes in the electromagnetic field. In particular, we show the existence of a new type of localized electromagnetic wave whose field intensity has a triple-hump structure. For typical parameter values, the triple-hump solitons propagate with larger Mach numbers that are closer to the sonic limit than the single- as well as the double-hump solitons, but carry a lesser amount of the electromagnetic field energy. A comparison between the different types of solutions is carried out. The possibility of the existence of trapped electromagnetic modes having a larger number of humps is also discussed. copyright 1998 American Institute of Physics

Nonlinear dynamics aspects of modern storage rings

International Nuclear Information System (INIS)

Helleman, R.H.G.; Kheifets, S.A.

1986-01-01

It is argued that the nonlinearity of storage rings becomes an essential problem as the design parameters of each new machine are pushed further and further. Yet the familiar methods of classical mechanics do not allow determination of single particle orbits over reasonable lengths of time. It is also argued that the single particle dynamics of a storage ring is possibly one of the cleanest and simplest nonlinear dynamical systems available with very few degrees of freedom. Hence, reasons are found for accelerator physicists to be interested in nonlinear dynamics and for researchers in nonlinear dynamics to be interested in modern storage rings. The more familiar methods of treating nonlinear systems routinely used in acclerator theory are discussed, pointing out some of their limitations and pitfalls. 39 refs., 1 fig

Integrability in Dynamical Systems: Florida Workshop in Nonlinear Astronomy, 3rd, University of Florida, Gainesville, Oct. 1, 2, 1987, Proceedings

International Nuclear Information System (INIS)

Buchler, J.R.; Ipser, J.R.; Williams, C.A.

1988-01-01

Recent advances in theoretical celestial mechanics are examined in reviews and reports. Topics addressed include resonant integrable models of galaxies, new integrable systems, Painleve expansions for integrable and nonintegrable ordinary differential equations, and particle-simulation solutions of the Vlasov equation in general relativity. Consideration is given to repulsive and attractive double-bubble space-times, the integrability of magnetic-confinement systems, Hannay's angle and Berry's phase in the classical adiabatic motion of charged particles, the integrability of the nonlinear wave equations, normalization in the face of integrability, and simplifications toward the integrability of perturbed Keplerian systems

MAGNUS-3D: Accelerator magnet calculations in 3-dimensions

Science.gov (United States)

Pissanetzky, S.

1988-12-01

MAGNUS-3D is a professional finite element code for nonlinear magnetic engineering. MAGNUS-3D can solve numerically any general problem of linear or nonlinear magnetostatics in three dimensions. The problem is formulated in a domain with Dirichlet, Neumann or periodic boundary conditions, that can contain any combination of conductors of any shape in space, nonlinear magnetic materials with magnetic properties specified by magnetization tables, and nonlinear permanent magnets with any given demagnetization curve. MAGNUS-3D uses the two-scalar-potentials formulation of Magnetostatics and the finite element method, has an automatic 3D mesh generator, and advanced post-processing features that include graphics on a variety of supported devices, tabulation, and calculation of design quantities required in Magnetic Engineering. MAGNUS-3D is a general purpose 3D code, but it has been extensively used for accelerator work and many special features required for accelerator engineering have been incorporated into the code. One of such features is the calculation of field harmonic coefficients averaged in the direction of the beam, so important for the design of magnet ends. Another feature is its ability to calculate line integrals of any field component along the direction of the beam, or plot the field as a function of the z coordinate. MAGNUS-3D has found applications to the design of accelerator magnets and spectrometers, steering magnets, wigglers and undulators for free electron lasers, microtrons and magnets for synchrotron light sources, as well as magnets for NMR and medical applications, recording heads and various magnetic devices. There are three more programs closely associated with MAGNUS-3D. MAGNUS-GKS is the graphical postprocessor for the package; it supports a numer of output devices, including color vector or bit map devices. WIRE is an independent program that can calculate the field produced by any configuration of electric conductors in space, at any

An integrated analog O/E/O link for multi-channel laser neurons

Energy Technology Data Exchange (ETDEWEB)

Nahmias, Mitchell A., E-mail: mnahmias@princeton.edu; Tait, Alexander N.; Tolias, Leonidas; Chang, Matthew P.; Ferreira de Lima, Thomas; Shastri, Bhavin J.; Prucnal, Paul R. [Electrical Engineering Department, Princeton University, 41 Olden St, Princeton, New Jersey 08540 (United States)

2016-04-11

We demonstrate an analog O/E/O electronic link to allow integrated laser neurons to accept many distinguishable, high bandwidth input signals simultaneously. This device utilizes wavelength division multiplexing to achieve multi-channel fan-in, a photodetector to sum signals together, and a laser cavity to perform a nonlinear operation. Its speed outpaces accelerated-time neuromorphic electronics, and it represents a viable direction towards scalable networking approaches.

Acceleration of a trailing positron bunch in a plasma wakefield accelerator

International Nuclear Information System (INIS)

Doche, A.; Beekman, C.; Corde, S.

2017-01-01

High gradients of energy gain and high energy efficiency are necessary parameters for compact, cost-efficient and high-energy particle colliders. Plasma Wakefield Accelerators (PWFA) offer both, making them attractive candidates for next-generation colliders. Here in these devices, a charge-density plasma wave is excited by an ultra-relativistic bunch of charged particles (the drive bunch). The energy in the wave can be extracted by a second bunch (the trailing bunch), as this bunch propagates in the wake of the drive bunch. While a trailing electron bunch was accelerated in a plasma with more than a gigaelectronvolt of energy gain, accelerating a trailing positron bunch in a plasma is much more challenging as the plasma response can be asymmetric for positrons and electrons. We report the demonstration of the energy gain by a distinct trailing positron bunch in a plasma wakefield accelerator, spanning nonlinear to quasi-linear regimes, and unveil the beam loading process underlying the accelerator energy efficiency. A positron bunch is used to drive the plasma wake in the experiment, though the quasi-linear wake structure could as easily be formed by an electron bunch or a laser driver. Finally, the results thus mark the first acceleration of a distinct positron bunch in plasma-based particle accelerators.

Experimental studies of plasma wake-field acceleration and focusing

International Nuclear Information System (INIS)

Rosenzweig, J.B.; Cole, B.; Ho, C.; Argonne National Lab., IL

1989-01-01

More than four years after the initial proposal of the Plasma Wake-field Accelerator (PWFA), it continues to be the object of much investigation, due to the promise of the ultra-high accelerating gradients that can exist in relativistic plasma waves driven in the wake of charged particle beams. These large amplitude plasma wake-fields are of interest in the laboratory, both for the wealth of basic nonlinear plasma wave phenomena which can be studied, as well as for the applications of acceleration of focusing of electrons and positrons in future linear colliders. Plasma wake-field waves are also of importance in nature, due to their possible role in direct cosmic ray acceleration. The purpose of the present work is to review the recent experimental advances made in PWFA research at Argonne National Laboratory, in which many interesting beam and plasma phenomena have been observed. Emphasis is given to discussion of the nonlinear aspects of the PWFA beam-plasma interaction. 29 refs., 13 figs

Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging

KAUST Repository

Desmal, Abdulla

2016-03-01

Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using

Infinite stochastic acceleration of charged particles from non-relativistic initial energies

International Nuclear Information System (INIS)

Buts, V.A.; Manujlenko, O.V.; Turkin, Yu.A.

1997-01-01

Stochastic charged particle acceleration by electro-magnetic field due to overlapping of non-linear cyclotron resonances is considered. It was shown that non-relativistic charged particles are involved in infinitive stochastic acceleration regime. This effect can be used for stochastic acceleration or for plasma heating by regular electro-magnetic fields

Model-based Acceleration Control of Turbofan Engines with a Hammerstein-Wiener Representation

Science.gov (United States)

Wang, Jiqiang; Ye, Zhifeng; Hu, Zhongzhi; Wu, Xin; Dimirovsky, Georgi; Yue, Hong

2017-05-01

Acceleration control of turbofan engines is conventionally designed through either schedule-based or acceleration-based approach. With the widespread acceptance of model-based design in aviation industry, it becomes necessary to investigate the issues associated with model-based design for acceleration control. In this paper, the challenges for implementing model-based acceleration control are explained; a novel Hammerstein-Wiener representation of engine models is introduced; based on the Hammerstein-Wiener model, a nonlinear generalized minimum variance type of optimal control law is derived; the feature of the proposed approach is that it does not require the inversion operation that usually upsets those nonlinear control techniques. The effectiveness of the proposed control design method is validated through a detailed numerical study.

Stochastic Simulation of Integrated Circuits with Nonlinear Black-Box Components via Augmented Deterministic Equivalents

Directory of Open Access Journals (Sweden)

MANFREDI, P.

2014-11-01

Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.

Accelerated Computing in Magnetic Resonance Imaging: Real-Time Imaging Using Nonlinear Inverse Reconstruction

Directory of Open Access Journals (Sweden)

Sebastian Schaetz

2017-01-01

Full Text Available Purpose. To develop generic optimization strategies for image reconstruction using graphical processing units (GPUs in magnetic resonance imaging (MRI and to exemplarily report on our experience with a highly accelerated implementation of the nonlinear inversion (NLINV algorithm for dynamic MRI with high frame rates. Methods. The NLINV algorithm is optimized and ported to run on a multi-GPU single-node server. The algorithm is mapped to multiple GPUs by decomposing the data domain along the channel dimension. Furthermore, the algorithm is decomposed along the temporal domain by relaxing a temporal regularization constraint, allowing the algorithm to work on multiple frames in parallel. Finally, an autotuning method is presented that is capable of combining different decomposition variants to achieve optimal algorithm performance in different imaging scenarios. Results. The algorithm is successfully ported to a multi-GPU system and allows online image reconstruction with high frame rates. Real-time reconstruction with low latency and frame rates up to 30 frames per second is demonstrated. Conclusion. Novel parallel decomposition methods are presented which are applicable to many iterative algorithms for dynamic MRI. Using these methods to parallelize the NLINV algorithm on multiple GPUs, it is possible to achieve online image reconstruction with high frame rates.

Nonlinear dynamics of vortices in ultraclean type-II superconductors: Integrable wave equations in cylindrical geometry

International Nuclear Information System (INIS)

Coffey, M.W.

1996-01-01

Due to their short coherence lengths and relatively large energy gaps, the high-transition temperature superconductors are very likely candidates as ultraclean materials at low temperature. This class of materials features significantly modified vortex dynamics, with very little dissipation at low temperature. The motion is then dominated by wave propagation, being in general nonlinear. Here two-dimensional vortex motion is investigated in the ultraclean regime for a superconductor described in cylindrical geometry. The small-amplitude limit is assumed, and the focus is on the long-wavelength limit. Results for both zero and nonzero Hall force are presented, with the effects of nonlocal vortex interaction and vortex inertia being included within London theory. Linear and nonlinear problems are studied, with a predisposition toward the more analytically tractable situations. For a nonlinear problem in 2+1 dimensions, the cylindrical Kadomtsev-Petviashvili equation is derived. Hall angle measurements on high-T c superconductors indicate the need to investigate the properties of such a completely integrable wave equation. copyright 1996 The American Physical Society

KLYNAC: Compact linear accelerator with integrated power supply

Energy Technology Data Exchange (ETDEWEB)

Malyzhenkov, Alexander [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-05-16

Accelerators and accelerator-based light sources have a wide range of applications in science, engineering technology and medicine. Today the scienti c community is working towards improving the quality of the accelerated beam and its parameters while trying to develop technology for reducing accelerator size. This work describes a design of a compact linear accelerator (linac) prototype, resonant Klynac device, which is a combined linear accelerator and its power supply - klystron. The intended purpose of a Klynac device is to provide a compact and inexpensive alternative to a conventional 1 to 6 MeV accelerator, which typically requires a separate RF source, an accelerator itself and all the associated hardware. Because the Klynac is a single structure, it has the potential to be much less sensitive to temperature variations than a system with separate klystron and linac. We start by introducing a simpli ed theoretical model for a Klynac device. We then demonstrate how a prototype is designed step-by-step using particle-in-cell simulation studies for mono- resonant and bi-resonant structures. Finally, we discuss design options from a stability point of view and required input power as well as behavior of competing modes for the actual built device.

Implementation of a variable-step integration technique for nonlinear structural dynamic analysis

International Nuclear Information System (INIS)

Underwood, P.; Park, K.C.

1977-01-01

The paper presents the implementation of a recently developed unconditionally stable implicit time integration method into a production computer code for the transient response analysis of nonlinear structural dynamic systems. The time integrator is packaged with two significant features; a variable step size that is automatically determined and this is accomplished without additional matrix refactorizations. The equations of motion solved by the time integrator must be cast in the pseudo-force form, and this provides the mechanism for controlling the step size. Step size control is accomplished by extrapolating the pseudo-force to the next time (the predicted pseudo-force), then performing the integration step and then recomputing the pseudo-force based on the current solution (the correct pseudo-force); from this data an error norm is constructed, the value of which determines the step size for the next step. To avoid refactoring the required matrix with each step size change a matrix scaling technique is employed, which allows step sizes to change by a factor of 100 without refactoring. If during a computer run the integrator determines it can run with a step size larger than 100 times the original minimum step size, the matrix is refactored to take advantage of the larger step size. The strategy for effecting these features are discussed in detail. (Auth.)

Distinguishing linear vs. nonlinear integration in CA1 radial oblique dendrites: it’s about time

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José Francisco eGómez González

2011-11-01

Full Text Available It was recently shown that multiple excitatory inputs to CA1 pyramidal neuron dendrites must be activated nearly simultaneously to generate local dendritic spikes and superlinear responses at the soma; even slight input desynchronization prevented local spike initiation (Gasparini, 2006;Losonczy, 2006. This led to the conjecture that CA1 pyramidal neurons may only express their nonlinear integrative capabilities during the highly synchronized sharp waves and ripples that occur during slow wave sleep and resting/consummatory behavior, whereas during active exploration and REM sleep (theta rhythm, inadequate synchronization of excitation would lead CA1 pyramidal cells to function as essentially linear devices. Using a detailed single neuron model, we replicated the experimentally observed synchronization effect for brief inputs mimicking single synaptic release events. When synapses were driven instead by double pulses, more representative of the bursty inputs that occur in vivo, we found that the tolerance for input desynchronization was increased by more than an order of magnitude. The effect depended mainly on paired pulse facilitation of NMDA receptor-mediated responses at Schaffer collateral synapses. Our results suggest that CA1 pyramidal cells could function as nonlinear integrative units in all major hippocampal states.

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

Science.gov (United States)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

Studies and measurements of linear coupling and nonlinearities in hadron circular accelerators

International Nuclear Information System (INIS)

Franchi, A.

2006-01-01

In this thesis a beam-based method has been developed to measure the strength and the polarity of corrector magnets (skew quadrupoles and sextupoles) in circular accelerators. The algorithm is based on the harmonic analysis (via FFT) of beam position monitor (BPM) data taken turn by turn from an accelerator in operation. It has been shown that, from the differences of the spectral line amplitudes between two consecutive BPMs, both the strength and the polarity of non-linear elements placed in between can be measured. The method has been successfully tested using existing BPM data from the SPS of CERN. A second beam-based method has been studied for a fast measurement and correction of betatron coupling driven by skew quadrupole field errors and tilted focusing quadrupoles. In this thesis it has been shown how the correction for minimizing the coupling stop band C can be performed in a single machine cycle from the harmonic analysis of multi-BPM data. The method has been successfully applied to RHIC. A third theoretical achievement is a new description of the betatron motion close to the difference resonance in presence of linear coupling. New formulae describing the exchange of RMS resonances have been derived here making use of Lie algebra providing a better description of the emittance behavior. A new way to decouple the equations of motion and explicit expressions for the individual single particle invariants have been found. For the first time emittance exchange studies have been carried out in the SIS-18 of GSI. Applications of this manipulation are: emittance equilibration under consideration for future operations of the SIS-18 as booster for the SIS-100; emittance transfer during multi-turn injection to improve the efficiency and to protect the injection septum in high intensity operations, by shifting part of the horizontal emittance into the vertical plane. Multi-particle simulations with 2D PIC space-charge solver have been run to infer heuristic scaling

Studies and measurements of linear coupling and nonlinearities in hadron circular accelerators

Energy Technology Data Exchange (ETDEWEB)

Franchi, A.

