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1

Meshless analysis of geometrically nonlinear beams  

Microsoft Academic Search

The meshless method is applied to the response analysis of a geometrically nonlinear beam. The corresponding nonlinear strain operator matrix and tangent rigidity matrix are given. The computational results agree well with Holden's analytic solution. It is found that the meshless method is more efficient for large displacement.

J. M. Xia; D. M. Wei; R. H. Jin

2008-01-01

2

Meshless analysis of geometrically nonlinear beams  

NASA Astrophysics Data System (ADS)

The meshless method is applied to the response analysis of a geometrically nonlinear beam. The corresponding nonlinear strain operator matrix and tangent rigidity matrix are given. The computational results agree well with Holden's analytic solution. It is found that the meshless method is more efficient for large displacement.

Xia, J. M.; Wei, D. M.; Jin, R. H.

2008-02-01

3

Effects of geometric nonlinearities on the response of optimized box beam structures  

NASA Astrophysics Data System (ADS)

The present minimum-mass designs for a two-spar rectangular box beam were derived on the basis of linear-buckling FEM analysis constraints. In order to ascertain the effects of any geometric nonlinearities on these designs, each was subjected to a geometrically nonlinear FEM analysis. In all cases, the structure collapses below the design load, and does so in a mode which differs from that of linear theory. This discrepancy is attributable to such nonlinear panel-interaction mechanisms as rib-crusing loads. The optimized design is highly sensitive to crushing loads, relative to the nonoptimal design.

Ragon, S.; Gurdal, Z.

1993-04-01

4

Geometrically nonlinear bending analysis of Metal-Ceramic composite beams under thermomechanical loading  

NASA Astrophysics Data System (ADS)

A new method is developed to derive equilibrium equations of Metal-Ceramic beams based on first order shear deformation plate theory which is named first order shear deformation beam theory2(FSDBT2). Equilibrium equations obtained from conventional method (FSDBT1) is compared with FSDBT2 and the case of cylindrical bending of Metal-Ceramic composite plates for non-linear thermomechanical deformations and various loadings and boundary conditions. These equations are solved by using three different methods (analytical, perturbation technique and finite element solution). The through-thickness variation of the volume fraction of the ceramic phase in a Metal-Ceramic beam is assumed to be given by a power-law type function. The non-linear strain-displacement relations in the von-Kármán sense are used to study the effect of geometric non-linearity. Also, four other representative averaging estimation methods, the linear rule, Mori-Tanaka, Self-Consistent and Wakashima-Tsukamoto schemes, by comparing with the power-law type function are also investigated. Temperature distribution through the thickness of the beams in thermal loadings is obtained by solving the one-dimensional heat transfer equation. Finally it is concluded that for Metal-Ceramic composites, these two theories result in identical static responses. Also the displacement field and equilibrium equations in the case of cylindrical bending of Metal-Ceramic plates are the same as those supposed in FSDBT2.

Torabizadeh, Mohammad Amin

2013-07-01

5

Geometric nonlinear effects on the planar dynamics of a pivoted flexible beam encountering a point-surface impact  

Microsoft Academic Search

Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics\\u000a undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems\\u000a have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted\\u000a flexible beam is investigated. The Hertzian contact

Qing Li; Tianshu Wang; Xingrui Ma

2009-01-01

6

Coarsening of ion-beam-induced surface ripple in Si: Nonlinear effect vs. geometrical shadowing  

SciTech Connect

The temporal evolution of a periodic ripple pattern on a silicon surface undergoing erosion by 30 keV argon ion bombardment has been studied for two angles of ion incidence of 60 deg. and 70 deg. using ex situ atomic force microscopy (AFM) in ambient condition. The roughness amplitude (w) grows exponentially with sputtering time for both the angle of ion incidence followed by a slow growth process that saturates eventually with almost constant amplitude. Within the exponential growth regime of amplitude, however, ripple wavelength (l) remains constant initially and increases subsequently as a power law fashion l{proportional_to}t{sup n}, where n=0.47{+-}0.02 for a 60 deg. angle of ion incidence followed by a saturation. Wavelength coarsening was also observed for 70 deg. but ordering in the periodic ripple pattern is destroyed quickly for 70 deg. as compared to 60 deg. . The ripple orientation, average ripple wavelength at the initial stage of ripple evolution, and the exponential growth of ripple amplitude can be described by a linear continuum model. While the wavelength coarsening could possibly be explained in the light of recent hydrodynamic model based continuum theory, the subsequent saturation of wavelength and amplitude was attributed to the effect of geometrical shadowing. This is an experimental result that probably gives a hint about the upper limit of the energy of ion beam rippling for applying the recently developed type of nonlinear continuum model.

Datta, Debi Prasad; Chini, Tapas Kumar [Surface Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India)

2007-08-15

7

A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations  

Microsoft Academic Search

Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the\\u000a geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ\\u000a substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also\\u000a vary significantly. In the current work, we

Ignacio Romero

2008-01-01

8

On nonlinear frequency veering and mode localization of a beam with geometric imperfection resting on elastic foundation  

NASA Astrophysics Data System (ADS)

This work presents an investigation on the effect of an initial geometric imperfection wavelength, amplitude and degree of localization on the in-plane nonlinear natural frequencies veering and mode localization of an elastic Euler-Bernoulli beam resting on a Winkler elastic foundation. The beam is assumed to be pinned-pinned with a linear torsional spring at one end. The effect of the axial force induced by mid-plane stretching is accounted for in the derivation of the mathematical model, due to its known importance and significant effect on the nonlinear dynamic behavior of the beam, as it was proved and presented in earlier investigations. The governing partial differential equation is discretized using the assumed mode method and the resulting nonlinear temporal equation was solved using the harmonic balance method to obtain results for the nonlinear natural frequencies and mode shapes. The results are presented in the form of characteristic curves which show the variations of the nonlinear natural frequencies of the first three modes of vibration, for a selected range of physical parameters like; torsional spring constant, elastic foundation stiffness and amplitude and wavelength of a localized and non-localized initial slack.

Al-Qaisia, A. A.; Hamdan, M. N.

2013-09-01

9

A nonlinear composite beam theory  

Microsoft Academic Search

Presented here is a general theory for the three-dimensional nonlinear dynamics of elastic anisotropic initially straight beams undergoing moderate displacements and rotations. The theory fully accounts for geometric nonlinearities (large rotations and displacements) by using local stress and strain measures and an exact coordinate transformation, which result in nonlinear curvature and strain-displacement expressions that contain the von Karman strains as

Perngjin F. Pai; Ali H. Nayfeh

1992-01-01

10

Stationary nonlinear Airy beams  

SciTech Connect

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.