2006-07-01

In this thesis a beam-based method has been developed to measure the strength and the polarity of corrector magnets (skew quadrupoles and sextupoles) in circular accelerators. The algorithm is based on the harmonic analysis (via FFT) of beam position monitor (BPM) data taken turn by turn from an accelerator in operation. It has been shown that, from the differences of the spectral line amplitudes between two consecutive BPMs, both the strength and the polarity of non-linear elements placed in between can be measured. The method has been successfully tested using existing BPM data from the SPS of CERN. A second beam-based method has been studied for a fast measurement and correction of betatron coupling driven by skew quadrupole field errors and tilted focusing quadrupoles. In this thesis it has been shown how the correction for minimizing the coupling stop band C can be performed in a single machine cycle from the harmonic analysis of multi-BPM data. The method has been successfully applied to RHIC. A third theoretical achievement is a new description of the betatron motion close to the difference resonance in presence of linear coupling. New formulae describing the exchange of RMS resonances have been derived here making use of Lie algebra providing a better description of the emittance behavior. A new way to decouple the equations of motion and explicit expressions for the individual single particle invariants have been found. For the first time emittance exchange studies have been carried out in the SIS-18 of GSI. Applications of this manipulation are: emittance equilibration under consideration for future operations of the SIS-18 as booster for the SIS-100; emittance transfer during multi-turn injection to improve the efficiency and to protect the injection septum in high intensity operations, by shifting part of the horizontal emittance into the vertical plane. Multi-particle simulations with 2D PIC space-charge solver have been run to infer heuristic scaling

Omnibus risk assessment via accelerated failure time kernel machine modeling.

Science.gov (United States)

Sinnott, Jennifer A; Cai, Tianxi

2013-12-01

Integrating genomic information with traditional clinical risk factors to improve the prediction of disease outcomes could profoundly change the practice of medicine. However, the large number of potential markers and possible complexity of the relationship between markers and disease make it difficult to construct accurate risk prediction models. Standard approaches for identifying important markers often rely on marginal associations or linearity assumptions and may not capture non-linear or interactive effects. In recent years, much work has been done to group genes into pathways and networks. Integrating such biological knowledge into statistical learning could potentially improve model interpretability and reliability. One effective approach is to employ a kernel machine (KM) framework, which can capture nonlinear effects if nonlinear kernels are used (Scholkopf and Smola, 2002; Liu et al., 2007, 2008). For survival outcomes, KM regression modeling and testing procedures have been derived under a proportional hazards (PH) assumption (Li and Luan, 2003; Cai, Tonini, and Lin, 2011). In this article, we derive testing and prediction methods for KM regression under the accelerated failure time (AFT) model, a useful alternative to the PH model. We approximate the null distribution of our test statistic using resampling procedures. When multiple kernels are of potential interest, it may be unclear in advance which kernel to use for testing and estimation. We propose a robust Omnibus Test that combines information across kernels, and an approach for selecting the best kernel for estimation. The methods are illustrated with an application in breast cancer. © 2013, The International Biometric Society.

Compact accelerator for medical therapy

Science.gov (United States)

Caporaso, George J.; Chen, Yu-Jiuan; Hawkins, Steven A.; Sampayan, Stephen E.; Paul, Arthur C.

2010-05-04

A compact accelerator system having an integrated particle generator-linear accelerator with a compact, small-scale construction capable of producing an energetic (.about.70-250 MeV) proton beam or other nuclei and transporting the beam direction to a medical therapy patient without the need for bending magnets or other hardware often required for remote beam transport. The integrated particle generator-accelerator is actuable as a unitary body on a support structure to enable scanning of a particle beam by direction actuation of the particle generator-accelerator.

Cosmological effects of nonlinear electrodynamics

International Nuclear Information System (INIS)

Novello, M; Goulart, E; Salim, J M; Bergliaffa, S E Perez

2007-01-01

It will be shown that a given realization of nonlinear electrodynamics, used as a source of Einstein's equations, generates a cosmological model with interesting features, namely a phase of current cosmic acceleration, and the absence of an initial singularity, thus pointing to a way of solving two important problems in cosmology

Laser wakefield acceleration

International Nuclear Information System (INIS)

Esarey, E.; Ting, A.; Sprangle, P.

1989-01-01

The laser wakefield accelerator (LWFA) is a novel plasma based electron acceleration scheme which utilizes a relativistic optical guiding mechanism for laser pulse propagation. In the LWFA, a short, high power, single frequency laser pulse is propagated through a plasma. As the laser pulse propagates, its radial and axial ponderomotive forces nonresonantly generate large amplitude plasma waves (wakefields) with a phase velocity equal to the group velocity of the pulse. A properly phased electron bunch may then be accelerated by the axial wakefield and focused by the transverse wakefield. Optical guiding of the laser pulse in the plasma is necessary in order to achieve high energies in a single stage of acceleration. At sufficiently high laser powers, optical guiding may be achieved through relativistic effects associated with the plasma electrons. Preliminary analysis indicates that this scheme may overcome some of the difficulties present in the plasma beat wave accelerator and in the plasma wakefield accelerator. Analytical and numerical calculations are presented which study both laser pulse propagation within a plasma as well as the subsequent generation of large amplitude plasma waves. In addition, the generation of large amplitude plasma waves in regimes where the plasma waves become highly nonlinear is examined

Nonlinear photonic metasurfaces

Science.gov (United States)

Li, Guixin; Zhang, Shuang; Zentgraf, Thomas

2017-03-01

Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.

Decomposition of a hierarchy of nonlinear evolution equations

International Nuclear Information System (INIS)

Geng Xianguo

2003-01-01

The generalized Hamiltonian structures for a hierarchy of nonlinear evolution equations are established with the aid of the trace identity. Using the nonlinearization approach, the hierarchy of nonlinear evolution equations is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals and their generator are presented, based on which the finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the hierarchy of nonlinear evolution equations are reduced to solving the compatible Hamiltonian systems of ordinary differential equations

Monoenergetic laser wakefield acceleration

Directory of Open Access Journals (Sweden)

N. E. Andreev

2000-02-01

Full Text Available Three dimensional test particle simulations are applied to optimization of the plasma-channeled laser wakefield accelerator (LWFA operating in a weakly nonlinear regime. Electron beam energy spread, emittance, and luminosity depend upon the proportion of the electron bunch size to the plasma wavelength. This proportion tends to improve with the laser wavelength increase. We simulate a prospective two-stage ∼1GeV LWFA with controlled energy spread and emittance. The input parameters correspond to realistic capabilities of the BNL Accelerator Test Facility that features a picosecond-terawatt CO_{2} laser and a high-brightness electron gun.

Explicit integration with GPU acceleration for large kinetic networks

International Nuclear Information System (INIS)

Brock, Benjamin; Belt, Andrew; Billings, Jay Jay; Guidry, Mike

2015-01-01

We demonstrate the first implementation of recently-developed fast explicit kinetic integration algorithms on modern graphics processing unit (GPU) accelerators. Taking as a generic test case a Type Ia supernova explosion with an extremely stiff thermonuclear network having 150 isotopic species and 1604 reactions coupled to hydrodynamics using operator splitting, we demonstrate the capability to solve of order 100 realistic kinetic networks in parallel in the same time that standard implicit methods can solve a single such network on a CPU. This orders-of-magnitude decrease in computation time for solving systems of realistic kinetic networks implies that important coupled, multiphysics problems in various scientific and technical fields that were intractable, or could be simulated only with highly schematic kinetic networks, are now computationally feasible.

Nonlinear radiation generation processes in the auroral acceleration region

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R. Pottelette

2017-11-01

Full Text Available It is known from laboratory plasma experiments that double layers (DLs radiate in the electromagnetic spectrum; but this is only known qualitatively. In these experiments, it was shown that the electron beam created on the high-potential side of a DL generates nonlinear structures which couple to electromagnetic waves and act as a sender antenna. In the Earth auroral region, observations performed by auroral spacecraft have shown that DLs occur naturally in the source region of intense radio emissions called auroral kilometric radiation (AKR. Very high time-, spatial-, and temporal-resolution measurements are needed in order to characterize waves and particle distributions in the vicinity of DLs, which are moving transient structures. We report observations from the FAST satellite of a localized large-amplitude parallel electric field (∼ 300 mV m−1 recorded at the edges of the auroral density cavity. In agreement with laboratory experiments, on the high-potential side of the DL, elementary radiation events are detected. They occur substantially above the local electron gyrofrequency and are associated with the presence of electron holes. The velocity of these nonlinear structures can be derived from the measurement of the Doppler-shifted AKR frequency spectrum above the electron gyrofrequency. The generated electron holes appear as the nonlinear evolution of electrostatic waves generated by the electron–electron two-stream instability because they propagate at about half the beam velocity. It is pointed out that, in the vicinity of a DL, the shape of the electron distribution gives rise to a significant power recorded in the left-hand polarized ordinary (LO mode.

Calibration of the nonlinear ring model at the Diamond Light Source

CERN Document Server

Bartolini, R; Rehm, G; Martin, I P S

2011-01-01

Nonlinear beam dynamics plays a crucial role in defining the performance of a storage ring. The beam lifetime, the injection efficiency, and the dynamic and momentum apertures available to the beam are optimized during the design phase by a proper optimization of the linear lattice and of the distribution of sextupole families. The correct implementation of the design model, especially the nonlinear part, is a nontrivial accelerator physics task. Several parameters of the nonlinear dynamics can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these parameters are extracted from the analysis of turn-by-turn data after the excitation of betatron oscillations of the particles in the ring. We present the experimental results of the campaign of measurements carried out at the Diamond storage ring to characterize the nonlinear beam dynamics. A combination of frequency map analysis with the detuning with momentum measurements has allowed for a precise calibration ...

Electromagnetic nonlinearities in a Roebel-cable-based accelerator magnet prototype: variational approach

Science.gov (United States)

Ruuskanen, J.; Stenvall, A.; Lahtinen, V.; Pardo, E.

2017-02-01

Superconducting magnets are the most expensive series of components produced in the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN). When developing such magnets beyond state-of-the-art technology, one possible option is to use high-temperature superconductors (HTS) that are capable of tolerating much higher magnetic fields than low-temperature superconductors (LTS), carrying simultaneously high current densities. Significant cost reductions due to decreased prototype construction needs can be achieved by careful modelling of the magnets. Simulations are used, e.g. for designing magnets fulfilling the field quality requirements of the beampipe, and adequate protection by studying the losses occurring during charging and discharging. We model the hysteresis losses and the magnetic field nonlinearity in the beampipe as a function of the magnet’s current. These simulations rely on the minimum magnetic energy variation principle, with optimization algorithms provided by the open-source optimization library interior point optimizer. We utilize this methodology to investigate a research and development accelerator magnet prototype made of REBCO Roebel cable. The applicability of this approach, when the magnetic field dependence of the superconductor’s critical current density is considered, is discussed. We also scrutinize the influence of the necessary modelling decisions one needs to make with this approach. The results show that different decisions can lead to notably different results, and experiments are required to study the electromagnetic behaviour of such magnets further.

POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

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FAOUZI HADDOUCHI

2015-11-01

Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

Energy Technology Data Exchange (ETDEWEB)

Oevguen, A. [Eastern Mediterranean Univ., Famagusta (Country Unknown). Dept. of Physics

2017-02-15

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields. (orig.)

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

Science.gov (United States)

Övgün, A.

2017-02-01

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.

An integrated nonlinear optical loop mirror in silicon photonics for all-optical signal processing

Directory of Open Access Journals (Sweden)

Zifei Wang

2018-02-01

Full Text Available The nonlinear optical loop mirror (NOLM has been studied for several decades and has attracted considerable attention for applications in high data rate optical communications and all-optical signal processing. The majority of NOLM research has focused on silica fiber-based implementations. While various fiber designs have been considered to increase the nonlinearity and manage dispersion, several meters to hundreds of meters of fiber are still required. On the other hand, there is increasing interest in developing photonic integrated circuits for realizing signal processing functions. In this paper, we realize the first-ever passive integrated NOLM in silicon photonics and demonstrate its application for all-optical signal processing. In particular, we show wavelength conversion of 10 Gb/s return-to-zero on-off keying (RZ-OOK signals over a wavelength range of 30 nm with error-free operation and a power penalty of less than 2.5 dB, we achieve error-free nonreturn to zero (NRZ-to-RZ modulation format conversion at 10 Gb/s also with a power penalty of less than 2.8 dB, and we obtain error-free all-optical time-division demultiplexing of a 40 Gb/s RZ-OOK data signal into its 10 Gb/s tributary channels with a maximum power penalty of 3.5 dB.

The design and performance of Static Var Compensators for particle accelerators

CERN Document Server

Kahle, Karsten; Genton, Charles-Mathieu

2015-01-01

Particle accelerators, and in particular synchrotrons, represent large cycling non-linear loads connected to the electrical distribution network. This paper discusses the typical design and performance of Static Var Compensators (SVCs) to obtain the excellent power quality levels required for particle accelerator operation.

A chaos-based evolutionary algorithm for general nonlinear programming problems

International Nuclear Information System (INIS)

El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.

2016-01-01

In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.

First Integrals of Evolution Systems and Nonlinear Stability of Stationary Solutions for the Ideal Atmospheric, Oceanic Hydrodynamical and Plasma Models

International Nuclear Information System (INIS)

Gordin, V.A.

1998-01-01

First integral of the systems of nonlinear equations governing the behaviour of atmospheric, oceanic and MHD plasma models are determined. The Lyapunov stability conditions for the solutions under small initial disturbances are analyzed. (author)

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...

Adaptive Sliding Mode Control Method Based on Nonlinear Integral Sliding Surface for Agricultural Vehicle Steering Control

Directory of Open Access Journals (Sweden)

Taochang Li

2014-01-01

Full Text Available Automatic steering control is the key factor and essential condition in the realization of the automatic navigation control of agricultural vehicles. In order to get satisfactory steering control performance, an adaptive sliding mode control method based on a nonlinear integral sliding surface is proposed in this paper for agricultural vehicle steering control. First, the vehicle steering system is modeled as a second-order mathematic model; the system uncertainties and unmodeled dynamics as well as the external disturbances are regarded as the equivalent disturbances satisfying a certain boundary. Second, a transient process of the desired system response is constructed in each navigation control period. Based on the transient process, a nonlinear integral sliding surface is designed. Then the corresponding sliding mode control law is proposed to guarantee the fast response characteristics with no overshoot in the closed-loop steering control system. Meanwhile, the switching gain of sliding mode control is adaptively adjusted to alleviate the control input chattering by using the fuzzy control method. Finally, the effectiveness and the superiority of the proposed method are verified by a series of simulation and actual steering control experiments.

Study of coherent Synchrotron Radiation effects by means of a new simulation code based on the non-linear extension of the operator splitting method

International Nuclear Information System (INIS)

Dattoli, G.; Schiavi, A.; Migliorati, M.