Lotti, A. [Dipartimento di Fisica e Matematica, Universita del'Insubria, Via Valleggio 11, I-22100 Como (Italy); Centre de Physique Theorique, CNRS, Ecole Polytechnique, F-91128 Palaiseau (France); Faccio, D. [Dipartimento di Fisica e Matematica, Universita del'Insubria, Via Valleggio 11, I-22100 Como (Italy); School of Engineering and Physical Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Couairon, A. [Centre de Physique Theorique, CNRS, Ecole Polytechnique, F-91128 Palaiseau (France); Papazoglou, D. G. [Institute of Electronic Structure and Laser (IESL), Foundation for Research and Technology, Hellas (FORTH), P.O. Box 1527, GR-71110 Heraklion (Greece); Materials Science and Technology Department, University of Crete, GR-71003 Heraklion (Greece); Panagiotopoulos, P.; Tzortzakis, S. [Institute of Electronic Structure and Laser (IESL), Foundation for Research and Technology, Hellas (FORTH), P.O. Box 1527, GR-71110 Heraklion (Greece); Abdollahpour, D. [Institute of Electronic Structure and Laser (IESL), Foundation for Research and Technology, Hellas (FORTH), P.O. Box 1527, GR-71110 Heraklion (Greece); Physics Department, University of Crete, GR-71003 Heraklion (Greece)

2011-08-15

11

Dynamic analysis of geometrically nonlinear robot manipulators  

Microsoft Academic Search

In this paper, a method for the dynamic analysis of geometrically nonlinear elastic robot manipulators is presented. Robot arm elasticity is introduced using a finite element method which allows for the gross arm rotations. A shape function which accounts for the combined effects of rotary inertia and shear deformation is employed to describe the arm deformation relative to a selected

E. M. Bakp

1996-01-01

12

Nonlinear Geometric Effects in Bioinspired Multistable Structures  

NASA Astrophysics Data System (ADS)

Nature features many thin shell structures with spontaneous curvatures, where mechanical instabilities play important roles in the morphogenesis and functioning of the organisms. However, the large deformation and instability phenomena of shells due to geometric nonlinearity, which often arise in morphogenesis and nanofabrication, remain incompletely understood. Here, we create spontaneously curved shapes with pre-strains in tabletop experiments, and study their instabilities with a minimal theory based on linear elasticity. The development of such theoretical and experimental approaches will promote quantitative understanding of the morphogenesis of growing soft tissues, and meet the emergent needs of designing stretchable electronics, artificial muscles and bio-inspired robots.

Chen, Zi; Guo, Qiaohang; Chu, Kevin; Shillig, Steven; Li, Chi; Chen, Wenzhe; Taber, Larry; Holmes, Douglas

2013-03-01

13

Nonlinear Strain Measures, Shape Functions and Beam Elements for Dynamics of Flexible Beams  

Microsoft Academic Search

In this paper, we examine several aspects of the development of an explicit geometrically nonlinear beam element. These are: (i) linearization of the displacement field; (ii) the effect of a commonly adopted approximation for the nonlinear Lagrangian strain; and (iii) use of different-order shape functions for discretization. The issue of rigid-body check for a nonlinear beam element is also considered.

I. Sharf

1999-01-01

14

Geometric nonlinear formulation for thermal-rigid-flexible coupling system  

NASA Astrophysics Data System (ADS)

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

Fan, Wei; Liu, Jin-Yang

2013-09-01

15

Nonlinear forced vibration analysis of clamped functionally graded beams  

Microsoft Academic Search

Multiple time scale solutions are presented to study the nonlinear forced vibration of a beam made of symmetric functionally\\u000a graded (FG) materials based on Euler–Bernoulli beam theory and von Kármán geometric nonlinearity. It is assumed that material\\u000a properties follow either exponential or power law distributions through the thickness direction. A Galerkin procedure is used\\u000a to obtain a second-order nonlinear ordinary

A. Shooshtari; M. Rafiee

16

Geometrical nonlinearities on the static analysis of highly flexible steel cable-stayed bridges  

Microsoft Academic Search

An evaluation of the importance of geometrically nonlinear effects on the structural static analysis of steel cable-stayed bridges is presented. A finite element model is analyzed using linear, pseudo-linear and nonlinear methods. The pseudo-linear approach is based on the modified elastic modulus. The nonlinear analysis involves cable sag, large displacement and beam-column effects. The results confirm that both cable sag

A. M. S. Freire; J. H. O. Negrão; A. V. Lopes

2006-01-01

17

Geometrical approach to gaussian beam propagation.  

PubMed

The curvature of the wavefront and the spot size of a propagating Gaussian beam may be determined from simple geometrical transformations of the lateral foci. The analysis starts from the construction of the lateral foci in the case of a spherical Fabry-Perot. Then the cases of Gaussian beam propagation through media with different refractive indices, lenses, and simple optical systems are treated. Constructions show how propagation in the image space is readily determined in each case. This analysis is the generalization of the technique outlined by Deschamps and Mast. The geometrical constructions developed for simple cases are applied to the design of some special cases of interest in laser optics: cavities by a lens, laser zoom telescope, and ring cavity. PMID:20057839

Laures, P

1967-04-01

18

Hybrid analytical technique for the nonlinear analysis of curved beams  

Microsoft Academic Search

The application of a two-step hybrid technique to the geometrically nonlinear analysis of curved beams is used to demonstrate the potential of hybrid analytical techniques in nonlinear structural mechanics. The hybrid technique is based on successive use of the perturbation method and a classical direct variational procedure. The functions associated with the various-order terms in the perturbation expansion of the

A. K. Noor; C. M. Andersen

1992-01-01

19

On the importance of aerodynamic and structural geometrical nonlinearities in aeroelastic behavior of high-aspect-ratio wings  

Microsoft Academic Search

Theoretical development of a nonlinear aeroelastic analysis for high-aspect-ratio wings is presented. The analysis couples a geometrically exact beam theory with a nonplanar aerodynamic theory. The aim of the present effort is to investigate the effects of geometrical nonlinearities on the aeroelastic behavior of high-aspect-ratio wings. The focus of the present work is on characterizing the physical origins of nonlinearities

M. J. Patil; D. H. Hodges

2004-01-01

20

Nonlinear behavior of geometric phases induced by photon pairs  

SciTech Connect

In this study, we observe the nonlinear behavior of the two-photon geometric phase for polarization states using time-correlated photon pairs. This phase manifests as a shift of two-photon interference fringes. Under certain arrangements, the geometric phase can vary nonlinearly and become very sensitive to a change in the polarization state. Moreover, it is known that the geometric phase for N identically polarized photons is N times larger than that for one photon. Thus, the geometric phase for two photons can become two times more sensitive to a state change. This high sensitivity to a change in the polarization can be exploited for precision measurement of small polarization variation. We evaluate the signal-to-noise ratio of the measurement scheme using the nonlinear behavior of the geometric phase under technical noise and highlight the practical advantages of this scheme.

Kobayashi, H.; Ikeda, Y.; Tamate, S.; Nakanishi, T.; Kitano, M. [Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510 (Japan)

2011-06-15

21

GEOMETRICALLY NON-LINEAR FREE VIBRATION OF FULLY CLAMPED SYMMETRICALLY LAMINATED RECTANGULAR COMPOSITE PLATES  

Microsoft Academic Search

The geometrically non-linear free vibration of thin composite laminated plates is investigated by using a theoretical model based on Hamilton's principle and spectral analysis previously applied to obtain the non-linear mode shapes and resonance frequencies of thin straight structures, such as beams, plates and shells (Benamar et al. 1991Journal of Sound and Vibration149 , 179–195; 1993, 164, 295–316; 1990 Proceedings

B. Harras; R. Benamar; R. G. WHITE

2002-01-01

22

A predictor algorithm for fast geometrically-nonlinear dynamic analysis  

Microsoft Academic Search

An efficient predictor algorithm is presented for fast geometrically-nonlinear dynamic analysis. The basic concept of this algorithm entails the use of the predicted starting point close to the converged solution point in the iterative procedure of nonlinear dynamics. The predicted starting point is much closer to the converged solution than the conventionally adopted starting point, i.e. the previously converged solution

Ji Won Suk; Jong Hoon Kim; Yong Hyup Kim

2003-01-01

23

On the importance of aerodynamic and structural geometrical nonlinearities in aeroelastic behavior of high-aspect-ratio wings  

NASA Astrophysics Data System (ADS)

Theoretical development of a nonlinear aeroelastic analysis for high-aspect-ratio wings is presented. The analysis couples a geometrically exact beam theory with a nonplanar aerodynamic theory. The aim of the present effort is to investigate the effects of geometrical nonlinearities on the aeroelastic behavior of high-aspect-ratio wings. The focus of the present work is on characterizing the physical origins of nonlinearities and assessing their relative importance. Results presented show that the structural geometrical nonlinearities have a significant effect on the structural dynamics and on the dynamic aeroelastic characteristics of a high-aspect-ratio wing. The geometrically exact calculation of the angle of attack and aerodynamically consistent application of the airloads is also important for accurate aeroelastic characterization. On the other hand, the geometrical aerodynamic nonlinearity emerging from the nonplanar wake effects is quite negligible. Nonplanar effects were negligible for both the steady and unsteady airload calculations with the assumption of a fixed wake model.