2006-03-01

The coherent synchrotron radiation (CSR) is one of the main problems limiting the performance of high intensity electron accelerators. The complexity of the physical mechanisms underlying the onset of instabilities due to CSR demands for accurate descriptions, capable of including the large number of features of an actual accelerating device. A code devoted to the analysis of this type of problems should be fast and reliable, conditions that are usually hardly achieved at the same rime. In the past, codes based on Lie algebraic techniques , have been very efficient to treat transport problems in accelerators. The extension of these methods to the non-linear case is ideally suited to treat CSR instability problems. We report on the development of a numerical code, based on the solution of the Vlasov equation, with the inclusion of non-linear contribution due to wake field effects. The proposed solution method exploits an algebraic technique, using exponential operators. We show that the integration procedure is capable of reproducing the onset of an instability and the effects associated with bunching mechanisms leading to the growth of the instability itself. In addition, considerations on the threshold of the instability are also developed [it

Study of coherent synchrotron radiation effects by means of a new simulation code based on the non-linear extension of the operator splitting method

International Nuclear Information System (INIS)

Dattoli, G.; Migliorati, M.; Schiavi, A.

2007-01-01

The coherent synchrotron radiation (CSR) is one of the main problems limiting the performance of high-intensity electron accelerators. The complexity of the physical mechanisms underlying the onset of instabilities due to CSR demands for accurate descriptions, capable of including the large number of features of an actual accelerating device. A code devoted to the analysis of these types of problems should be fast and reliable, conditions that are usually hardly achieved at the same time. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problems in accelerators. The extension of these methods to the non-linear case is ideally suited to treat CSR instability problems. We report on the development of a numerical code, based on the solution of the Vlasov equation, with the inclusion of non-linear contribution due to wake field effects. The proposed solution method exploits an algebraic technique that uses the exponential operators. We show that the integration procedure is capable of reproducing the onset of instability and the effects associated with bunching mechanisms leading to the growth of the instability itself. In addition, considerations on the threshold of the instability are also developed

Nonlinear delta f Simulations of Collective Effects in Intense Charged Particle Beams

CERN Document Server

Hong Qi

2003-01-01

A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, ...

Nonlinear filtering for LIDAR signal processing

Directory of Open Access Journals (Sweden)

D. G. Lainiotis

1996-01-01

Full Text Available LIDAR (Laser Integrated Radar is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF, which has been the standard nonlinear filter in past engineering applications.

Source-to-accelerator quadrupole matching section for a compact linear accelerator

Science.gov (United States)

Seidl, P. A.; Persaud, A.; Ghiorso, W.; Ji, Q.; Waldron, W. L.; Lal, A.; Vinayakumar, K. B.; Schenkel, T.

2018-05-01

Recently, we presented a new approach for a compact radio-frequency (RF) accelerator structure and demonstrated the functionality of the individual components: acceleration units and focusing elements. In this paper, we combine these units to form a working accelerator structure: a matching section between the ion source extraction grids and the RF-acceleration unit and electrostatic focusing quadrupoles between successive acceleration units. The matching section consists of six electrostatic quadrupoles (ESQs) fabricated using 3D-printing techniques. The matching section enables us to capture more beam current and to match the beam envelope to conditions for stable transport in an acceleration lattice. We present data from an integrated accelerator consisting of the source, matching section, and an ESQ doublet sandwiched between two RF-acceleration units.

A Lie-admissible method of integration of Fokker-Planck equations with non-linear coefficients (exact and numerical solutions)

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type

Particle acceleration inside PWN: Simulation and observational constraints with INTEGRAL; Acceleration de particules au sein des vents relativistes de pulsar: simulation et contraintes observationelles avec le satellite INTEGRAL

Energy Technology Data Exchange (ETDEWEB)

Forot, M

2006-12-15

The context of this thesis is to gain new constraints on the different particle accelerators that occur in the complex environment of neutron stars: in the pulsar magnetosphere, in the striped wind or wave outside the light cylinder, in the jets and equatorial wind, and at the wind terminal shock. An important tool to constrain both the magnetic field and primary particle energies is to image the synchrotron ageing of the population, but it requires a careful modelling of the magnetic field evolution in the wind flow. The current models and understanding of these different accelerators, the acceleration processes and open questions have been reviewed in the first part of the thesis. The instrumental part of this work involves the IBIS imager, on board the INTEGRAL satellite, that provides images with 12' resolution from 17 keV to MeV where the SPI spectrometer takes over up, to 10 MeV, but with a reduced 2 degrees resolution. A new method for using the double-layer IBIS imager as a Compton telescope with coded mask aperture. Its performance has been measured. The Compton scattering information and the achieved sensitivity also open a new window for polarimetry in gamma rays. A method has been developed to extract the linear polarization properties and to check the instrument response for fake polarimetric signals in the various backgrounds and projection effects.

Particle acceleration inside PWN: Simulation and observational constraints with INTEGRAL; Acceleration de particules au sein des vents relativistes de pulsar: simulation et contraintes observationelles avec le satellite INTEGRAL

Energy Technology Data Exchange (ETDEWEB)

Forot, M

2006-12-15

The context of this thesis is to gain new constraints on the different particle accelerators that occur in the complex environment of neutron stars: in the pulsar magnetosphere, in the striped wind or wave outside the light cylinder, in the jets and equatorial wind, and at the wind terminal shock. An important tool to constrain both the magnetic field and primary particle energies is to image the synchrotron ageing of the population, but it requires a careful modelling of the magnetic field evolution in the wind flow. The current models and understanding of these different accelerators, the acceleration processes and open questions have been reviewed in the first part of the thesis. The instrumental part of this work involves the IBIS imager, on board the INTEGRAL satellite, that provides images with 12' resolution from 17 keV to MeV where the SPI spectrometer takes over up, to 10 MeV, but with a reduced 2 degrees resolution. A new method for using the double-layer IBIS imager as a Compton telescope with coded mask aperture. Its performance has been measured. The Compton scattering information and the achieved sensitivity also open a new window for polarimetry in gamma rays. A method has been developed to extract the linear polarization properties and to check the instrument response for fake polarimetric signals in the various backgrounds and projection effects.

3-D Model of Broadband Emission from Supernova Remnants Undergoing Non-linear Diffusive Shock Acceleration

Energy Technology Data Exchange (ETDEWEB)

Lee, Shiu-Hang; Kamae, Tuneyoshi; Ellison, Donald C.

2008-07-02

We present a 3-dimensional model of supernova remnants (SNRs) where the hydrodynamical evolution of the remnant is modeled consistently with nonlinear diffusive shock acceleration occurring at the outer blast wave. The model includes particle escape and diffusion outside of the forward shock, and particle interactions with arbitrary distributions of external ambient material, such as molecular clouds. We include synchrotron emission and cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton (IC), and Coulomb energy-loss. Boardband spectra have been calculated for typical parameters including dense regions of gas external to a 1000 year old SNR. In this paper, we describe the details of our model but do not attempt a detailed fit to any specific remnant. We also do not include magnetic field amplification (MFA), even though this effect may be important in some young remnants. In this first presentation of the model we don't attempt a detailed fit to any specific remnant. Our aim is to develop a flexible platform, which can be generalized to include effects such as MFA, and which can be easily adapted to various SNR environments, including Type Ia SNRs, which explode in a constant density medium, and Type II SNRs, which explode in a pre-supernova wind. When applied to a specific SNR, our model will predict cosmic-ray spectra and multi-wavelength morphology in projected images for instruments with varying spatial and spectral resolutions. We show examples of these spectra and images and emphasize the importance of measurements in the hard X-ray, GeV, and TeV gamma-ray bands for investigating key ingredients in the acceleration mechanism, and for deducing whether or not TeV emission is produced by IC from electrons or pion-decay from protons.

Experimental chaos in nonlinear vibration isolation system

International Nuclear Information System (INIS)

Lou Jingjun; Zhu Shijian; He Lin; He Qiwei

2009-01-01

The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.

A Design of Mechanical Frequency Converter Linear and Non-linear Spring Combination for Energy Harvesting

International Nuclear Information System (INIS)

Yamamoto, K; Fujita, T; Kanda, K; Maenaka, K; Badel, A; Formosa, F

2014-01-01

In this study, the improvement of energy harvesting from wideband vibration with random change by using a combination of linear and nonlinear spring system is investigated. The system consists of curved beam spring for non-linear buckling, which supports the linear mass-spring resonator. Applying shock acceleration generates a snap through action to the buckling spring. From the FEM analysis, we showed that the snap through acceleration from the buckling action has no relationship with the applied shock amplitude and duration. We use this uniform acceleration as an impulse shock source for the linear resonator. It is easy to obtain the maximum shock response from the uniform snap through acceleration by using a shock response spectrum (SRS) analysis method. At first we investigated the relationship between the snap-through behaviour and an initial curved deflection. Then a time response result for non-linear springs with snap through and minimum force that makes a buckling behaviour were obtained by FEM analysis. By obtaining the optimum SRS frequency for linear resonator, we decided its resonant frequency with the MATLAB simulator

Accelerator physics analysis with interactive tools

International Nuclear Information System (INIS)

Holt, J.A.; Michelotti, L.

1993-05-01

Work is in progress on interactive tools for linear and nonlinear accelerator design, analysis, and simulation using X-based graphics. The BEAMLINE and MXYZPTLK class libraries, were used with an X Windows graphics library to build a program for interactively editing lattices and studying their properties

Electron non-linearities in Langmuir waves with application to beat-wave experiments

International Nuclear Information System (INIS)

Bell, A.R.; Gibbon, P.

1988-01-01

Non-linear Langmuir waves are examined in the context of the beat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth, M.N. and Liu, C.S., Phys. Rev. Lett., 1972, 29, 701. In two or three dimensions, other electron non-linearities occur which involve electric and magnetic fields. The quasi-linear equations for these non-linearities are developed and solved numerically in a geometry representative of laser-driven beat waves. (author)

Multidimensional Plasma Wake Excitation in the Non-linear Blowout Regime

CERN Document Server

Vieira, J.; Silva, L.O.

2016-01-01

Plasma accelerators can sustain very high acceleration gradients. They are promising candidates for future generations of particle accelerators for sev- eral scientific, medical and technological applications. Current plasma based acceleration experiments operate in the relativistic regime, where the plasma response is strongly non-linear. We outline some of the key properties of wake- field excitation in these regimes. We outline a multidimensional theory for the excitation of plasma wakefields in connection with current experiments. We then use these results and provide design guidelines for the choice of laser and plasma parameters ensuring a stable laser wakefield accelerator that maximizes the quality of the accelerated electrons. We also mention some of the future challenges associated with this technology.

A model for particle acceleration in lower hybrid collapse

International Nuclear Information System (INIS)

Retterer, J.M.

1997-01-01

A model for particle acceleration during the nonlinear collapse of lower hybrid waves is described. Using the Musher-Sturman wave equation to describe the effects of nonlinear processes and a velocity diffusion equation for the particle velocity distribution, the model self-consistently describes the exchange of energy between the fields and the particles in the local plasma. Two-dimensional solutions are presented for the modulational instability of a plane wave and the collapse of a cylindrical wave packet. These calculations were motivated by sounding rocket observations in the vicinity of auroral arcs in the Earth close-quote s ionosphere, which have revealed the existence of large-amplitude lower-hybrid wave packets associated with ions accelerated to energies of 100 eV. The scaling of the sizes of these wave packets is consistent with the theory of lower-hybrid collapse and the observed lower-hybrid field amplitudes are adequate to accelerate the ionospheric ions to the observed energies

Optimization of piezoelectric cantilever energy harvesters including non-linear effects

International Nuclear Information System (INIS)

Patel, R; McWilliam, S; Popov, A A

2014-01-01

This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations. (paper)

Quantum Accelerator Modes from the Farey Tree

International Nuclear Information System (INIS)

Buchleitner, A.; D'Arcy, M.B.; Fishman, S.; Gardiner, S.A.; Guarneri, I.; Ma, Z.-Y.; Rebuzzini, L.; Summy, G.S.

2006-01-01

We show that mode locking finds a purely quantum nondissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode locking. A hierarchy for the rational numbers known as the Farey tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes

Finite-temperature Casimir effect in the presence of nonlinear dielectrics

DEFF Research Database (Denmark)

Kheirandish, Fardin; Amooghorban, Ehsan; Soltani, Morteza

2011-01-01

Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations to coupl......Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations...

A theoretical response of the electrostatic parallel plate to constant and low-frequency accelerations

International Nuclear Information System (INIS)

Lee, Ki Bang

2009-01-01

A theoretical response of an electrostatic gap-closing actuator based on parallel plates to constant and low-frequency accelerations has been derived as a function of the applied acceleration and voltage. The nonlinear equation of motion is obtained in a dimensionless form from the fact that the inertial and damping forces are neglected at a frequency much less than the resonant frequency of the parallel plate, and thereafter the nonlinear equation is solved for the stable inter-plate gap at the acceleration and voltage. From the derived solution, the pull-in acceleration is obtained as a function of the applied voltage, and the pull-in voltage is also expressed as a function of the acceleration. The closed-form solution is validated by comparison with a numerical solution. The theoretical solution is in excellent agreement with the numerical results when the actuator is exposed to a constant acceleration as well as a low-frequency acceleration. The theoretical solution and pull-in acceleration and voltage thus provide guidance to prescribe operational constraints for devices that use the parallel plate actuator and to predict the response of the electrostatic gap-closing parallel plates to constant and low-frequency acceleration

High energy plasma accelerators

International Nuclear Information System (INIS)

Tajima, T.

1985-05-01

Colinear intense laser beams ω 0 , kappa 0 and ω 1 , kappa 1 shone on a plasma with frequency separation equal to the electron plasma frequency ω/sub pe/ are capable of creating a coherent large longitudinal electric field E/sub L/ = mc ω/sub pe//e of the order of 1GeV/cm for a plasma density of 10 18 cm -3 through the laser beat excitation of plasma oscillations. Accompanying favorable and deleterious physical effects using this process for a high energy beat-wave accelerator are discussed: the longitudinal dephasing, pump depletion, the transverse laser diffraction, plasma turbulence effects, self-steepening, self-focusing, etc. The basic equation, the driven nonlinear Schroedinger equation, is derived to describe this system. Advanced accelerator concepts to overcome some of these problems are proposed, including the plasma fiber accelerator of various variations. An advanced laser architecture suitable for the beat-wave accelerator is suggested. Accelerator physics issues such as the luminosity are discussed. Applications of the present process to the current drive in a plasma and to the excitation of collective oscillations within nuclei are also discussed

Acceleration of charged particles by lasers in vacuum

International Nuclear Information System (INIS)

Cicchitelli, L.; Hora, H.; Scheid, W.

1989-01-01

For laser acceleration of electrons (and other charged particles) by lasers to the TeV energy range in vacuum, the scheme of trapping electrons in spatially moving and accelerated intensity gradients or minima of laser fields, the single electron motion in standing wave fields is evaluated in details numerically. Acceleration of the minima results in the acceleration of the electrons as expected from global results of the nonlinear forces. If half-wave length laser pulses propagating in vacuum are used the relativistic exact solutions are derived and evaluated. A disadvantage is the lateral motion requiring a large laser focus. For TeV electron energy, MJ KrF-laser pulses are necessary and the acceleration length is about 10 cm. copyright 1989 American Institute of Physics

Single-particle dynamics in a nonlinear accelerator lattice: attaining a large tune spread with octupoles in IOTA

Energy Technology Data Exchange (ETDEWEB)

Antipov, S. A.; Nagaitsev, S.; Valishev, A.