Patil, M. J.; Hodges, D. H.

2004-08-01

24

Multilayer beams: A geometrically exact formulation  

NASA Astrophysics Data System (ADS)

We review and extend our recent work on a new theory of multilayer structures, with particular emphasis on sandwich beams/1-D plates. Both the formulation of the equations of motion in the general dynamic case and the computational formulation of the resulting nonlinear equations of equilibrium in the static case based on a Galerkin projection are presented. Finite rotations of the layer cross sections are allowed, with shear deformation accounted for in each layer. There is no restriction on the layer thickness; the number of layers can vary between one and three. The deformed profile of a beam cross section is continuous, piecewise linear, with a motion in 2-D space identical to that of a planar multibody system that consists of three rigid links connected by hinges. With the dynamics of this multi (rigid/flexible) body being referred directly to an inertial frame, the equations of motion are derived via the balance of (1) the rate of kinetic energy and the power of resultant contact (internal) forces/couples, and (2) the power of assigned (external) forces/couples. The present formulation offers a general method for analyzing the dynamic response of flexible multilayer structures undergoing large deformation and large overall motion. With the layers not required to have equal length, the formulation permits the analysis of an important class of multilayer structures with ply drop-off. For sandwich structures, an approximated theory with infinitesimal relative outer-layer rotations superimposed onto finite core-layer rotation is deduced from the general nonlinear equations in a consistent manner. The classical linear theory of sandwich beams/1-D plates is recovered upon a consistent linearization. Using finite element basis functions in the Galerkin projection, we provide extensive numerical examples to verify the theoretical formulation and to illustrate its versatility.

Vu-Quoc, L.; Deng, H.; Ebcio?lu, I. K.

1996-05-01

25

Time history nonlinear earthquake response analysis considering materials and geometrical nonlinearity  

Microsoft Academic Search

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

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

2002-01-01

26

Geometric Heat Equation and Nonlinear Diffusion of Shapes and Images  

Microsoft Academic Search

Visual tasks often require a hierarchical representation of shapes and images in scales ranging from coarse to fine. A variety of linear and nonlinear smoothing techniques, such as Gaussian smoothing, anisotropic diffusion, regularization, etc., have been proposed, leading to scalespace representations. We propose ageometricsmoothing method based on local curvature for shapes and images. The deformation by curvature, or the geometric

Benjamin B. Kimia; Kaleem Siddiqi

1996-01-01

27

GEOMETRICALLY NONLINEAR ANALYSIS OF MICROSWITCHES USING THE LOCAL MESHFREE METHOD  

Microsoft Academic Search

In the modelling and simulation of the microelectro mechanical systems (MEMS) devices, for example the microswitch, the large deformation or t he geometrical nonlinearity should be considered. Due to the issue of the mesh distortion , the finite element method (FEM) is not effective for this large deformation analysis. In t his paper, a local meshfree formulation is developed for

Y. T. GU

2008-01-01

28

Topology synthesis of geometrically nonlinear compliant mechanisms using meshless methods  

Microsoft Academic Search

This paper presents a new method for topology optimization of geometrical nonlinear compliant mechanisms using the element-free Galerkin method (EFGM). The EFGM is employed as an alternative scheme to numerically solve the state equations by fully taking advantage of its capability in dealing with large displacement problems. In the meshless method, the imposition of essential boundary conditions is also addressed.

Yixian Du; Liping Chen; Zhen Luo

2008-01-01

29

Geometric methods in nonlinear analysis of data from brain imaging  

NASA Astrophysics Data System (ADS)

The aims of this series of papers are: (a) to formulate a geometric framework for non-linear analysis of global features of massive data sets; and (b) to quantify non-linear dependencies among (possibly) uncorrelated parameters that describe the data. In this paper, we consider an application of the methods to extract and characterize nonlinearities in the functional magnetic resonance imaging data and EEG of human brain (fMRI). A more general treatment of this theory applies to a wider variety of massive data sets; however, the usual technicalities for computation and accurate interpretation of abstract concepts remain a challenge for each individual area of application.

Eghbalnia, Hamid; Assadi, Amir H.

2001-11-01

30

The comparative body model in material and geometric nonlinear analysis of space R\\/C frames  

Microsoft Academic Search

Purpose – This paper aims to present a new numerical model for the stability and load-bearing capacity computation of space reinforced-concrete (R\\/C) frame structures. Both material and geometric nonlinearities are taken into account. The R\\/C cross-sections are assumed to undergo limited distortion under torsional action. Design\\/methodology\\/approach – A simple, global discretization using beam-column finite elements is preferred to a full,

Boris Trogrlic; Ante Mihanovic

2008-01-01

31

On linearization of the stiffness characteristics of flexible beams made of physically nonlinear materials  

Microsoft Academic Search

The geometry of flexible beams that are made of a physically nonlinear material and have a nearly linear load-deflection characteristic\\u000a is identified for a wide range of monotonic and harmonic loads. The geometrically nonlinear beam equations are used. The physically\\u000a nonlinear behavior of the material is described using a unified viscoplastic theory. A beam thickness criterion is formulated\\u000a to provide

Ya. A. Zhuk; I. K. Senchenkov

2006-01-01

32

Dynamic isolation systems using tunable nonlinear stiffness beams  

NASA Astrophysics Data System (ADS)

Vibration isolation devices are required to reduce the forcing into the supporting structure or to protect sensitive equipment from base excitation. A suspension system with a low natural frequency is required to improve isolation, but with linear supports the minimum stiffness is bounded by the static stiffness required to support the equipment. However, nonlinear high-static-low-dynamic-stiffness (HSLDS) mounts may be designed, for example by combining elastic springs in particular geometries, to give the required nonlinear force-displacement characteristics. Current approaches to realise the required nonlinear characteristics are often inconvenient. Furthermore, the weight of the supported equipment, the environment, or the structural stiffness may change. This paper investigates the design of HSLDS isolation mounts using beams of tunable geometric nonlinear stiffness. In order to obtain the nonlinear response required, we first study the case of generic beams subject to static loads that are able to tune their nonlinear force-displacement characteristics to ensure that the isolators have very low dynamic stiffness. Tuning is achieved by actuators at the ends of the beams that prescribe the axial displacement and rotation. Secondly, we study a composite beam with an initial thermal pre-stress, resulting in internal stresses that give the required nonlinear response.

Friswell, M. I.; Saavedra Flores, E. I.

2013-09-01

33

Nonlinear beam dynamics experimental program at SPEAR  

SciTech Connect

Since nonlinear effects can impose strict performance limitations on modern colliders and storage rings, future performance improvements depend on further understanding of nonlinear beam dynamics. Experimental studies of nonlinear beam motion in three-dimensional space have begun in SPEAR using turn-by-turn transverse and longitudinal phase-space monitors. This paper presents preliminary results from an on-going experiment in SPEAR.

Tran, P.; Pellegrini, C. [Univ. of California, Los Angeles, CA (United States); Cornacchia, M.; Lee, M.; Corbett, W. [Stanford Univ., CA (United States). Stanford Linear Accelerator Center

1995-03-01

34

Stop Bandwidths of Nonlinear Beam-Beam Resonances.  

National Technical Information Service (NTIS)

A general expression is given for the stop bandwidths, delta nu /sub N/, of nonlinear beam-beam resonances, which is expanded in powers of Y(s), the vertical beam orbit, and which is valid under certain assumptions regarding the orbits and charge distribu...

G. Parzen

1979-01-01

35

A perturbation approach for geometrically nonlinear structural analysis using a general purpose finite element code  

Microsoft Academic Search

In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is often done using finite element based incremental-iterative procedures. However standard finite element based nonlinear analysis of many practical structures is still

T. Rahman

2009-01-01

36

Multiple-Mode Nonlinear Free and Forced Vibrations of Beams Using Finite Element Method. Final Report, Period Ending January 31, 1987.  

National Technical Information Service (NTIS)

Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is deriv...

C. Mei K. Decha-Umphai

1987-01-01

37

Optical beam instabilities in nonlinear nanosuspensions.  

PubMed

We investigate the modulation instability of plane waves and the transverse instabilities of soliton stripe beams propagating in nonlinear nanosuspensions. We show that in these systems the process of modulational instability depends on the input beam conditions. On the other hand, the transverse instability of soliton stripes can exhibit new features as a result of 1D collapse caused by the exponential nonlinearity. PMID:17975638

El-Ganainy, R; Christodoulides, D N; Musslimani, Ziad H; Rotschild, C; Segev, M

2007-11-01

38

Geometric Properties of Dynamic Nonlinear Networks: Transversality, Local-Solvability and eventual Passivity  

Microsoft Academic Search

This paper gives several basic results on dynamic nonlinear networks from a geometric point of view. One of the main advantages of a geometric approach is that it is coordinate-free, i.e., results obtained by a geometric method do not depend on the particular choices of a tree, a loop matrix, state variables, etc. Therefore, the method is suitable for studying

T. Matsumoto; L. Chua; H. Kawakami; S. Ichiraku

1981-01-01

39

BEAM DYNAMICS: Intense DC beam nonlinear transport-analysis & simulation  

NASA Astrophysics Data System (ADS)

The intense dc beam nonlinear transport was analyzed with the Lie algebraic method, and the particle trajectories of the second order approximation were obtained. Based on the theoretical analysis a computer code was designed. To get self-consistent solutions, iteration procedures were used in the code. As an example, we calculated a beam line (drift-electrostatic quadrupole doublet-drift). The results agree to the results calculated by using the PIC method.

Lü, Jian-Qin; Zhao, Xiao-Song

2009-06-01

40

Modeling of the vibrating beam accelerometer nonlinearities  

NASA Astrophysics Data System (ADS)

Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.

Romanowski, P. A.; Knop, R. C.

41

Magneto-thermo-elastokinetics of geometrically nonlinear laminated composite plates. Part 1: foundation of the theory  

Microsoft Academic Search

A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed. In this context, the first-order transversely shearable plate theory in conjunction with von-Kármán geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic

Davresh Hasanyan; Liviu Librescu; Zhanming Qin; Damodar R. Ambur

2005-01-01

42

Magneto-thermo-elastokinetics of geometrically nonlinear laminated composite plates. Part 2: vibration and wave propagation  

Microsoft Academic Search

In Part 1 of this paper, the governing equations of geometrically nonlinear, anisotropic composite plates incorporating magneto-thermo-elastic effects have been derived. In order to gain insight into the implications of a number of geometrical and physical features of the system, three special cases are investigated: (i) free vibration of a plate strip immersed in a transversal magnetic field; (ii) free

Zhanming Qin; Davresh Hasanyan; Liviu Librescu; Damodar R. Ambur

2005-01-01

43

A geometric calibration method for cone beam CT systems  

SciTech Connect

Cone beam CT systems are being deployed in large numbers for small animal imaging, dental imaging, and other specialty applications. A new high-precision method for cone beam CT system calibration is presented in this paper. It uses multiple projection images acquired from rotating point-like objects (metal ball bearings) and the angle information generated from the rotating gantry system is also used. It is assumed that the whole system has a mechanically stable rotation center and that the detector does not have severe out-of-plane rotation (<2 deg.). Simple geometrical relationships between the orbital paths of individual BBs and five system parameters were derived. Computer simulations were employed to validate the accuracy of this method in the presence of noise. Equal or higher accuracy was achieved compared with previous methods. This method was implemented for the geometrical calibration of both a micro CT scanner and a breast CT scanner. The reconstructed tomographic images demonstrated that the proposed method is robust and easy to implement with high precision.

Yang, Kai; Kwan, Alexander L. C.; Miller, DeWitt F.; Boone, John M. [Department of Radiology, University of California, Davis Medical Center, 4701 X Street, Sacramento, California 95817 and Department of Biomedical Engineering, University of California, Davis, California 95616 (United States); Department of Radiology, University of California, Davis Medical Center, 4701 X Street, Sacramento, California 95817 (United States); Department of Radiology, University of California, Davis Medical Center, 4701 X Street, Sacramento, California 95817 and Department of Biomedical Engineering, University of California, Davis, California 95616 (United States)

2006-06-15

44

Geometric structure of multiple time-scale nonlinear dynamical systems  

Microsoft Academic Search

A new methodology to analyze time-scale structure of smooth finite-dimensional nonlinear dynamical systems is developed. This approach does not assume apriori knowledge of slow and fast variables for special coordinates that simplify the form of the nonlinear dynamics. Conventional approaches to analyze time-scale structure of nonlinear dynamics such as singular perturbation theory proceed from such specialized apriori knowledge which is

Sanjay Bharadwaj

1999-01-01

45

Beam splitter entangler for nonlinear bosonic fields  

NASA Astrophysics Data System (ADS)

Some years ago Katriel and Solomon [1] described applications to the characterization of the photon statistics of nonideal lasers, nonclassical light, and deformed photon states using f-deformed coherent states. In this letter, we study the effect of a beam splitter on these nonlinear coherent states. We find that these states are useful for generating quantum entanglement as the deformation parameter gets farther form the unity and for strong input field regimes. The results are confirmed through the Werhl entropy.

Abdel-Khalek, S.; Berrada, K.; Raymond Ooi, C. H.

2012-09-01

46

Cubic nonlinearity in shear wave beams with different polarizations  

PubMed Central

A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal. Comparisons are made with effects of quadratic nonlinearity in compressional wave beams.

Wochner, Mark S.; Hamilton, Mark F.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.

2008-01-01

47

Modeling and measurement of geometrically nonlinear damping in a microcantilever-nanotube system.  