2017-04-01

Fermilab is constructing the Integrable Optics Test Accelerator (IOTA) as the centerpiece of the Accelerator R&D Program towards high-intensity circular machines. One of the factors limiting the beam intensity in present circular accelerators is collective instabilities, which can be suppressed by a spread of betatron frequencies (tunes) through the Landau damping mechanism or by an external damper, if the instability is slow enough. The spread is usually created by octupole magnets, which introduce the tune dependence on the amplitude and, in some cases, by a chromatic spread (tune dependence on particle's momentum). The introduction of octupoles usually lead to a resonant behavior and a reduction of the dynamic aperture. One of the goals of the IOTA research program is to achieve a high betatron tune spread, while retaining a large dynamic aperture using conventional octupole magnets in a special but realistic accelerator configuration. In this report, we present results of computer simulations of an electron beam in the IOTA by particle tracking and the Frequency Map Analysis. The results show that the ring's octupole magnets can be configured to provide a betatron tune shift of 0.08 (for particles at large amplitudes) with the dynamical aperture of over 20 beam sigma for a 150-MeV electron beam. The influence of the synchrotron motion, lattice errors, and magnet imperfections is insignificant for the parameters and levels of tolerances set by the design of the ring. The described octupole insert could be beneficial for suppression of space-charge induced instabilities in high intensity machines.

Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

Science.gov (United States)

Brædstrup, Christian; Egholm, David

2013-04-01

Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

Community Petascale Project for Accelerator Science and Simulation: Advancing Computational Science for Future Accelerators and Accelerator Technologies

Energy Technology Data Exchange (ETDEWEB)

Spentzouris, P.; /Fermilab; Cary, J.; /Tech-X, Boulder; McInnes, L.C.; /Argonne; Mori, W.; /UCLA; Ng, C.; /SLAC; Ng, E.; Ryne, R.; /LBL, Berkeley

2011-11-14

The design and performance optimization of particle accelerators are essential for the success of the DOE scientific program in the next decade. Particle accelerators are very complex systems whose accurate description involves a large number of degrees of freedom and requires the inclusion of many physics processes. Building on the success of the SciDAC-1 Accelerator Science and Technology project, the SciDAC-2 Community Petascale Project for Accelerator Science and Simulation (ComPASS) is developing a comprehensive set of interoperable components for beam dynamics, electromagnetics, electron cooling, and laser/plasma acceleration modelling. ComPASS is providing accelerator scientists the tools required to enable the necessary accelerator simulation paradigm shift from high-fidelity single physics process modeling (covered under SciDAC1) to high-fidelity multiphysics modeling. Our computational frameworks have been used to model the behavior of a large number of accelerators and accelerator R&D experiments, assisting both their design and performance optimization. As parallel computational applications, the ComPASS codes have been shown to make effective use of thousands of processors. ComPASS is in the first year of executing its plan to develop the next-generation HPC accelerator modeling tools. ComPASS aims to develop an integrated simulation environment that will utilize existing and new accelerator physics modules with petascale capabilities, by employing modern computing and solver technologies. The ComPASS vision is to deliver to accelerator scientists a virtual accelerator and virtual prototyping modeling environment, with the necessary multiphysics, multiscale capabilities. The plan for this development includes delivering accelerator modeling applications appropriate for each stage of the ComPASS software evolution. Such applications are already being used to address challenging problems in accelerator design and optimization. The ComPASS organization

Experimental verification of a bridge-shaped, nonlinear vibration energy harvester

Energy Technology Data Exchange (ETDEWEB)

Gafforelli, Giacomo, E-mail: giacomo.gafforelli@polimi.it; Corigliano, Alberto [Department of Civil and Environmental Engineering, Politecnico di Milano, Milano, 20133 (Italy); Xu, Ruize; Kim, Sang-Gook [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

2014-11-17

This paper reports a comprehensive modeling and experimental characterization of a bridge shaped nonlinear energy harvester. A doubly clamped beam at large deflection requires stretching strain in addition to the bending strain to be geometrically compatible, which stiffens the beam as the beam deflects and transforms the dynamics to a nonlinear regime. The Duffing mode non-linear resonance widens the frequency bandwidth significantly at higher frequencies than the linear resonant frequency. The modeling includes a nonlinear measure of strain coupled with piezoelectric constitutive equations which end up in nonlinear coupling terms in the equations of motion. The main result supports that the power generation is bounded by the mechanical damping for both linear and nonlinear harvesters. Modeling also shows the power generation is over a wider bandwidth in the nonlinear case. A prototype is manufactured and tested to measure the power generation at different load resistances and acceleration amplitudes. The prototype shows a nonlinear behavior with well-matched experimental data to the modeling.

CUDA accelerated simulation of needle insertions in deformable tissue

International Nuclear Information System (INIS)

Patriciu, Alexandru

2012-01-01

This paper presents a stiff needle-deformable tissue interaction model. The model uses a mesh-less discretization of continuum; avoiding thus the expensive remeshing required by the finite element models. The proposed model can accommodate both linear and nonlinear material characteristics. The needle-deformable tissue interaction is modeled through fundamental boundaries. The forces applied by the needle on the tissue are divided in tangent forces and constraint forces. The constraint forces are adaptively computed such that the material is properly constrained by the needle. The implementation is accelerated using NVidia CUDA. We present detailed analysis of the execution timing in both serial and parallel case. The proposed needle insertion model was integrated in a custom software that loads DICOM images, generate the deformable model, and can simulate different insertion strategies.

SYMMETRY, HAMILTONIAN PROBLEMS AND WAVELETS IN ACCELERATOR PHYSICS

International Nuclear Information System (INIS)

FEDOROVA, A.; ZEITLIN, M.; PARSA, Z.

2000-01-01

In this paper the authors consider applications of methods from wavelet analysis to nonlinear dynamical problems related to accelerator physics. In this approach they take into account underlying algebraical, geometrical and topological structures of corresponding problems

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Rasmussen, Kim; Henning, D.; Gabriel, H.

1996-01-01

We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...

Nonlinear optimization

CERN Document Server

Ruszczynski, Andrzej

2011-01-01

Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation

CERN Document Server

Kamvissis, Spyridon; Miller, Peter D

2003-01-01

This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing

Nonlinear evolution of f(R) cosmologies. I. Methodology

International Nuclear Information System (INIS)

Oyaizu, Hiroaki

2008-01-01

We introduce the method and the implementation of a cosmological simulation of a class of metric-variation f(R) models that accelerate the cosmological expansion without a cosmological constant and evade solar-system bounds of small-field deviations to general relativity. Such simulations are shown to reduce to solving a nonlinear Poisson equation for the scalar degree of freedom introduced by the f(R) modifications. We detail the method to efficiently solve the nonlinear Poisson equation by using a Newton-Gauss-Seidel relaxation scheme coupled with the multigrid method to accelerate the convergence. The simulations are shown to satisfy tests comparing the simulated outcome to analytical solutions for simple situations, and the dynamics of the simulations are tested with orbital and Zeldovich collapse tests. Finally, we present several static and dynamical simulations using realistic cosmological parameters to highlight the differences between standard physics and f(R) physics. In general, we find that the f(R) modifications result in stronger gravitational attraction that enhances the dark matter power spectrum by ∼20% for large but observationally allowed f(R) modifications. A more detailed study of the nonlinear f(R) effects on the power spectrum are presented in a companion paper.

Cubication of conservative nonlinear oscillators

International Nuclear Information System (INIS)

Belendez, Augusto; Alvarez, Mariela L; Fernandez, Elena; Pascual, Inmaculada

2009-01-01

A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.

A solution to nonlinearity problems

International Nuclear Information System (INIS)

Neuffer, D.V.

1989-01-01

New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron or transport line are presented. In a simplest form, correction elements are places at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule, forming an accurate quasi-local canceling approximation to the nonlinearity. The F, C, and D correctors may also be used to obtain precise control of the horizontal, coupled, and vertical motion. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in beam transport have been obtained. 13 refs., 1 fig., 1 tab

Epsilon topological accelerating algorithms for difference method for initial-value problems

International Nuclear Information System (INIS)

Hristea, V.; Posirca, M.

1992-01-01

Linear and nonlinear parabolic equations can be solved by discretization methods which lead to linear and nonlinear algebraic systems. The iterative methods (e.g. Gauss - Seidel) show a very slow convergence and instability in the case of nonlinear equations. This paper proposes an ε topological algorithm for accelerating slow iterative methods used in the thermohydraulic code COBRA and the dynamic code ADEP. The results show an executing time approximately ten times lower than original algorithms. (Author)

Application of semi-empirical modeling and non-linear regression to unfolding fast neutron spectra from integral reaction rate data

International Nuclear Information System (INIS)

Harker, Y.D.

1976-01-01

A semi-empirical analytical expression representing a fast reactor neutron spectrum has been developed. This expression was used in a non-linear regression computer routine to obtain from measured multiple foil integral reaction data the neutron spectrum inside the Coupled Fast Reactivity Measurement Facility. In this application six parameters in the analytical expression for neutron spectrum were adjusted in the non-linear fitting process to maximize consistency between calculated and measured integral reaction rates for a set of 15 dosimetry detector foils. In two-thirds of the observations the calculated integral agreed with its respective measured value to within the experimental standard deviation, and in all but one case agreement within two standard deviations was obtained. Based on this quality of fit the estimated 70 to 75 percent confidence intervals for the derived spectrum are 10 to 20 percent for the energy range 100 eV to 1 MeV, 10 to 50 percent for 1 MeV to 10 MeV and 50 to 90 percent for 10 MeV to 18 MeV. The analytical model has demonstrated a flexibility to describe salient features of neutron spectra of the fast reactor type. The use of regression analysis with this model has produced a stable method to derive neutron spectra from a limited amount of integral data

A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems

International Nuclear Information System (INIS)

Xia Tiecheng; Chen Xiaohong; Chen Dengyuan

2004-01-01

An eigenvalue problem and the associated new Lax integrable hierarchy of nonlinear evolution equations are presented in this paper. As two reductions, the generalized nonlinear Schroedinger equations and the generalized mKdV equations are obtained. Zero curvature representation and bi-Hamiltonian structure are established for the whole hierarchy based on a pair of Hamiltonian operators (Lenard's operators), and it is shown that the hierarchy of nonlinear evolution equations is integrable in Liouville's sense. Thus the hierarchy of nonlinear evolution equations has infinitely many commuting symmetries and conservation laws. Moreover the eigenvalue problem is nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalue functions. Finally finite-dimensional Liouville integrable system are found, and the involutive solutions of the hierarchy of equations are given. In particular, the involutive solutions are developed for the system of generalized nonlinear Schroedinger equations

Electron Acceleration in Supernovae and Millimeter Perspectives

Directory of Open Access Journals (Sweden)

Keiichi Maeda

2014-12-01

Full Text Available Supernovae launch a strong shock wave by the interaction of the expanding ejecta and surrounding circumstellar matter (CSM. At the shock, electrons are accelerated to relativistic speed, creating observed synchrotron emissions in radio wavelengths. In this paper, I suggest that SNe (i.e., < 1 year since the explosion provide a unique site to study the electron acceleration mechanism. I argue that the eciency of the acceleration at the young SN shock is much lower than conventionally assumed, and that the electrons emitting in the cm wavelengths are not fully in the Diffusive Shock Acceleration (DSA regime. Thus radio emissions from young SNe record information on the yet-unresolved 'injection' mechanism. I also present perspectives of millimeter (mm observations of SNe - this will provide opportunities to uniquely determine the shock physics and the acceleration efficiency, to test the non-linear DSA mechanism and provide a characteristic electron energy scale with which the DSA start dominating the electron acceleration.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

Science.gov (United States)

Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.

2018-05-01

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

Two Step Acceleration Process of Electrons in the Outer Van Allen Radiation Belt by Time Domain Electric Field Bursts and Large Amplitude Chorus Waves

Science.gov (United States)

Agapitov, O. V.; Mozer, F.; Artemyev, A.; Krasnoselskikh, V.; Lejosne, S.

2014-12-01

A huge number of different non-linear structures (double layers, electron holes, non-linear whistlers, etc) have been observed by the electric field experiment on the Van Allen Probes in conjunction with relativistic electron acceleration in the Earth's outer radiation belt. These structures, found as short duration (~0.1 msec) quasi-periodic bursts of electric field in the high time resolution electric field waveform, have been called Time Domain Structures (TDS). They can quite effectively interact with radiation belt electrons. Due to the trapping of electrons into these non-linear structures, they are accelerated up to ~10 keV and their pitch angles are changed, especially for low energies (˜1 keV). Large amplitude electric field perturbations cause non-linear resonant trapping of electrons into the effective potential of the TDS and these electrons are then accelerated in the non-homogeneous magnetic field. These locally accelerated electrons create the "seed population" of several keV electrons that can be accelerated by coherent, large amplitude, upper band whistler waves to MeV energies in this two step acceleration process. All the elements of this chain acceleration mechanism have been observed by the Van Allen Probes.

Neural Networks for Modeling and Control of Particle Accelerators

Science.gov (United States)

Edelen, A. L.; Biedron, S. G.; Chase, B. E.; Edstrom, D.; Milton, S. V.; Stabile, P.

2016-04-01

Particle accelerators are host to myriad nonlinear and complex physical phenomena. They often involve a multitude of interacting systems, are subject to tight performance demands, and should be able to run for extended periods of time with minimal interruptions. Often times, traditional control techniques cannot fully meet these requirements. One promising avenue is to introduce machine learning and sophisticated control techniques inspired by artificial intelligence, particularly in light of recent theoretical and practical advances in these fields. Within machine learning and artificial intelligence, neural networks are particularly well-suited to modeling, control, and diagnostic analysis of complex, nonlinear, and time-varying systems, as well as systems with large parameter spaces. Consequently, the use of neural network-based modeling and control techniques could be of significant benefit to particle accelerators. For the same reasons, particle accelerators are also ideal test-beds for these techniques. Many early attempts to apply neural networks to particle accelerators yielded mixed results due to the relative immaturity of the technology for such tasks. The purpose of this paper is to re-introduce neural networks to the particle accelerator community and report on some work in neural network control that is being conducted as part of a dedicated collaboration between Fermilab and Colorado State University (CSU). We describe some of the challenges of particle accelerator control, highlight recent advances in neural network techniques, discuss some promising avenues for incorporating neural networks into particle accelerator control systems, and describe a neural network-based control system that is being developed for resonance control of an RF electron gun at the Fermilab Accelerator Science and Technology (FAST) facility, including initial experimental results from a benchmark controller.

Probing the deep nonlinear stage of the ablative Rayleigh-Taylor instability in indirect drive experiments on the National Ignition Facility

Energy Technology Data Exchange (ETDEWEB)

Casner, A., E-mail: alexis.casner@cea.fr; Masse, L.; Liberatore, S.; Loiseau, P.; Masson-Laborde, P. E.; Jacquet, L. [CEA, DAM, DIF, F-91297 Arpajon (France); Martinez, D.; Moore, A. S.; Seugling, R.; Felker, S.; Haan, S. W.; Remington, B. A.; Smalyuk, V. A. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Farrell, M.; Giraldez, E.; Nikroo, A. [General Atomics, San Diego, California 92121 (United States)

2015-05-15

Academic tests in physical regimes not encountered in Inertial Confinement Fusion will help to build a better understanding of hydrodynamic instabilities and constitute the scientifically grounded validation complementary to fully integrated experiments. Under the National Ignition Facility (NIF) Discovery Science program, recent indirect drive experiments have been carried out to study the ablative Rayleigh-Taylor Instability (RTI) in transition from weakly nonlinear to highly nonlinear regime [A. Casner et al., Phys. Plasmas 19, 082708 (2012)]. In these experiments, a modulated package is accelerated by a 175 eV radiative temperature plateau created by a room temperature gas-filled platform irradiated by 60 NIF laser beams. The unique capabilities of the NIF are harnessed to accelerate this planar sample over much larger distances (≃1.4 mm) and longer time periods (≃12 ns) than previously achieved. This extended acceleration could eventually allow entering into a turbulent-like regime not precluded by the theory for the RTI at the ablation front. Simultaneous measurements of the foil trajectory and the subsequent RTI growth are performed and compared with radiative hydrodynamics simulations. We present RTI growth measurements for two-dimensional single-mode and broadband multimode modulations. The dependence of RTI growth on initial conditions and ablative stabilization is emphasized, and we demonstrate for the first time in indirect-drive a bubble-competition, bubble-merger regime for the RTI at ablation front.