PubMed

Nonlinear mechanical systems promise broadband resonance and instantaneous hysteretic switching that can be used for high sensitivity sensing. However, to introduce nonlinear resonances in widely used microcantilever systems, such as AFM probes, requires driving the cantilever to an amplitude that is too large for any practical applications. We introduce a novel design for a microcantilever with a strong nonlinearity at small cantilever oscillation amplitude arising from the geometrical integration of a single BN nanotube. The dynamics of the system was modeled theoretically and confirmed experimentally. The system, besides providing a practical design of a nonlinear microcantilever-based probe, demonstrates also an effective method of studying the nonlinear damping properties of the attached nanotube. Beyond the typical linear mechanical damping, the nonlinear damping contribution from the attached nanotube was found to be essential for understanding the dynamical behavior of the designed system. Experimental results obtained through laser microvibrometry validated the developed model incorporating the nonlinear damping contribution. PMID:24010552

Jeong, Bongwon; Cho, Hanna; Yu, Min-Feng; Vakakis, Alexander F; McFarland, Donald Michael; Bergman, Lawrence A

2013-09-11

48

Beam stability and nonlinear dynamics. Summary report  

SciTech Connect

A {open_quotes}Beam Stability and Nonlinear Dynamics{close_quotes} Symposium was held October 3-5, 1996 at the Institute for Theoretical Physics (ITP) in Santa Barbara. This was one of the 3 symposia hosted by the ITP and supported by its sponsor, the National Science Foundation, as part of our {open_quotes}New Ideas for Particle Accelerators{close_quotes} program. The symposia was organized and chaired by Dr. Zohreh Parsa of ITP/ Brookhaven National Laboratory. The purpose of this symposium was to deal with some of the fundamental theoretical problems of accelerator physics by bringing together leaders from accelerator physics communities, mathematics, and other fields of physics. The focus was on nonlinear dynamics and beam stability. The symposium began with some defining talks on relevant mathematical topics such as single-particle Hamiltonian dynamics, chaos, and new ideas in symplectic integrators. The physics topics included single-particle and many-particle dynamics. These topics concern circular accelerators in which particles circulate for a very large number of turns as well as linear accelerators where space charge and wakefields induced in accelerating cavities play a strong role. A major question is to determine the best model for numerical simulations in order to accurately reproduce behavior of beams in real accelerators and to predict long-term or long distance stability. Comparison with experiment is recognized as an important tool in improving models.

Parsa, Z.

1996-12-31

49

Stationary High Intensity Wave Beams in Media with Saturable Nonlinearity  

Microsoft Academic Search

Stationary properties of high intensity wave beams in weakly inhomogeneous media with a saturable nonlinearity are investigated by means of a consistent asymptotic method. It is shown that the strongest effects of the nonlinearity are most important within a certain range of the medium parameters and explicit formulas for the beam intensity and the beam phase velocity are obtained in

I. A. Molotkov; V. A. Eremenko; D. Anderson; M. Lisak

2000-01-01

50

Sensitive measurement of optical nonlinearities using a single beam  

Microsoft Academic Search

A sensitive single-beam technique for measuring both the nonlinear refractive index and nonlinear absorption coefficient for a wide variety of materials is reported. The authors describe the experimental details and present a comprehensive theoretical analysis including cases where nonlinear refraction is accompanied by nonlinear absorption. In these experiments, the transmittance of a sample is measured through a finite aperture in

MANSOOR SHEIK-BAHAE; ALI A. SAID; T.-H. Wei; D. J. Hagan; E. W. Van Stryland

1990-01-01

51

Design optimization of geometrically nonlinear truss structures considering cardinality constraints  

Microsoft Academic Search

The structural optimization problem of choosing the profile of each member belonging to a framed structure in order to minimize its weight while satisfying stress, displacement, stability, and other applicable constraints is often complicated by the requirement of considering non-linear structural behavior. The problem is further complicated if the members are to be chosen from a discrete set of commercially

Afonso C. C. Lemonge; Michelli M. Silva; Helio J. C. Barbosa

2011-01-01

52

Beam stability & nonlinear dynamics. Formal report  

SciTech Connect

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

Parsa, Z. [ed.

1996-12-31

53

Overview of magnetic nonlinear beam dynamics in the RHIC  

SciTech Connect

In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed.

Luo,Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, f.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, g.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.

2009-05-04

54

Nonlinear vibration of viscoelastic sandwich beams by the harmonic balance and finite element methods  

NASA Astrophysics Data System (ADS)

This paper deals with geometrically nonlinear vibrations of sandwich beams with viscoelastic materials. For this purpose, a new finite element formulation has been developed, in which a zig-zag model is used to describe the displacement field. The viscoelastic behaviour is handled by using hereditary integrals and their relationships with complex moduli. An efficient solution procedure based on the harmonic balance method is also developed. To demonstrate its abilities, various problems of nonlinear vibrations of sandwich beams are considered. First, the results derived from the proposed approach are compared with those of nonlinear dynamic analyses using direct time integration and to experimental data. Then, the influence of the vibration amplitude on the damping properties of sandwich beams is investigated. The effect of an initial axial strain is also examined.

Jacques, N.; Daya, E. M.; Potier-Ferry, M.

2010-09-01

55

Geometrically Nonlinear Analysis of Rectangular Glass Plates by the Finite Element Method.  

National Technical Information Service (NTIS)

The need for a re-evaluation of the window glass design process has led to the development of a finite element model for stress analysis of geometrically nonlinear, uniformly loaded rectangular plates. The formulation uses a rectangular finite element wit...

A. H. J. Al-Tayyib

1980-01-01

56

Comparison of the geometrically nonlinear and linear theories of martensitic transformation  

Microsoft Academic Search

Over the last few years, a continuum model based on finite or nonlinear thermoelasticity has been developed and successfully used to study crystalline solids that undergo a martensitic phase transformation. A geometrically linear version of this model was developed independently and has been widely used in the materials science literature. This paper presents the two theories and evaluates them by

K. Bhattacharya

1993-01-01

57

Topology synthesis of thermomechanical compliant mechanisms with geometrical nonlinearities using meshless method  

Microsoft Academic Search

The element-free Galerkin (EFG) method, one of the important meshless methods, is integrated into topology optimization and a new topology optimization method for designing thermomechanical actuated compliant mechanisms with geometrical nonlinearities is presented. The meshless method is employed to discretize the governing equations and the bulk density field. Using meshless method to analyze the thermomechanical model is better consistent with

Yi-xian Du; Li-ping Chen; Qi-hua Tian; Zheng-jia Wu

2009-01-01

58

Focused optical and acoustic beams in media with nonlinear absorption  

NASA Astrophysics Data System (ADS)

Optical and acoustic beams are known to be useful for medical and biological applications, such as diagnostics, surgery, etc. At high intensities both nonlinear lens effects and nonlinear absorption can be significant for the beams. The nonlinear absorption arises due to two-photon optical processes or acoustic shock wave formation. The present work is devoted to the theoretical description of nonlinear beam propagation and focal spot formation taking into account the competition between focusing, diffraction and absorption. We derived a new nonlinear integro- differential equation describing the spatial evolution of the beam width. The general analytical solution of this equation is obtained for arbitrary boundary conditions. The simple formulas are derived for the angle divergence in the far field, as well as for beam width at nonlinear waist. The results of the analysis of these key parameters in different situations are presented.

Rudenko, O. V.; Sukhorukov, A. A.

1996-11-01

59

Simulation of Hamiltonian light-beam propagation in nonlinear media  

Microsoft Academic Search

The simulation of nonlinear wave propagation in the ray regime, i.e., in the limit of geometrical optics, is dis- cussed. The medium involved is nonlinear, which means that the field amplitudes affect the constitutive pa- rameters (e.g., dielectric constant) involved in the propagation formalism. Conventionally, linear ray propa- gation is computed by the use of Hamilton's ray equations whose terms

Menashe Sonnenschein; Dan Censor

1998-01-01

60

Stress resultant geometrically non-linear shell theory with drilling rotations. Part 3: Linearized kinematics  

NASA Astrophysics Data System (ADS)

A consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically nonlinear shell theory considered in Parts 1 and 2 of this work. It was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three-dimensional geometrically nonlinear continuum with independent rotation field. In the finite element implementation of the presented shell theory, relying on the modified method of incompatible modes, we were able to construct a four-node shell element which delivers a very high-level performance. In order to simplify finite element implementation, a shallow reference configuration is assumed over each shell finite element. This approach does not impair the element performance for the present four-node element. The results obtained herein match those obtained with the state-of-the-art implementations based on the classical shell theory, over the complete set of standard benchmark problems.

Ibrahimbegovic, Adnan; Frey, Francois

1994-11-01

61

Nonlinear free vibrations of beams in space due to internal resonance  

NASA Astrophysics Data System (ADS)

The geometrically nonlinear free vibrations of beams with rectangular cross section are investigated using a p-version finite element method. The beams may vibrate in space, hence they may experience longitudinal, torsional and non-planar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The geometrical nonlinearity is taken into account by considering Green's nonlinear strain tensor. Isotropic and elastic beams are investigated and generalised Hooke's law is used. The equation of motion is derived by the principle of virtual work. Mostly clamped-clamped beams are investigated, although other boundary conditions are considered for validation purposes. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. One constant term, odd and even harmonics are assumed in the Fourier series and convergence with the number of harmonics is analysed. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of backbone curves. Coupling between modes is investigated, internal resonances are found and the ensuing multimodal oscillations are described. Some of the couplings discovered lead from planar oscillations to oscillations in the three dimensional space.

Stoykov, S.; Ribeiro, P.

2011-08-01

62

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion  

NASA Astrophysics Data System (ADS)

Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.

McBride, A. T.; Javili, A.; Steinmann, P.; Bargmann, S.

2011-10-01

63

Addressing geometric nonlinearities with cantilever microelectromechanical systems: Beyond the Duffing model  

NASA Astrophysics Data System (ADS)

We report on low-temperature measurements performed on microelectromechanical systems driven deeply into the nonlinear regime. The materials are kept in their elastic domain while the observed nonlinearity is purely of geometrical origin. Two techniques are used, harmonic drive and free decay. For each case, we present an analytic theory fitting the data. The harmonic drive is fit with a modified Lorentzian line shape obtained from an extended version of Landau and Lifshitz’s nonlinear theory. The evolution in the time domain is fit with an amplitude-dependent frequency decaying function derived from the Lindstedt-Poincaré theory of nonlinear differential equations. The technique is perfectly generic and can be straightforwardly adapted to any mechanical device made of ideally elastic constituents, and which can be reduced to a single degree of freedom, for an experimental definition of its nonlinear dynamics equation.

Collin, E.; Bunkov, Yu. M.; Godfrin, H.

2010-12-01

64

Nonlinear Flexural Deflection of Thermoplastic Foam Core Sandwich Beam  

Microsoft Academic Search

Nonlinear flexural deflection behavior of foam core sandwich beams hasbeen experimentally investigated. The experimental data were compared with the predicted results obtained from a proposed analytical method and the finite element analysis. Sandwich beams with thermoplastic foam core and carbon\\/epoxy fabric faces were manufactured using the vacuum bagging process. To investigate the effect of the face thickness on the nonlinear

Kwang Joon Yoon; C. K. Kim; Hoon C. Park

2002-01-01

65

Nonlinear Dynamics of a Beam on Elastic Foundation  

Microsoft Academic Search

The nonlinear dynamics of a simply supported beam resting on a nonlinear spring bed with cubic stiffness is analyzed. The continuous differential operator describing the mathematical model of the system is discretized through the classical Galerkin procedure and its nonlinear dynamic behavior is investigated using the method of Normal Forms. This model can be regarded as a simple system describing

F. Pellicano; F. Mastroddi

1997-01-01

66

Non-linear dynamic analysis of beams with variable stiffness  

Microsoft Academic Search

In this paper the analog equation method (AEM), a BEM-based method, is employed to the non-linear dynamic analysis of a Bernoulli–Euler beam with variable stiffness undergoing large deflections, under general boundary conditions which maybe non-linear. As the cross-sectional properties of the beam vary along its axis, the coefficients of the differential equations governing the dynamic equilibrium of the beam are

J. T. Katsikadelis; G. C. Tsiatas

2004-01-01

67

A geometric construction of traveling waves in a generalized nonlinear dispersive-dissipative equation  

NASA Astrophysics Data System (ADS)

This paper is concerned with a generalized nonlinear dispersive-dissipative equation which is found in many areas of application including waves in a thermoconvective liquid layer, plasma waves and nonlinear electromagnetic waves. It is known that solitary waves for a special case of this equation are formed ahead of conventional chaotic-like irregular structures. Using a dynamical systems approach, specifically based on geometric singular perturbation theory and center manifold theory, we construct traveling waves for this model equation. This also includes some numerical calculations. The occurrence of solitary waves and oscillatory kink or shock waves is shown.

Mansour, M. B. A.

2013-07-01

68

FIRST-ORDER SYSTEM LEAST SQUARES (FOSLS) FOR GEOMETRICALLY NONLINEAR ELASTICITY  

Microsoft Academic Search

We present a rst-order system least-squares (FOSLS) method to approximate the solution to the equations of geometrically nonlinear elasticity in two dimensions. With assumptions of regularity on the problem, we show H1 equivalence of the norm induced by the FOSLS functional in the case of pure displacement boundary conditions as well as local convergence of Newton's method in a nested

T. A. MANTEUFFEL; S. F. MCCORMICK; J. G. SCHMIDTyy; C. R. WESTPHALzz

69

Geometrically nonlinear bending of thin-walled shells and plates under creep-damage conditions  

Microsoft Academic Search

Summary   A phenomenological constitutive model for characterization of creep and damage processes in metals is applied to the simulation\\u000a of mechanical behaviour of thin-walled shells and plates. Basic equations of the shell theory are formulated with geometrical\\u000a nonlinearities at finite time-dependent deflections of shells and plates in moderate bending. Numerical solutions of initial\\/boundary-value\\u000a problems have been obtained for rectangular thin

H. Altenbach; O. Morachkovsky; K. Naumenko; A. Sychov

1997-01-01

70

Shallow shell finite element for the large deflection geometrically nonlinear analysis of shells and plates  

Microsoft Academic Search

An investigation into the large deflection, geometrically nonlinear behaviour of shells is carried out in the present paper. The finite element method is used in conjunction with linearised incrementation and the Newton-Raphson iterative technique.The finite element used is based on independent strain assumptions insofar as it is allowed by the compatibility equations. Strain-displacement relationships based on shallow shell formulation are

A. B. Sabir; M. S. Djoudi

1995-01-01

71

Nonlinear plasma and beam physics in plasma wake-fields  

SciTech Connect

In experimental studies of the Plasma Wake-field Accelerator performed to date at the Argonne Advanced Accelerator Test Facility, significant nonlinearities in both plasma and beam behavior have been observed. The plasma waves driven in the wake of the intense driving beam in these experiments exhibit three-dimensional nonlinear behavior which has as yet no quantitative theoretical explanation. This nonlinearity is due in part to the self-pinching of the driving beam in the plasma, as the denser self-focused beam can excite larger amplitude plasma waves. The self-pinching is a process with interesting nonlinear aspects: the initial evolution of the beam envelope and the subsequent approach to Bennett equilibrium through phase mixing. 35 refs., 10 figs.

Rosenzweig, J.B.

1990-02-12

72

Effect of Kerr nonlinearity on an Airy beam  

SciTech Connect

The effect of Kerr nonlinearity on an Airy beam is investigated by using the nonlinear Schroedinger equation. Based on the moments method, the evolution of the Airy beam width in the rms sense is analytically described. Numerical simulations indicate that the central parts of the major lobe of the Airy beam initially give rise to radial compression during propagation in a focusing medium, even though the rms beam width broadens. The partial collapse of the center parts of the major lobe of the beam appear below the threshold for a global collapse. The evolutions of the field distributions of the Airy beams are different during propagation in different Kerr media while the beams still travel along the parabolic trajectory just as the beam propagates in free space.