Relative Nonlinear Electrodynamics Interaction of Charged Particles with Strong and Super Strong Laser Fields

CERN Document Server

Avetissian, Hamlet

2006-01-01

This book covers a large class of fundamental investigations into Relativistic Nonlinear Electrodynamics. It explores the interaction between charged particles and strong laser fields, mainly concentrating on contemporary problems of x-ray lasers, new type small set-up high-energy accelerators of charged particles, as well as electron-positron pair production from super powerful laser fields of relativistic intensities. It will also discuss nonlinear phenomena of threshold nature that eliminate the concurrent inverse processes in the problems of Laser Accelerator and Free Electron Laser, thus creating new opportunities for solving these problems.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

Science.gov (United States)

Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

2014-11-21

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

Acceleration of cosmic rays in SNR shock waves

International Nuclear Information System (INIS)

Drury, L.O'C.; Markiewicz, W.J.; Voelk, H.J.

1988-01-01

The time dependence of the energy density of cosmic rays accelerated in the outer shock of a supernova is studied in simple nonlinear models. The solutions are classified in their dependence on the parameters of the system. (orig.)

An Integrated Enterprise Accelerator Database for the SLC Control System

International Nuclear Information System (INIS)

2002-01-01

Since its inception in the early 1980's, the SLC Control System has been driven by a highly structured memory-resident real-time database. While efficient, its rigid structure and file-based sources makes it difficult to maintain and extract relevant information. The goal of transforming the sources for this database into a relational form is to enable it to be part of a Control System Enterprise Database that is an integrated central repository for SLC accelerator device and Control System data with links to other associated databases. We have taken the concepts developed for the NLC Enterprise Database and used them to create and load a relational model of the online SLC Control System database. This database contains data and structure to allow querying and reporting on beamline devices, their associations and parameters. In the future this will be extended to allow generation of EPICS and SLC database files, setup of applications and links to other databases such as accelerator maintenance, archive data, financial and personnel records, cabling information, documentation etc. The database is implemented using Oracle 8i. In the short term it will be updated daily in batch from the online SLC database. In the longer term, it will serve as the primary source for Control System static data, an R and D platform for the NLC, and contribute to SLC Control System operations

Fourier-based integration of quasi-periodic gait accelerations for drift-free displacement estimation using inertial sensors.

Science.gov (United States)

Sabatini, Angelo Maria; Ligorio, Gabriele; Mannini, Andrea

2015-11-23

In biomechanical studies Optical Motion Capture Systems (OMCS) are considered the gold standard for determining the orientation and the position (pose) of an object in a global reference frame. However, the use of OMCS can be difficult, which has prompted research on alternative sensing technologies, such as body-worn inertial sensors. We developed a drift-free method to estimate the three-dimensional (3D) displacement of a body part during cyclical motions using body-worn inertial sensors. We performed the Fourier analysis of the stride-by-stride estimates of the linear acceleration, which were obtained by transposing the specific forces measured by the tri-axial accelerometer into the global frame using a quaternion-based orientation estimation algorithm and detecting when each stride began using a gait-segmentation algorithm. The time integration was performed analytically using the Fourier series coefficients; the inverse Fourier series was then taken for reconstructing the displacement over each single stride. The displacement traces were concatenated and spline-interpolated to obtain the entire trace. The method was applied to estimate the motion of the lower trunk of healthy subjects that walked on a treadmill and it was validated using OMCS reference 3D displacement data; different approaches were tested for transposing the measured specific force into the global frame, segmenting the gait and performing time integration (numerically and analytically). The width of the limits of agreements were computed between each tested method and the OMCS reference method for each anatomical direction: Medio-Lateral (ML), VerTical (VT) and Antero-Posterior (AP); using the proposed method, it was observed that the vertical component of displacement (VT) was within ±4 mm (±1.96 standard deviation) of OMCS data and each component of horizontal displacement (ML and AP) was within ±9 mm of OMCS data. Fourier harmonic analysis was applied to model stride-by-stride linear

A General Accelerated Degradation Model Based on the Wiener Process.

Science.gov (United States)

Liu, Le; Li, Xiaoyang; Sun, Fuqiang; Wang, Ning

2016-12-06

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

A General Accelerated Degradation Model Based on the Wiener Process

Directory of Open Access Journals (Sweden)

Le Liu

2016-12-01

Full Text Available Accelerated degradation testing (ADT is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

Technology of magnetically driven accelerators

International Nuclear Information System (INIS)

Brix, D.L.; Hawkins, S.A.; Poor, S.E.; Reginato, L.L.; Smith, M.W.

1985-01-01

The marriage of Induction Linac technology with Nonlinear Magnetic Modulators has produced some unique capabilities. It appears possible to produce electron beams with average currents measured in amperes, at gradients exceeding 1 MeV/meter, and with power efficiencies approaching 50%. A 2 MeV, 5 kA electron accelerator has been constructed at the Lawrence Livermore National Laboratory (LLNL) to demonstrate these concepts and to provide a test facility for high brightness sources. The pulse drive for the accelerator is based on state-of-the-art magnetic pulse compressors with very high peak power capability, repetition rates exceeding a kilohertz and excellent reliability

Technology of magnetically driven accelerators

International Nuclear Information System (INIS)

Birx, D.L.; Hawkins, S.A.; Poor, S.E.; Reginato, L.L.; Smith, M.W.

1985-01-01

The marriage of Induction Linac technology with Nonlinear Magnetic Modulators has produced some unique capabilities. It appears possible to produce electron beams with average currents measured in amperes, at gradients exceeding 1 MeV/meter, and with power efficiencies approach 50%. A 2 MeV, 5 kA electron accelerator has been constructed at the Lawrence Livermore National Laboratory (LLNL) to demonstrate these concepts and to provide a test facility for high brightness sources. The pulse drive for the accelerator is based on state-of-the-art magnetic pulse compressors with very high peak power capability, repetition rates exceeding a kilohertz and excellent reliability

Nonlinear structural damage detection using support vector machines

Science.gov (United States)

Xiao, Li; Qu, Wenzhong

2012-04-01

An actual structure including connections and interfaces may exist nonlinear. Because of many complicated problems about nonlinear structural health monitoring (SHM), relatively little progress have been made in this aspect. Statistical pattern recognition techniques have been demonstrated to be competitive with other methods when applied to real engineering datasets. When a structure existing 'breathing' cracks that open and close under operational loading may cause a linear structural system to respond to its operational and environmental loads in a nonlinear manner nonlinear. In this paper, a vibration-based structural health monitoring when the structure exists cracks is investigated with autoregressive support vector machine (AR-SVM). Vibration experiments are carried out with a model frame. Time-series data in different cases such as: initial linear structure; linear structure with mass changed; nonlinear structure; nonlinear structure with mass changed are acquired.AR model of acceleration time-series is established, and different kernel function types and corresponding parameters are chosen and compared, which can more accurate, more effectively locate the damage. Different cases damaged states and different damage positions have been recognized successfully. AR-SVM method for the insufficient training samples is proved to be practical and efficient on structure nonlinear damage detection.

Quantum-dot-based integrated non-linear sources

DEFF Research Database (Denmark)

Bernard, Alice; Mariani, Silvia; Andronico, Alessio

2015-01-01

The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter...

Recent advances in computational-analytical integral transforms for convection-diffusion problems

Science.gov (United States)

Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.; Almeida, A. P.

2017-10-01

An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numerical-analytical methodology for partial differential equations. Special emphasis is given to novel algorithm implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.

Fully nonlinear time-domain simulation of a backward bent duct buoy floating wave energy converter using an acceleration potential method

Directory of Open Access Journals (Sweden)

Kyoung-Rok Lee

2013-12-01

Full Text Available A floating Oscillating Water Column (OWC wave energy converter, a Backward Bent Duct Buoy (BBDB, was simulated using a state-of-the-art, two-dimensional, fully-nonlinear Numerical Wave Tank (NWT technique. The hydrodynamic performance of the floating OWC device was evaluated in the time domain. The acceleration potential method, with a full-updated kernel matrix calculation associated with a mode decomposition scheme, was implemented to obtain accurate estimates of the hydrodynamic force and displacement of a freely floating BBDB. The developed NWT was based on the potential theory and the boundary element method with constant panels on the boundaries. The mixed Eulerian-Lagrangian (MEL approach was employed to capture the nonlinear free surfaces inside the chamber that interacted with a pneumatic pressure, induced by the time-varying airflow velocity at the air duct. A special viscous damping was applied to the chamber free surface to represent the viscous energy loss due to the BBDB's shape and motions. The viscous damping coefficient was properly selected using a comparison of the experimental data. The calculated surface elevation, inside and outside the chamber, with a tuned viscous damping correlated reasonably well with the experimental data for various incident wave conditions. The conservation of the total wave energy in the computational domain was confirmed over the entire range of wave frequencies.

Geometric Structure of the Classical Lagrange-d’Alambert Principle and Its Application to Integrable Nonlinear Dynamical Systems

Directory of Open Access Journals (Sweden)

Anatolij K. Prykarpatski

2017-12-01

Full Text Available The classical Lagrange-d’Alembert principle had a decisive influence on formation of modern analytical mechanics which culminated in modern Hamilton and Poisson mechanics. Being mainly interested in the geometric interpretation of this principle, we devoted our review to its deep relationships to modern Lie-algebraic aspects of the integrability theory of nonlinear heavenly type dynamical systems and its so called Lax-Sato counterpart. We have also analyzed old and recent investigations of the classical M. A. Buhl problem of describing compatible linear vector field equations, its general M.G. Pfeiffer and modern Lax-Sato type special solutions. Especially we analyzed the related Lie-algebraic structures and integrability properties of a very interesting class of nonlinear dynamical systems called the dispersionless heavenly type equations, which were initiated by Plebański and later analyzed in a series of articles. As effective tools the AKS-algebraic and related R -structure schemes are used to study the orbits of the corresponding co-adjoint actions, which are intimately related to the classical Lie-Poisson structures on them. It is demonstrated that their compatibility condition coincides with the corresponding heavenly type equations under consideration. It is also shown that all these equations originate in this way and can be represented as a Lax-Sato compatibility condition for specially constructed loop vector fields on the torus. Typical examples of such heavenly type equations, demonstrating in detail their integrability via the scheme devised herein, are presented.

Nonlinearities in modified gravity cosmology: Signatures of modified gravity in the nonlinear matter power spectrum

International Nuclear Information System (INIS)

Cui Weiguang; Zhang Pengjie; Yang Xiaohu

2010-01-01

A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter ζ, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (ζ=1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < or approx. 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < or approx. 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance of including the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size, and initial redshift). We find that, the nonlinear power spectra can differ by ∼30% for 10% deviation from GR (|ζ-1|=0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.

Trapping and dark current in plasma-based accelerators

International Nuclear Information System (INIS)

Schroder, C.B.; Esarey, E.; Shadwick, B.A.; Leemans, W.P.

2004-01-01

The trapping of thermal electrons in a nonlinear plasma wave of arbitrary phase velocity is investigated. The threshold plasma wave amplitude for trapping plasma electrons is calculated, thereby determining the fraction trapped and the expected dark current in a plasma-based accelerator. It is shown that the presence of a laser field (e.g., trapping in the self-modulated regime of the laser wakefield accelerator) increases the trapping threshold. Implications for experimental and numerical laser-plasma studies are discussed

Design automation for integrated nonlinear logic circuits (Conference Presentation)

Science.gov (United States)

Van Vaerenbergh, Thomas; Pelc, Jason; Santori, Charles; Bose, Ranojoy; Kielpinski, Dave; Beausoleil, Raymond G.

2016-05-01

A key enabler of the IT revolution of the late 20th century was the development of electronic design automation (EDA) tools allowing engineers to manage the complexity of electronic circuits with transistor counts now reaching into the billions. Recently, we have been developing large-scale nonlinear photonic integrated logic circuits for next generation all-optical information processing. At this time a sufficiently powerful EDA-style software tool chain to design this type of complex circuits does not yet exist. Here we describe a hierarchical approach to automating the design and validation of photonic integrated circuits, which can scale to several orders of magnitude higher complexity than the state of the art. Most photonic integrated circuits developed today consist of a small number of components, and only limited hierarchy. For example, a simple photonic transceiver may contain on the order of 10 building-block components, consisting of grating couplers for photonic I/O, modulators, and signal splitters/combiners. Because this is relatively easy to lay out by hand (or simple script) existing photonic design tools have relatively little automation in comparison to electronics tools. But demonstrating all-optical logic will require significantly more complex photonic circuits containing up to 1,000 components, hence becoming infeasible to design manually. Our design framework is based off Python-based software from Luceda Photonics which provides an environment to describe components, simulate their behavior, and export design files (GDS) to foundries for fabrication. At a fundamental level, a photonic component is described as a parametric cell (PCell) similarly to electronics design. PCells are described by geometric characteristics of their layout. A critical part of the design framework is the implementation of PCells as Python objects. PCell objects can then use inheritance to simplify design, and hierarchical designs can be made by creating composite

Nonlinear Dynamics in Spear Wigglers

International Nuclear Information System (INIS)

2002-01-01

BL11, the most recently installed wiggler in the SPEAR storage ring at SSRL, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and with closed orbit shifts were used to characterize the nonlinear fields of the SPEAR insertion devices (IDs). Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different than the flip coil measurements made along a straight line. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Corrector magnets to cancel the BL11 nonlinear fields are presently under construction

Long-time integration methods for mesoscopic models of pattern-forming systems

International Nuclear Information System (INIS)

Abukhdeir, Nasser Mohieddin; Vlachos, Dionisios G.; Katsoulakis, Markos; Plexousakis, Michael

2011-01-01

Spectral methods for simulation of a mesoscopic diffusion model of surface pattern formation are evaluated for long simulation times. Backwards-differencing time-integration, coupled with an underlying Newton-Krylov nonlinear solver (SUNDIALS-CVODE), is found to substantially accelerate simulations, without the typical requirement of preconditioning. Quasi-equilibrium simulations of patterned phases predicted by the model are shown to agree well with linear stability analysis. Simulation results of the effect of repulsive particle-particle interactions on pattern relaxation time and short/long-range order are discussed.

Nonlinear optical interactions in silicon waveguides

Directory of Open Access Journals (Sweden)

Kuyken B.

2017-03-01

Full Text Available The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.

Cavity nonlinear optics with layered materials

Directory of Open Access Journals (Sweden)

Fryett Taylor

2017-12-01

Full Text Available Unprecedented material compatibility and ease of integration, in addition to the unique and diverse optoelectronic properties of layered materials, have generated significant interest in their utilization in nanophotonic devices. While initial nanophotonic experiments with layered materials primarily focused on light sources, modulators, and detectors, recent efforts have included nonlinear optical devices. In this paper, we review the current state of cavity-enhanced nonlinear optics with layered materials. Along with conventional nonlinear optics related to harmonic generation, we report on emerging directions of nonlinear optics, where layered materials can potentially play a significant role.