Chen Ruipin; Chu Xiuxiang [School of Sciences, Zhejiang A and F University, Lin'an, Zhejiang 311300 (China); Yin Chaofu; Wang Hui [Institute of information optics, Zhejiang Normal University, Jinhua, Zhejiang 321004 (China)

2010-10-15

73

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

NASA Astrophysics Data System (ADS)

We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional problems, we adopt a B-spline based Galerkin method, a particular case of the more general isogeometric analysis. We propose error estimators using higher order "enhanced" solutions, which are based on the concept of enrichment of the original B-spline basis by means of the "pure" k-refinement procedure typical of isogeometric analysis. We provide several numerical examples for linear and nonlinear output functionals, corresponding to the rotation, displacements and strain energy of the rod, and we compare the effectiveness of the proposed error estimators.

Dedè, L.; Santos, H. A. F. A.

2012-01-01

74

Reshaping the trajectory and spectrum of nonlinear Airy beams.  

PubMed

We demonstrate theoretically and experimentally that a finite Airy beam changes its trajectory while maintaining its acceleration in nonlinear photorefractive media. During this process, the spatial spectrum reshapes dramatically, leading to negative (or positive) spectral defects on the initial spectral distribution under a self-focusing (or defocusing) nonlinearity. PMID:22859132

Hu, Yi; Sun, Zhe; Bongiovanni, Domenico; Song, Daohong; Lou, Cibo; Xu, Jingjun; Chen, Zhigang; Morandotti, Roberto

2012-08-01

75

Aeroelastic coupling of geometrically nonlinear structures and linear unsteady aerodynamics: Two formulations  

NASA Astrophysics Data System (ADS)

Two different time domain formulations of integrating commonly used frequency-domain unsteady aerodynamic models based on a modal approach with full order finite element models for structures with geometric nonlinearities are presented. Both approaches are tailored to flight vehicle configurations where geometric stiffness effects are important but where deformations are moderate, flow is attached, and linear unsteady aerodynamic modeling is adequate, such as low aspect ratio wings or joined-wing and strut-braced wings at small to moderate angles of attack. Results obtained using the two approaches are compared using both planar and non-planar wing configurations. Sub-critical and post-flutter speeds are considered. It is demonstrated that the two methods lead to the same steady solution for the sub-critical case after the transients subside. It is also shown that the two methods predict the amplitude and frequency of limit cycle oscillation (when present) with the same accuracy.

Demasi, L.; Livne, E.

2009-07-01

76

Non-Linear Vibration of Beams with Internal Resonance by the Hierarchical Finite-Element Method  

NASA Astrophysics Data System (ADS)

The hierarchical finite-element (HFEM) and the harmonic balance methods (HBM) are used to investigate the geometrically non-linear free and steady-state forced vibrations of uniform, slender beams. The beam analogue of von Kármán's non-linear strain-displacement relationships are employed and the middle plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and are solved by a continuation method, 1:3 and 1:5 internal resonances are discovered and their consequences are discussed. The convergence properties of the HFEM are analyzed and it is demonstrated that the HFEM model requires far fewer degrees of freedom than the h -version of the FEM models presented in the literature.

Ribeiro, P.; Petyt, M.

1999-07-01

77

Using Nonlinear RF Acceleration for FEL Beam Conditioning  

SciTech Connect

We consider a new approach to condition an electron beam using nonlinear effects in the RF field. We demonstrate that such effects can generate a desirable--for the FEL interaction--radial variation of the particle's energy in the beam, and calculate the induced energy spread in the limit of weak field.

Stupakov, G.; Huang, Z.; /SLAC

2005-12-14

78

Nonlinear evolution of longitudinal bunched-beam instabilities  

Microsoft Academic Search

Numerical results of the nonlinear evolution of longitudinal instabilities of bunched beams are presented. Saturation effects due to the decoherence (tune spread) are categorized according to the magnitude and type of impedances. New phenomenon of non-saturating instability (beam splitting) is described

A. Gerasimov

1993-01-01

79

A novel laser displacement sensor with improved robustness toward geometrical fluctuations of the laser beam  

NASA Astrophysics Data System (ADS)

The measuring accuracy of conventional laser displacement sensors reduces over time as a result of geometrical fluctuations of the laser beam. Accordingly, the present study proposes a new laser displacement sensor in which the effects of geometrical fluctuations of the laser beam are minimized by means of a high-speed rotating optical diffuser. The performance of the proposed sensor is evaluated experimentally using a laboratory-built prototype. The experimental results show that the sensor achieves a higher measuring accuracy than a conventional laser displacement sensor based on a triangulation method. As a result, the proposed sensor provides an ideal solution for a wide range of automatic optical inspection and industrial applications.

Liu, Chien-Sheng; Jiang, Sheng-Hong

2013-10-01

80

Multi-Modal Geometrical Non-Linear Free Vibration of Fully Clamped Composite Laminated Plates  

NASA Astrophysics Data System (ADS)

The geometrically non-linear free vibration of thin composite laminated plates is investigated using the hierarchical finite-element (HFEM) and the harmonic-balance methods (HBM). Von Kármán's non-linear strain-displacement relationships are employed and the mid-plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and are solved by a continuation method. The convergence properties of the HFEM and of the HBM are analyzed. Internal resonances are discovered and the consequent multi-modal and multi-frequency vibration of the plates is shown. The variation of the plates' mode shape and the effect of the fibres' orientation are investigated.

Ribeiro, P.; Petyt, M.

1999-08-01

81

Riemann problem for kinematical conservation laws and geometrical features of nonlinear wavefronts  

NASA Astrophysics Data System (ADS)

A pair of kinematical conservation laws (KCL) in a ray coordinate system ({xi},t) are the basic equations governing the evolution of a moving curve in two space dimensions. We first study elementary wave solutions and then the Riemann problem for KCL when the metric g, associated with the coordinate {xi} designating different rays, is an arbitrary function of the velocity of propagation m of the moving curve. We assume that m>1 (m is appropriately normalized), for which the system of KCL becomes hyperbolic. We interpret the images of the elementary wave solutions in the ({xi},t)-plane to the (x,y)-plane as elementary shapes of the moving curve (or a nonlinear wavefront when interpreted in a physical system) and then describe their geometrical properties. Solutions of the Riemann problem with different initial data give the shapes of the nonlinear wavefront with different combinations of elementary shapes. Finally, we study all possible interactions of elementary shapes.

Baskar, S.; Prasad, Phoolan

2004-08-01

82

Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods  

PubMed Central

Mechanistic models based on systems of nonlinear differential equations can help provide a quantitative understanding of complex physical or biological phenomena. The use of such models to describe nonlinear interactions in molecular biology has a long history; however, it is only recently that advances in computing have allowed these models to be set within a statistical framework, further increasing their usefulness and binding modelling and experimental approaches more tightly together. A probabilistic approach to modelling allows us to quantify uncertainty in both the model parameters and the model predictions, as well as in the model hypotheses themselves. In this paper, the Bayesian approach to statistical inference is adopted and we examine the significant challenges that arise when performing inference over nonlinear ordinary differential equation models describing cell signalling pathways and enzymatic circadian control; in particular, we address the difficulties arising owing to strong nonlinear correlation structures, high dimensionality and non-identifiability of parameters. We demonstrate how recently introduced differential geometric Markov chain Monte Carlo methodology alleviates many of these issues by making proposals based on local sensitivity information, which ultimately allows us to perform effective statistical analysis. Along the way, we highlight the deep link between the sensitivity analysis of such dynamic system models and the underlying Riemannian geometry of the induced posterior probability distributions.