Nonlinear Fokker-Planck Equations Fundamentals and Applications

CERN Document Server

Frank, Till Daniel

2005-01-01

Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, popul...

Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.

1998-01-01

We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....

A simple predistortion technique for suppression of nonlinear effects in periodic signals generated by nonlinear transducers

Science.gov (United States)

Novak, A.; Simon, L.; Lotton, P.

2018-04-01

Mechanical transducers, such as shakers, loudspeakers and compression drivers that are used as excitation devices to excite acoustical or mechanical nonlinear systems under test are imperfect. Due to their nonlinear behaviour, unwanted contributions appear at their output besides the wanted part of the signal. Since these devices are used to study nonlinear systems, it should be required to measure properly the systems under test by overcoming the influence of the nonlinear excitation device. In this paper, a simple method that corrects distorted output signal of the excitation device by means of predistortion of its input signal is presented. A periodic signal is applied to the input of the excitation device and, from analysing the output signal of the device, the input signal is modified in such a way that the undesirable spectral components in the output of the excitation device are cancelled out after few iterations of real-time processing. The experimental results provided on an electrodynamic shaker show that the spectral purity of the generated acceleration output approaches 100 dB after few iterations (1 s). This output signal, applied to the system under test, is thus cleaned from the undesirable components produced by the excitation device; this is an important condition to ensure a correct measurement of the nonlinear system under test.

Cosmic Ray Acceleration in Supernova Remnants

International Nuclear Information System (INIS)

O'C Drury, Luke

2005-01-01

This paper describes some recent developments in our understanding of cosmic ray acceleration in supernova remnant shocks. It is pointed out that while good agreement now exists as to steady nonlinear modifications to the shock structure, there is also growing evidence that the mesoscopic scales may not in fact be steady and that significant instabilities associated with magnetic field amplification may be a feature of strong collisionless plasma shocks. There is strong observational evidence for such magnetic field amplification, and it appears to solve a number of long-standing issues concerned with acceleration of cosmic rays in supernova remnants

Estimating the angular velocity of a rigid body moving in the plane from tangential and centripetal acceleration measurements

International Nuclear Information System (INIS)

Cardou, Philippe; Angeles, Jorge

2008-01-01

Two methods are available for the estimation of the angular velocity of a rigid body from point-acceleration measurements: (i) the time-integration of the angular acceleration and (ii) the square-rooting of the centripetal acceleration. The inaccuracy of the first method is due mainly to the accumulation of the error on the angular acceleration throughout the time-integration process, which does not prevent that it be used successfully in crash tests with dummies, since these experiments never last more than one second. On the other hand, the error resulting from the second method is stable through time, but becomes inaccurate whenever the rigid body angular velocity approaches zero, which occurs in many applications. In order to take advantage of the complementarity of these two methods, a fusion of their estimates is proposed. To this end, the accelerometer measurements are modeled as exact signals contaminated with bias errors and Gaussian white noise. The relations between the variables at stake are written in the form of a nonlinear state-space system in which the angular velocity and the angular acceleration are state variables. Consequently, a minimum-variance-error estimate of the state vector is obtained by means of extended Kalman filtering. The performance of the proposed estimation method is assessed by means of simulation. Apparently, the resulting estimation method is more robust than the existing accelerometer-only methods and competitive with gyroscope measurements. Moreover, it allows the identification and the compensation of any bias error in the accelerometer measurements, which is a significant advantage over gyroscopes

Two-dimensional nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed

International Nuclear Information System (INIS)

Ghayesh, Mergen H.; Amabili, Marco; Farokhi, Hamed

2013-01-01

In the present study, the coupled nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed is investigated employing a numerical technique. The equations of motion for both the transverse and longitudinal motions are obtained using Newton’s second law of motion and the constitutive relations. A two-parameter rheological model of the Kelvin–Voigt energy dissipation mechanism is employed in the modelling of the viscoelastic beam material, in which the material time derivative is used in the viscoelastic constitutive relation. The Galerkin method is then applied to the coupled nonlinear equations, which are in the form of partial differential equations, resulting in a set of nonlinear ordinary differential equations (ODEs) with time-dependent coefficients due to the axial acceleration. A change of variables is then introduced to this set of ODEs to transform them into a set of first-order ordinary differential equations. A variable step-size modified Rosenbrock method is used to conduct direct time integration upon this new set of first-order nonlinear ODEs. The mean axial speed and the amplitude of the speed variations, which are taken as bifurcation parameters, are varied, resulting in the bifurcation diagrams of Poincaré maps of the system. The dynamical characteristics of the system are examined more precisely via plotting time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms (FFTs)

Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report

International Nuclear Information System (INIS)

Tataronis, J. A.

2004-01-01

This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory

Fringing-field effects in acceleration columns

International Nuclear Information System (INIS)

Yavor, M.I.; Weick, H.; Wollnik, H.

1999-01-01

Fringing-field effects in acceleration columns are investigated, based on the fringing-field integral method. Transfer matrices at the effective boundaries of the acceleration column are obtained, as well as the general transfer matrix of the region separating two homogeneous electrostatic fields with different field strengths. The accuracy of the fringing-field integral method is investigated

Nonlinear integral equations for thermodynamics of the sl(r + 1) Uimin-Sutherland model

International Nuclear Information System (INIS)

Tsuboi, Zengo

2003-01-01

We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the those from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIEs). In particular, a subset of these NLIEs forms a system of NLIEs which contains only a finite number of unknown functions. For r=1, this subset of NLIEs reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIEs is clarified. Based on our new NLIEs, we also calculate the high-temperature expansion of the free energy

Adaptive Actor-Critic Design-Based Integral Sliding-Mode Control for Partially Unknown Nonlinear Systems With Input Disturbances.

Science.gov (United States)

Fan, Quan-Yong; Yang, Guang-Hong

2016-01-01

This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.

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

Science.gov (United States)

Chen, Hsin-Yuan; Yang, Chi-Ching

2001-08-01

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

Regularized iterative integration combined with non-linear diffusion filtering for phase-contrast x-ray computed tomography.

Science.gov (United States)

Burger, Karin; Koehler, Thomas; Chabior, Michael; Allner, Sebastian; Marschner, Mathias; Fehringer, Andreas; Willner, Marian; Pfeiffer, Franz; Noël, Peter

2014-12-29

Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.

COMBINING LONG MEMORY AND NONLINEAR MODEL OUTPUTS FOR INFLATION FORECAST

OpenAIRE

Heri Kuswanto; Irhamah Alimuhajin; Laylia Afidah

2014-01-01

Long memory and nonlinearity have been proven as two models that are easily to be mistaken. In other words, nonlinearity is a strong candidate of spurious long memory by introducing a certain degree of fractional integration that lies in the region of long memory. Indeed, nonlinear process belongs to short memory with zero integration order. The idea of the forecast is to obtain the future condition with minimum error. Some researches argued that no matter what the model is, the important thi...

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.

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

Science.gov (United States)

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

Human responses at work may exhibit nonlinear properties where small changes in the initial task conditions can lead to large changes in system behavior. Therefore, it is important to study such nonlinearity to gain a better understanding of human performance under a variety of physical, perceptual, and cognitive tasks conditions. The main objective of this study was to investigate whether the human trunk kinematics data during a manual lifting task exhibits nonlinear behavior in terms of determinist chaos. Data related to kinematics of the trunk with respect to the pelvis were collected using Industrial Lumbar Motion Monitor (ILMM), and analyzed applying the nonlinear dynamical systems methodology. Nonlinear dynamics quantifiers of Lyapunov exponents and Kaplan-Yorke dimensions were calculated and analyzed under different task conditions. The study showed that human trunk kinematics during manual lifting exhibits chaotic behavior in terms of trunk sagittal angular displacement, velocity and acceleration. The findings support the importance of accounting for nonlinear dynamical properties of biomechanical responses to lifting tasks.

Prediction of spectral acceleration response ordinates based on PGA attenuation

Science.gov (United States)

Graizer, V.; Kalkan, E.

2009-01-01

Developed herein is a new peak ground acceleration (PGA)-based predictive model for 5% damped pseudospectral acceleration (SA) ordinates of free-field horizontal component of ground motion from shallow-crustal earthquakes. The predictive model of ground motion spectral shape (i.e., normalized spectrum) is generated as a continuous function of few parameters. The proposed model eliminates the classical exhausted matrix of estimator coefficients, and provides significant ease in its implementation. It is structured on the Next Generation Attenuation (NGA) database with a number of additions from recent Californian events including 2003 San Simeon and 2004 Parkfield earthquakes. A unique feature of the model is its new functional form explicitly integrating PGA as a scaling factor. The spectral shape model is parameterized within an approximation function using moment magnitude, closest distance to the fault (fault distance) and VS30 (average shear-wave velocity in the upper 30 m) as independent variables. Mean values of its estimator coefficients were computed by fitting an approximation function to spectral shape of each record using robust nonlinear optimization. Proposed spectral shape model is independent of the PGA attenuation, allowing utilization of various PGA attenuation relations to estimate the response spectrum of earthquake recordings.

The Use of Conditional Probability Integral Transformation Method for Testing Accelerated Failure Time Models

Directory of Open Access Journals (Sweden)

Abdalla Ahmed Abdel-Ghaly

2016-06-01

Full Text Available This paper suggests the use of the conditional probability integral transformation (CPIT method as a goodness of fit (GOF technique in the field of accelerated life testing (ALT, specifically for validating the underlying distributional assumption in accelerated failure time (AFT model. The method is based on transforming the data into independent and identically distributed (i.i.d Uniform (0, 1 random variables and then applying the modified Watson statistic to test the uniformity of the transformed random variables. This technique is used to validate each of the exponential, Weibull and lognormal distributions' assumptions in AFT model under constant stress and complete sampling. The performance of the CPIT method is investigated via a simulation study. It is concluded that this method performs well in case of exponential and lognormal distributions. Finally, a real life example is provided to illustrate the application of the proposed procedure.

A novel method for non-parametric identification of nonlinear restoring forces in nonlinear vibrations from noisy response data: A conservative system

International Nuclear Information System (INIS)

Jang, T. S.; Kwon, S. H.; Han, S. L.

2009-01-01

A novel procedure is proposed to identify the functional form of nonlinear restoring forces in the nonlinear oscillatory motion of a conservative system. Although the problem of identification has a unique solution, formulation results in a Volterra-type of integral equation of the 'first' kind: the solution lacks stability because the integral equation is the 'first' kind. Thus, the new problem at hand is ill-posed. Inevitable small errors during the identification procedure can make the prediction of nonlinear restoring forces useless. We overcome the difficulty by using a stabilization technique of Landweber's regularization in this study. The capability of the proposed procedure is investigated through numerical examples

Integration of complex-wide mixed low-level waste activities for program acceleration and optimization

International Nuclear Information System (INIS)

McKenney, D.E.

1998-01-01

In July 1996, the US Department of Energy (DOE) chartered a contractor-led effort to develop a suite of technically defensible, integrated alternatives which would allow the Environmental Management program to accomplish its mission objectives in an accelerated fashion and at a reduced cost. These alternatives, or opportunities, could then be evaluated by DOE and stakeholders for possible implementation, given precursor requirements (regulatory changes, etc.) could be met and benefits to the Complex realized. This contractor effort initially focused on six waste types, one of which was Mixed Low-Level Waste (MLLW). Many opportunities were identified by the contractor team for integrating MLLW activities across the DOE Complex. These opportunities were further narrowed to six that had the most promise for implementation and savings to the DOE Complex. The opportunities include six items: (1) the consolidation of individual site analytical services procurement efforts, (2) the consolidation of individual site MLLW treatment services procurement efforts, (3) establishment of ''de minimus'' radioactivity levels, (4) standardization of characterization requirements, (5) increased utilization of existing DOE treatment facilities, and (6) using a combination of DOE and commercial MLLW disposal capacity. The results of the integration effort showed that by managing MLLW activities across the DOE Complex as a cohesive unit rather than as independent site efforts, the DOE could improve the rate of progress toward meeting its objectives and reduce its overall MLLW program costs. Savings potential for MLLW, if the identified opportunities could be implemented, could total $224 million or more. Implementation of the opportunities also could result in the acceleration of the MLLW ''work off schedule'' across the DOE Complex by five years

Oscillations in nonlinear systems

CERN Document Server

Hale, Jack K

2015-01-01

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

Science.gov (United States)

Erler, Norbert; Groß, Michael

2015-05-01

Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.

The Study of Non-Linear Acceleration of Particles during Substorms Using Multi-Scale Simulations

International Nuclear Information System (INIS)

Ashour-Abdalla, Maha

2011-01-01

To understand particle acceleration during magnetospheric substorms we must consider the problem on multple scales ranging from the large scale changes in the entire magnetosphere to the microphysics of wave particle interactions. In this paper we present two examples that demonstrate the complexity of substorm particle acceleration and its multi-scale nature. The first substorm provided us with an excellent example of ion acceleration. On March 1, 2008 four THEMIS spacecraft were in a line extending from 8 R E to 23 R E in the magnetotail during a very large substorm during which ions were accelerated to >500 keV. We used a combination of a global magnetohydrodynamic and large scale kinetic simulations to model the ion acceleration and found that the ions gained energy by non-adiabatic trajectories across the substorm electric field in a narrow region extending across the magnetotail between x = -10 R E and x = -15 R E . In this strip called the 'wall region' the ions move rapidly in azimuth and gain 100s of keV. In the second example we studied the acceleration of electrons associated with a pair of dipolarization fronts during a substorm on February 15, 2008. During this substorm three THEMIS spacecraft were grouped in the near-Earth magnetotail (x ∼-10 R E ) and observed electron acceleration of >100 keV accompanied by intense plasma waves. We used the MHD simulations and analytic theory to show that adiabatic motion (betatron and Fermi acceleration) was insufficient to account for the electron acceleration and that kinetic processes associated with the plasma waves were important.

Particle acceleration in regions of magnetic flux emergence: a statistical approach using test-particle- and MHD-simulations

Science.gov (United States)

Vlahos, Loukas; Archontis, Vasilis; Isliker, Heinz

We consider 3D nonlinear MHD simulations of an emerging flux tube, from the convection zone into the corona, focusing on the coronal part of the simulations. We first analyze the statistical nature and spatial structure of the electric field, calculating histograms and making use of iso-contour visualizations. Then test-particle simulations are performed for electrons, in order to study heating and acceleration phenomena, as well as to determine HXR emission. This study is done by comparatively exploring quiet, turbulent explosive, and mildly explosive phases of the MHD simulations. Also, the importance of collisional and relativistic effects is assessed, and the role of the integration time is investigated. Particular aim of this project is to verify the quasi- linear assumptions made in standard transport models, and to identify possible transport effects that cannot be captured with the latter. In order to determine the relation of our results to Fermi acceleration and Fokker-Planck modeling, we determine the standard transport coefficients. After all, we find that the electric field of the MHD simulations must be downscaled in order to prevent an un-physically high degree of acceleration, and the value chosen for the scale factor strongly affects the results. In different MHD time-instances we find heating to take place, and acceleration that depends on the level of MHD turbulence. Also, acceleration appears to be a transient phenomenon, there is a kind of saturation effect, and the parallel dynamics clearly dominate the energetics. The HXR spectra are not yet really compatible with observations, we have though to further explore the scaling of the electric field and the integration times used.

Analysis of nonlinear behavior of loudspeakers using the instantaneous frequency

DEFF Research Database (Denmark)

Huang, Hai; Jacobsen, Finn

2003-01-01

on the Fourier transform. In this work, a new method using the instantaneous frequency is introduced for describing and characterizing loudspeaker nonlinearities. First, numerical integration is applied to simulate the nonlinearities of loudspeakers caused by two nonlinear parameters, force factor and stiffness...

Efficient simulation of multimodal nonlinear propagation in step-index fibers

DEFF Research Database (Denmark)

Lægsgaard, Jesper

2017-01-01

A numerical approach to nonlinear propagation in waveguides based on real-space Gaussian quadrature integration of the nonlinear polarization during propagation is investigated and compared with the more conventional approach based on expressing the nonlinear polarization by a sum of mode overlap...

Modulational effects in accelerators

International Nuclear Information System (INIS)

Satogata, T.

1997-01-01

We discuss effects of field modulations in accelerators, specifically those that can be used for operational beam diagnostics and beam halo control. In transverse beam dynamics, combined effects of nonlinear resonances and tune modulations influence diffusion rates with applied tune modulation has been demonstrated. In the longitudinal domain, applied RF phase and voltage modulations provide mechanisms for parasitic halo transport, useful in slow crystal extraction. Experimental experiences with transverse tune and RF modulations are also discussed

PAC++: Object-oriented platform for accelerator codes

International Nuclear Information System (INIS)

Malitsky, N.; Reshetov, A.; Bourianoff, G.

1994-06-01

Software packages in accelerator physics have relatively long life cycles. They had been developed and used for a wide range of accelerators in the past as well as for the current projects. For example, the basic algorithms written in the first accelerator Program TRANSPORT are actual for design of most magnet systems. Most of these packages had been implemented on Fortran. But this language is rather inconvenient as a basic language for large integrated projects that possibly could include real-time data acquisition, data base access, graphic riser interface modules (GUI), arid other features. Some later accelerator programs had been based on object-oriented tools (primarily, C++ language). These range from systems for advanced theoretical studies to control system software. For the new generations of accelerators it would be desirable to have an integrated platform in which all simulation and control tasks will be considered with one point of view. In this report the basic principles of an object-oriented platform for accelerator research software (PAC++) are suggested and analyzed. Primary objectives of this work are to enable efficient self-explaining realization of the accelerator concepts and to provide an integrated environment for the updating and the developing of the code

Accelerator and Electrodynamics Capability Review

International Nuclear Information System (INIS)

Jones, Kevin W.

2010-01-01

Los Alamos National Laboratory (LANL) uses capability reviews to assess the science, technology and engineering (STE) quality and institutional integration and to advise Laboratory Management on the current and future health of the STE. Capability reviews address the STE integration that LANL uses to meet mission requirements. The Capability Review Committees serve a dual role of providing assessment of the Laboratory's technical contributions and integration towards its missions and providing advice to Laboratory Management. The assessments and advice are documented in reports prepared by the Capability Review Committees that are delivered to the Director and to the Principal Associate Director for Science, Technology and Engineering (PADSTE). Laboratory Management will use this report for STE assessment and planning. LANL has defined fifteen STE capabilities. Electrodynamics and Accelerators is one of the seven STE capabilities that LANL Management (Director, PADSTE, technical Associate Directors) has identified for review in Fiscal Year (FY) 2010. Accelerators and electrodynamics at LANL comprise a blend of large-scale facilities and innovative small-scale research with a growing focus on national security applications. This review is organized into five topical areas: (1) Free Electron Lasers; (2) Linear Accelerator Science and Technology; (3) Advanced Electromagnetics; (4) Next Generation Accelerator Concepts; and (5) National Security Accelerator Applications. The focus is on innovative technology with an emphasis on applications relevant to Laboratory mission. The role of Laboratory Directed Research and Development (LDRD) in support of accelerators/electrodynamics will be discussed. The review provides an opportunity for interaction with early career staff. Program sponsors and customers will provide their input on the value of the accelerator and electrodynamics capability to the Laboratory mission.

Accelerator and electrodynamics capability review

Energy Technology Data Exchange (ETDEWEB)

Jones, Kevin W [Los Alamos National Laboratory

2010-01-01

Los Alamos National Laboratory (LANL) uses capability reviews to assess the science, technology and engineering (STE) quality and institutional integration and to advise Laboratory Management on the current and future health of the STE. Capability reviews address the STE integration that LANL uses to meet mission requirements. The Capability Review Committees serve a dual role of providing assessment of the Laboratory's technical contributions and integration towards its missions and providing advice to Laboratory Management. The assessments and advice are documented in reports prepared by the Capability Review Committees that are delivered to the Director and to the Principal Associate Director for Science, Technology and Engineering (PADSTE). Laboratory Management will use this report for STE assessment and planning. LANL has defined fifteen STE capabilities. Electrodynamics and Accelerators is one of the seven STE capabilities that LANL Management (Director, PADSTE, technical Associate Directors) has identified for review in Fiscal Year (FY) 2010. Accelerators and electrodynamics at LANL comprise a blend of large-scale facilities and innovative small-scale research with a growing focus on national security applications. This review is organized into five topical areas: (1) Free Electron Lasers; (2) Linear Accelerator Science and Technology; (3) Advanced Electromagnetics; (4) Next Generation Accelerator Concepts; and (5) National Security Accelerator Applications. The focus is on innovative technology with an emphasis on applications relevant to Laboratory mission. The role of Laboratory Directed Research and Development (LDRD) in support of accelerators/electrodynamics will be discussed. The review provides an opportunity for interaction with early career staff. Program sponsors and customers will provide their input on the value of the accelerator and electrodynamics capability to the Laboratory mission.

Nonlinear singular perturbation problems of arbitrary real orders

International Nuclear Information System (INIS)

Bijura, Angelina M.

2003-10-01

Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

Direct and accelerated parameter mapping using the unscented Kalman filter.

Science.gov (United States)

Zhao, Li; Feng, Xue; Meyer, Craig H

2016-05-01

To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem. In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling. Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies. This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping. © 2015 Wiley Periodicals, Inc.

Nonlinear adaptive observer-based sliding mode control for LAMOST mount driving

International Nuclear Information System (INIS)

Zhou Wangping; Guo Wei; Yu Li; Yang Changsong; Zheng Yi

2010-01-01

Heavy disturbances caused mainly by wind and friction in the mount drive system greatly impair the pointing accuracy of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). To overcome this negative effect, a third order Higher Order Sliding Mode (HOSM) controller is proposed. The key part of this approach is to design an appropriate observer which obtains the acceleration state. A nonlinear adaptive observer is proposed in which a novel polynomial model is applied to estimate the internal disturbances of the mount drive system. Theoretical analysis demonstrates the stability of the proposed observer. Simulation results show that this nonlinear adaptive observer can obtain a high precision acceleration signal which completes the HOSM controller. Furthermore, the HOSM approach can easily satisfy the position tracking requirements of the LAMOST mount drive system.

Integrated condition monitoring of a fleet of offshore wind turbines with focus on acceleration streaming processing

International Nuclear Information System (INIS)

Helsen, Jan; Gioia, Nicoletta; Peeters, Cédric; Jordaens, Pieter-Jan

2017-01-01

Particularly offshore there is a trend to cluster wind turbines in large wind farms, and in the near future to operate such a farm as an integrated power production plant. Predictability of individual turbine behavior across the entire fleet is key in such a strategy. Failure of turbine subcomponents should be detected well in advance to allow early planning of all necessary maintenance actions; Such that they can be performed during low wind and low electricity demand periods. In order to obtain the insights to predict component failure, it is necessary to have an integrated clean dataset spanning all turbines of the fleet for a sufficiently long period of time. This paper illustrates our big-data approach to do this. In addition, advanced failure detection algorithms are necessary to detect failures in this dataset. This paper discusses a multi-level monitoring approach that consists of a combination of machine learning and advanced physics based signal-processing techniques. The advantage of combining different data sources to detect system degradation is in the higher certainty due to multivariable criteria. In order to able to perform long-term acceleration data signal processing at high frequency a streaming processing approach is necessary. This allows the data to be analysed as the sensors generate it. This paper illustrates this streaming concept on 5kHz acceleration data. A continuous spectrogram is generated from the data-stream. Real-life offshore wind turbine data is used. Using this streaming approach for calculating bearing failure features on continuous acceleration data will support failure propagation detection. (paper)

Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

Directory of Open Access Journals (Sweden)

Alsaedi Ahmed

2009-01-01

Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.

Proof of the path integral representation of the nonlinear Fokker-Planck equation by means of Fourier series

International Nuclear Information System (INIS)

Dekker, H.

1978-01-01

The lagrangian for the action occurring in the path integral solution of the nonlinear Fokker-Planck equation with constant diffusion function is derived by means of a straightforward Fourier series analysis. In this manner the path between the prepoint and the postpoint in the short time propagator is not restricted a priori to the usually considered straight line. Earlier results by Graham, Stratonovich, Horsthemke and Back, and the author's are recovered and thus put on much safer ground. (Auth.)

Developing an active artificial hair cell using nonlinear feedback control

Science.gov (United States)

Joyce, Bryan S.; Tarazaga, Pablo A.

2015-09-01

The hair cells in the mammalian cochlea convert sound-induced vibrations into electrical signals. These cells have inspired a variety of artificial hair cells (AHCs) to serve as biologically inspired sound, fluid flow, and acceleration sensors and could one day replace damaged hair cells in humans. Most of these AHCs rely on passive transduction of stimulus while it is known that the biological cochlea employs active processes to amplify sound-induced vibrations and improve sound detection. In this work, an active AHC mimics the active, nonlinear behavior of the cochlea. The AHC consists of a piezoelectric bimorph beam subjected to a base excitation. A feedback control law is used to reduce the linear damping of the beam and introduce a cubic damping term which gives the AHC the desired nonlinear behavior. Model and experimental results show the AHC amplifies the response due to small base accelerations, has a higher frequency sensitivity than the passive system, and exhibits a compressive nonlinearity like that of the mammalian cochlea. This bio-inspired accelerometer could lead to new sensors with lower thresholds of detection, improved frequency sensitivities, and wider dynamic ranges.

Rigorous bounds on survival times in circular accelerators and efficient computation of fringe-field transfer maps

International Nuclear Information System (INIS)

Hoffstaetter, G.H.

1994-12-01

Analyzing stability of particle motion in storage rings contributes to the general field of stability analysis in weakly nonlinear motion. A method which we call pseudo invariant estimation (PIE) is used to compute lower bounds on the survival time in circular accelerators. The pseudeo invariants needed for this approach are computed via nonlinear perturbative normal form theory and the required global maxima of the highly complicated multivariate functions could only be rigorously bound with an extension of interval arithmetic. The bounds on the survival times are large enough to the relevant; the same is true for the lower bounds on dynamical aperatures, which can be computed. The PIE method can lead to novel design criteria with the objective of maximizing the survival time. A major effort in the direction of rigourous predictions only makes sense if accurate models of accelerators are available. Fringe fields often have a significant influence on optical properties, but the computation of fringe-field maps by DA based integration is slower by several orders of magnitude than DA evaluation of the propagator for main-field maps. A novel computation of fringe-field effects called symplectic scaling (SYSCA) is introduced. It exploits the advantages of Lie transformations, generating functions, and scaling properties and is extremely accurate. The computation of fringe-field maps is typically made nearly two orders of magnitude faster. (orig.)

Grey-box state-space identification of nonlinear mechanical vibrations

Science.gov (United States)

Noël, J. P.; Schoukens, J.

2018-05-01

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.

Supersymmetric Yang-Mills fields as an integrable system and connections with other non-linear systems

International Nuclear Information System (INIS)

Chau, L.L.

1983-01-01

Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references

Intrinsic Nonlinearities and Layout Impacts of 100 V Integrated Power MOSFETs in Partial SOI Process

DEFF Research Database (Denmark)

Fan, Lin; Knott, Arnold; Jørgensen, Ivan Harald Holger

Parasitic capacitances of power semiconductors are a part of the key design parameters of state-of-the-art very high frequency (VHF) power supplies. In this poster, four 100 V integrated power MOSFETs with different layout structures are designed, implemented, and analyzed in a 0.18 ȝm partial...... Silicon-on-Insulator (SOI) process with a die area 2.31 mm2.  A small-signal model of power MOSFETs is proposed to systematically analyze the nonlinear parasitic capacitances in different transistor states: off-state, sub-threshold region, and on-state in the linear region. 3D plots are used to summarize...

Energy loss of a high charge bunched electron beam in plasma: Simulations, scaling, and accelerating wakefields

Directory of Open Access Journals (Sweden)

J. B. Rosenzweig

2004-06-01

Full Text Available The energy loss and gain of a beam in the nonlinear, “blowout” regime of the plasma wakefield accelerator, which features ultrahigh accelerating fields, linear transverse focusing forces, and nonlinear plasma motion, has been asserted, through previous observations in simulations, to scale linearly with beam charge. Additionally, from a recent analysis by Barov et al., it has been concluded that for an infinitesimally short beam, the energy loss is indeed predicted to scale linearly with beam charge for arbitrarily large beam charge. This scaling is predicted to hold despite the onset of a relativistic, nonlinear response by the plasma, when the number of beam particles occupying a cubic plasma skin depth exceeds that of plasma electrons within the same volume. This paper is intended to explore the deviations from linear energy loss using 2D particle-in-cell simulations that arise in the case of experimentally relevant finite length beams. The peak accelerating field in the plasma wave excited behind the finite-length beam is also examined, with the artifact of wave spiking adding to the apparent persistence of linear scaling of the peak field amplitude into the nonlinear regime. At large enough normalized charge, the linear scaling of both decelerating and accelerating fields collapses, with serious consequences for plasma wave excitation efficiency. Using the results of parametric particle-in-cell studies, the implications of these results for observing severe deviations from linear scaling in present and planned experiments are discussed.

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

Towards MRI-guided linear accelerator control: gating on an MRI accelerator.

Science.gov (United States)

Crijns, S P M; Kok, J G M; Lagendijk, J J W; Raaymakers, B W

2011-08-07

To boost the possibilities of image guidance in radiotherapy by providing images with superior soft-tissue contrast during treatment, we pursue diagnostic quality MRI functionality integrated with a linear accelerator. Large respiration-induced semi-periodic target excursions hamper treatment of cancer of the abdominal organs. Methods to compensate in real time for such motion are gating and tracking. These strategies are most effective in cases where anatomic motion can be visualized directly, which supports the use of an integrated MRI accelerator. We establish here an infrastructure needed to realize gated radiation delivery based on MR feedback and demonstrate its potential as a first step towards more advanced image guidance techniques. The position of a phantom subjected to one-dimensional periodic translation is tracked with the MR scanner. Real-time communication with the MR scanner and control of the radiation beam are established. Based on the time-resolved position of the phantom, gated radiation delivery to the phantom is realized. Dose distributions for dynamic delivery conditions with varying gating windows are recorded on gafchromic film. The similarity between dynamically and statically obtained dose profiles gradually increases as the gating window is decreased. With gating windows of 5 mm, we obtain sharp dose profiles. We validate our gating implementation by comparing measured dose profiles to theoretical profiles calculated using the knowledge of the imposed motion pattern. Excellent correspondence is observed. At the same time, we show that real-time on-line reconstruction of the accumulated dose can be performed using time-resolved target position information. This facilitates plan adaptation not only on a fraction-to-fraction scale but also during one fraction, which is especially valuable in highly accelerated treatment strategies. With the currently established framework and upcoming improvements to our prototype-integrated MRI accelerator

Deploying electromagnetic particle-in-cell (EM-PIC) codes on Xeon Phi accelerators boards

Science.gov (United States)

Fonseca, Ricardo

2014-10-01

The complexity of the phenomena involved in several relevant plasma physics scenarios, where highly nonlinear and kinetic processes dominate, makes purely theoretical descriptions impossible. Further understanding of these scenarios requires detailed numerical modeling, but fully relativistic particle-in-cell codes such as OSIRIS are computationally intensive. The quest towards Exaflop computer systems has lead to the development of HPC systems based on add-on accelerator cards, such as GPGPUs and more recently the Xeon Phi accelerators that power the current number 1 system in the world. These cards, also referred to as Intel Many Integrated Core Architecture (MIC) offer peak theoretical performances of >1 TFlop/s for general purpose calculations in a single board, and are receiving significant attention as an attractive alternative to CPUs for plasma modeling. In this work we report on our efforts towards the deployment of an EM-PIC code on a Xeon Phi architecture system. We will focus on the parallelization and vectorization strategies followed, and present a detailed performance evaluation of code performance in comparison with the CPU code.

Integrated Navigation System Design for Micro Planetary Rovers: Comparison of Absolute Heading Estimation Algorithms and Nonlinear Filtering

Science.gov (United States)

Ilyas, Muhammad; Hong, Beomjin; Cho, Kuk; Baeg, Seung-Ho; Park, Sangdeok

2016-01-01

This paper provides algorithms to fuse relative and absolute microelectromechanical systems (MEMS) navigation sensors, suitable for micro planetary rovers, to provide a more accurate estimation of navigation information, specifically, attitude and position. Planetary rovers have extremely slow speed (~1 cm/s) and lack conventional navigation sensors/systems, hence the general methods of terrestrial navigation may not be applicable to these applications. While relative attitude and position can be tracked in a way similar to those for ground robots, absolute navigation information is hard to achieve on a remote celestial body, like Moon or Mars, in contrast to terrestrial applications. In this study, two absolute attitude estimation algorithms were developed and compared for accuracy and robustness. The estimated absolute attitude was fused with the relative attitude sensors in a framework of nonlinear filters. The nonlinear Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) were compared in pursuit of better accuracy and reliability in this nonlinear estimation problem, using only on-board low cost MEMS sensors. Experimental results confirmed the viability of the proposed algorithms and the sensor suite, for low cost and low weight micro planetary rovers. It is demonstrated that integrating the relative and absolute navigation MEMS sensors reduces the navigation errors to the desired level. PMID:27223293

Dynamical Aperture Control in Accelerator Lattices With Multipole Potentials

CERN Document Server

Morozov, I

2017-01-01

We develop tools for symbolic representation of a non-linear accelerator model and analytical methods for description of non-linear dynamics. Information relevant to the dynamic aperture (DA) is then obtained from this model and can be used for indirect DA control or as a complement to direct numerical optimization. We apply two analytical methods and use multipole magnets to satisfy derived analytical constraints. The accelerator model is represented as a product of unperturbed and perturbed exponential operators with the exponent of the perturbed operator given as a power series in the perturbation parameter. Normal forms can be applied to this representation and the lattice parameters are used to control the normal form Hamiltonian and normal form transformation. Hamiltonian control is used to compute a control term or controlled operator. Lattice parameters are then fitted to satisfy the imposed control constraints. Theoretical results, as well as illustrative examples, are presented.

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits.

Science.gov (United States)

Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté

2015-12-24

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits.

Integration Test of the High Voltage Hall Accelerator System Components

Science.gov (United States)

Kamhawi, Hani; Haag, Thomas; Huang, Wensheng; Pinero, Luis; Peterson, Todd; Dankanich, John

2013-01-01

NASA Glenn Research Center is developing a 4 kilowatt-class Hall propulsion system for implementation in NASA science missions. NASA science mission performance analysis was completed using the latest high voltage Hall accelerator (HiVHAc) and Aerojet-Rocketdyne's state-of-the-art BPT-4000 Hall thruster performance curves. Mission analysis results indicated that the HiVHAc thruster out performs the BPT-4000 thruster for all but one of the missions studied. Tests of the HiVHAc system major components were performed. Performance evaluation of the HiVHAc thruster at NASA Glenn's vacuum facility 5 indicated that thruster performance was lower than performance levels attained during tests in vacuum facility 12 due to the lower background pressures attained during vacuum facility 5 tests when compared to vacuum facility 12. Voltage-Current characterization of the HiVHAc thruster in vacuum facility 5 showed that the HiVHAc thruster can operate stably for a wide range of anode flow rates for discharge voltages between 250 and 600 volts. A Colorado Power Electronics enhanced brassboard power processing unit was tested in vacuum for 1,500 hours and the unit demonstrated discharge module efficiency of 96.3% at 3.9 kilowatts and 650 volts. Stand-alone open and closed loop tests of a VACCO TRL 6 xenon flow control module were also performed. An integrated test of the HiVHAc thruster, brassboard power processing unit, and xenon flow control module was performed and confirmed that integrated operation of the HiVHAc system major components. Future plans include continuing the maturation of the HiVHAc system major components and the performance of a single-string integration test.

Piezoelectric Non-linear Nanomechanical Temperature and Acceleration Intensive Clocks (PENNTAC)

Science.gov (United States)

2014-05-01

amplifiers”, Applied Physics Letters , vol. 96, 234101, 2010. [4] Miller, N.J. “Escape statistics for parameter sweeps through bifurcations”, Phys. Rev. E...Device Letters , Vol. 33, Issue 5, 2012, pp. 724-726. J. S.-Fernandez, G. Piazza, “Thermal Nonlinearities in Contour Mode AlN Resonators”, IEEE Journal...Rinaldi, H. Pak, D. Fry, D. Bail , D. Stevens, Gianluca Piazza, “A 586 MHz Microcontroller Compensated MEMS Oscillator Based on Ovenized Aluminum

Single Particle Linear and Nonlinear Dynamics

International Nuclear Information System (INIS)

Cai, Y

2004-01-01

I will give a comprehensive review of existing particle tracking tools to assess long-term particle stability for small and large accelerators in the presence of realistic magnetic imperfections and machine misalignments. The emphasis will be on the tracking and analysis tools based upon the differential algebra, Lie operator, and ''polymorphism''. Using these tools, a uniform linear and non-linear analysis will be outlined as an application of the normal form

Cyclotron Acceleration of Relativistic Electrons through Landau Resonance with Obliquely Propagating Whistler Mode Chorus Emissions

Science.gov (United States)

Omura, Y.; Hsieh, Y. K.; Foster, J. C.; Erickson, P. J.; Kletzing, C.; Baker, D. N.

2017-12-01

A recent test particle simulation of obliquely propagating whistler mode wave-particle interaction [Hsieh and Omura, 2017] shows that the perpendicular wave electric field can play a significant role in trapping and accelerating relativistic electrons through Landau resonance. A further theoretical and numerical investigation verifies that there occurs nonlinear wave trapping of relativistic electrons by the nonlinear Lorentz force of the perpendicular wave magnetic field. An electron moving with a parallel velocity equal to the parallel phase velocity of an obliquely propagating wave basically see a stationary wave phase. Since the electron position is displaced from its gyrocenter by a distance ρ*sin(φ), where ρ is the gyroradius and φ is the gyrophase, the wave phase is modulated with the gyromotion, and the stationary wave fields as seen by the electron are expanded as series of Bessel functions Jn with phase variations n*φ. The J1 components of the wave electric and magnetic fields rotate in the right-hand direction with the gyrofrequency, and they can be in resonance with the electron undergoing the gyromotion, resulting in effective electron acceleration and pitch angle scattering. We have performed a subpacket analysis of chorus waveforms observed by the Van Allen Probes [Foster et al., 2017], and calculated the energy gain by the cyclotron acceleration through Landau resonance. We compare the efficiencies of accelerations by cyclotron and Landau resonances in typical events of rapid electron acceleration observed by the Van Allen Probes.References:[1] Hsieh, Y.-K., and Y. Omura (2017), Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere, J. Geophys. Res. Space Physics, 122, 675-694, doi:10.1002/2016JA023255.[2] Foster, J. C., P. J. Erickson, Y. Omura, D. N. Baker, C. A. Kletzing, and S. G. Claudepierre (2017), Van Allen Probes observations of prompt MeV radiation belt electron acceleration in nonlinear

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Low-amplitude instability as a premise for the spontaneous symmetry breaking in the new integrable semidiscrete nonlinear system

International Nuclear Information System (INIS)

Vakhnenko, Oleksiy O.; Vakhnenko, Vyacheslav O.

2014-01-01

The new integrable semidiscrete multicomponent nonlinear system characterized by two coupling parameters is presented. Relying upon the lowest local conservation laws the concise form of the system is given and its selfconsistent symmetric parametrization in terms of four independent field variables is found. The comprehensive analysis of quartic dispersion equation for the system low-amplitude excitations is made. The criteria distinguishing the domains of stability and instability of low-amplitude excitations are formulated and a collection of qualitatively distinct realizations of a dispersion law are graphically presented. The loop-like structure of a low-amplitude dispersion law of reduced system emerging within certain windows of adjustable coupling parameter turns out to resemble the loop-like structure of a dispersion law typical of beam-plasma oscillations. Basing on the peculiarities of low-amplitude dispersion law as the function of adjustable coupling parameter it is possible to predict the windows of spontaneous symmetry breaking even without an explicit knowledge of the system Lagrangian function. Having been rewritten in terms of properly chosen modified field variables the reduced four wave integrable system can be qualified as consisting of two coupled nonlinear lattice subsystems, namely the self-dual ladder network and the vibrational ones

Nonlinear electrostatic emittance compensation in kA, fs electron bunches

International Nuclear Information System (INIS)

Geer, S.B. van der; Loos, M.J. de; Botman, J.I.M.; Luiten, O.J.; Wiel, M.J. van der

2002-01-01

Nonlinear space-charge effects play an important role in emittance growth in the production of kA electron bunches with a bunch length much smaller than the bunch diameter. We propose a scheme employing the radial third-order component of an electrostatic acceleration field, to fully compensate the nonlinear space-charge effects. This results in minimal transverse root-mean-square emittance. The principle is demonstrated using our design simulations of a device for the production of high-quality, high-current, subpicosecond electron bunches using electrostatic acceleration in a 1 GV/m field. Simulations using the GPT code produce a bunch of 100 pC and 73 fs full width at half maximum pulse width, resulting in a peak current of about 1.2 kA at an energy of 2 MeV. The compensation scheme reduces the root-mean-square emittance by 34% to 0.4π mm mrad

Cast dielectric composite linear accelerator

Science.gov (United States)

Sanders, David M [Livermore, CA; Sampayan, Stephen [Manteca, CA; Slenes, Kirk [Albuquerque, NM; Stoller, H M [Albuquerque, NM

2009-11-10

A linear accelerator having cast dielectric composite layers integrally formed with conductor electrodes in a solventless fabrication process, with the cast dielectric composite preferably having a nanoparticle filler in an organic polymer such as a thermosetting resin. By incorporating this cast dielectric composite the dielectric constant of critical insulating layers of the transmission lines of the accelerator are increased while simultaneously maintaining high dielectric strengths for the accelerator.

The constructive approach to nonlinear quantum field theory

International Nuclear Information System (INIS)

Segal, I.

1976-01-01

The general situation in nonlinear quantum field theory is outlined. The author discusses a reversion to the canonical quantization formalism and develops it to the maximal level attainable on the basis of advances in the past decade in nonlinear scattering and functional integration. (B.R.H.)

Damage Evaluation of Critical Components of Tilted Support Spring Nonlinear System under a Rectangular Pulse

Directory of Open Access Journals (Sweden)

Ningning Duan

2015-01-01

Full Text Available Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear packaging system with critical components were obtained under a rectangular pulse. To evaluate the damage characteristics of shocks to packaged products with critical components, a concept of the damage boundary surface was presented and applied to a titled support spring system, with the dimensionless critical acceleration of the system, the dimensionless critical velocity, and the frequency parameter ratio of the system taken as the three basic parameters. Based on the numerical results, the effects of the frequency parameter ratio, the mass ratio, the dimensionless peak pulse acceleration, the angle of the system, and the damping ratio on the damage boundary surface of critical components were discussed. It was demonstrated that with the increase of the frequency parameter ratio, the decrease of the angle, and/or the increase of the mass ratio, the safety zone of critical components can be broadened, and increasing the dimensionless peak pulse acceleration or the damping ratio may lead to a decrease of the damage zone for critical components. The results may lead to a thorough understanding of the design principles for the tilted support spring nonlinear system.

Canonical harmonic tracking of charged particles in circular accelerators

International Nuclear Information System (INIS)

Kvardakov, V.; Levichev, E.

2006-01-01

Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed

Canonical harmonic tracking of charged particles in circular accelerators

Science.gov (United States)

Kvardakov, V.; Levichev, E.

2006-03-01

Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed.

Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1

International Nuclear Information System (INIS)

Krivitsky, V.S.; Vladimirov, S.V.

1991-01-01

An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)

SHOCK, Nonlinear Dynamic Structure Analysis, Spring and Mass Model, Runge-Kutta-Gill Method

International Nuclear Information System (INIS)

Gabrielson, V. K.

1981-01-01

1 - Description of problem or function: SHOCK calculates the dynamic response of a structure modeled as a spring-mass system having one or two degrees of freedom for each mass when subjected to specified environments. The code determines the behavior of each lumped mass (displacement, velocity, and acceleration for each degree of freedom) and the behavior of each spring or coupling (force, shear, moment, and displacement) as a function of time. Two types of models, axial, having one degree of freedom, and lateral, having two degrees of freedom at each mass can be processed. Damping can be included in all models and shock spectrums of responses can be obtained. 2 - Method of solution: Two methods of numerical integration of the second-order dynamic equations are provided: the Runge-Kutta-Gill method with variable step-size is recommended for highly nonlinear problems, and a variation of the Newmark-Beta method is available for use with large linear problems. 3 - Restrictions on the complexity of the problem: Maxima of: 100 masses, 200 springs or couplings. Complex arrangements of nonlinear options must be carefully checked by the user

Lasers and new methods of particle acceleration

International Nuclear Information System (INIS)

Parsa, Z.

1998-02-01

There has been a great progress in development of high power laser technology. Harnessing their potential for particle accelerators is a challenge and of great interest for development of future high energy colliders. The author discusses some of the advances and new methods of acceleration including plasma-based accelerators. The exponential increase in sophistication and power of all aspects of accelerator development and operation that has been demonstrated has been remarkable. This success has been driven by the inherent interest to gain new and deeper understanding of the universe around us. With the limitations of the conventional technology it may not be possible to meet the requirements of the future accelerators with demands for higher and higher energies and luminosities. It is believed that using the existing technology one can build a linear collider with about 1 TeV center of mass energy. However, it would be very difficult (or impossible) to build linear colliders with energies much above one or two TeV without a new method of acceleration. Laser driven high gradient accelerators are becoming more realistic and is expected to provide an alternative, (more compact, and more economical), to conventional accelerators in the future. The author discusses some of the new methods of particle acceleration, including laser and particle beam driven plasma based accelerators, near and far field accelerators. He also discusses the enhanced IFEL (Inverse Free Electron Laser) and NAIBEA (Nonlinear Amplification of Inverse-Beamstrahlung Electron Acceleration) schemes, laser driven photo-injector and the high energy physics requirements

Nonlinear dynamics and numerical uncertainties in CFD

Science.gov (United States)

Yee, H. C.; Sweby, P. K.

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.