Calderhead, Ben; Girolami, Mark

2011-01-01

83

Nonlinear propagation of strongly focused beams  

NASA Astrophysics Data System (ADS)

A model equation which describes the propagation of sound beams in a viscous fluid is developed using the oblate spheroidal coordinate system. This spheroidal beam equation (SBE) has a specific application to a theoretical prediction on focused high-frequency beams from a circular aperture. Aperture angle is not limited to be small. Numerical examples are displayed for sound pressure amplitudes of the first few harmonics along and across the beam axis when finite-amplitude sinusoidal waves are radiated in water from the source with uniform amplitude distribution. .

Ishiwata, Tsuneo; Kamakura, Tomoo

2000-07-01

84

Beam steering via peak power decay in nonlinear waveguide arrays  

NASA Astrophysics Data System (ADS)

We report the experimental observation and theoretical analysis of a novel beam-steering effect in periodic waveguide arrays that arises from the interplay between discrete diffraction, Kerr nonlinearity and any mechanism that effectively weakens the nonlinear part of the beam. In this regime the propagation direction shows increased sensitivity to the input angle and for a certain angular range around normal incidence a nonlinear beam may be guided to a direction opposite to that initially inserted. For continuous wave beams the role of this mechanism is played by absorption of any kind, such as three photon absorption, two photon absorption or even linear absorption. For pulsed beams we show that the same dynamics can arise due to strong normal temporal dispersion, while absorption is not necessary and can be a further enhancing or alternative factor. This observation falls under a more general dissipation-assisted beam velocity control mechanism in nonlinear optical lattices, which is also theoretically predicted by the effective particle approach.

Droulias, Sotiris; Lahini, Yoav; Kominis, Yannis; Papagiannis, Panagiotis; Bromberg, Yaron; Hizanidis, Kyriakos; Silberberg, Yaron

2013-09-01

85

Geometric nonlinear analysis of plates and cylindrical shells via a linearly conforming radial point interpolation method  

NASA Astrophysics Data System (ADS)

In this paper, the linearly conforming radial point interpolation method is extended for geometric nonlinear analysis of plates and cylindrical shells. The Sander’s nonlinear shell theory is utilized and the arc-length technique is implemented in conjunction with the modified Newton Raphson method to solve the nonlinear equilibrium equations. The radial and polynomial basis functions are employed to construct the shape functions with Delta function property using a set of arbitrarily distributed nodes in local support domains. Besides the conventional nodal integration, a stabilized conforming nodal integration is applied to restore the conformability and to improve the accuracy of solutions. Small rotations and deformations, as well as finite strains, are assumed for the present formulation. Comparisons of present solutions are made with the results reported in the literature and good agreements are obtained. The numerical examples have demonstrated that the present approach, combined with arc-length method, is quite effective in tracing the load-deflection paths of snap-through and snap-back phenomena in shell problems.

Zhao, X.; Liu, G. R.; Dai, K. Y.; Zhong, Z. H.; Li, G. Y.; Han, X.

2008-04-01

86

Gaussian beam diffraction in inhomogeneous media: solution in frame of complex geometrical optics  

NASA Astrophysics Data System (ADS)

The method of paraxial complex geometrical optics is presented to describe Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like media. The method modifies and specifies the results by Babic' (1968), Kirpichnikova (1971), Cerveny, Popov, Psencik (1982), Cerveny (1983, 2001), Timofeev (1995) and Pereverzev (1996) as applied to the optical problems. The method of paraxial complex geometrical optics reduces the problem of Gaussian beam diffraction in inhomogeneous media to the solution of the system of the ordinary differential equations of first order, which can be readily calculated numerically by the Runge-Kutta method. Thereby the paraxial complex geometrical optics radically simplifies description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. By the way of example the known analytical solution for Gaussianbeam diffraction both in a free space and in lens-like medium (Bornatici, Maj 2003) are presented. It is pointed out, that the method of paraxial complex geometrical optics turns out to be equivalent to the solutions of the abridged parabolic wave equation.

Kravtsov, Yu. A.; Berczynski, P.

2005-09-01

87

Nonlinear forms of laser beam propagation in a photopolymerizable medium  

Microsoft Academic Search

Detailed studies of the dynamics of a continuous wave, visible laser beam propagating in a photopolymerizable organosiloxane are presented. Experiments carried out at intensities ranging across ten orders of magnitude (3.2 x 10-5 Wcm-2 to 12732 Wcm-2) revealed three types of nonlinear behaviour. In the low-intensity regime, the beam self-trapped and exhibited complex oscillatory behaviour, which signified the excitation of

Ana B. Villafranca; Kalaichelvi Saravanamuttu

2009-01-01

88

Effects of geometric and material nonlinearities on tunable band gaps and low-frequency directionality of phononic crystals  

NASA Astrophysics Data System (ADS)

We investigate the effects of geometric and material nonlinearities introduced by deformation on the linear dynamic response of two-dimensional phononic crystals. Our analysis not only shows that deformation can be effectively used to tune the band gaps and the directionality of the propagating waves, but also reveals how geometric and material nonlinearities contribute to the tunable response of phononic crystals. Our numerical study provides a better understanding of the tunable response of phononic crystals and opens avenues for the design of systems with optimized properties and enhanced tunability.

Wang, Pai; Shim, Jongmin; Bertoldi, Katia

2013-07-01

89

A finite element formulation with stabilization matrix for geometrically non-linear shells  

NASA Astrophysics Data System (ADS)

An assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically nonlinear problems of isotropic and laminated composite shells. The present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement. The assumed independent strain field is divided into a lower order part and a higher order part. Subsequently, the lower order part is set equal to the displacement-dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix. The strains and the determinant of the Jacobian matrix are assumed to vary linearly in the thickness direction. This assumption allows analytical integration through thickness, independent of the number of plies. A nine-node element with a judiciously chosen set of higher order assumed strain field is developed. Numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation.

Kim, J. H.; Lee, S. W.

1992-06-01

90

Nonlinear vibrations of a viscoelastic beam  

Microsoft Academic Search

Averaging [2, 3] is used to examine the free transverse oscillations of a viscoelastic beam supported at the ends, the rheological properties being described by a certain cubic integral relationship. The forced principal and fractional resonant oscillations are considered for n=1, these being excited by a transverse periodic force; the limiting oscillations are determined that correspond to the principal resonance.

T. Kadyrbekov

1973-01-01

91

Bidirectional beam propagation method for multilayered dielectrics with quadratic nonlinearity  

Microsoft Academic Search

By employing an iterative procedure based on a bidirectional beam propagation method, we develop a numerical algorithm to model light propagation in multilayered structures with second-order nonlinearities. Examples of the applicability of this technique in describing second harmonic generation in photonic crystals are given

Andrea Locatelli; Filippo-Maria Pigozzo; Daniele Modotto; Antonio-Daniele Capobianco; Costantino De Angelis

2002-01-01

92

Galerkin finite element method for non-linear beam vibrations  

Microsoft Academic Search

A Galerkin finite element method is presented, for studying non-linear vibrations of beams describable in terms of moderately large bending theory. The transverse displacement term w alone is used, although several previous attempts to do the same with a Ritz element have failed. This, together with certain assumptions regarding the nature of the vibration, allows an eigenvalue-like quantity characteristic of

G. R. Bhashyam; G. Prathap

1980-01-01

93

Energy shedding during nonlinear self-focusing of optical beams.  

PubMed

Self-focusing of intense laser beams and pulses of light in real nonlinear media is in general accompanied by material losses that require corrections to the conservative Nonlinear Schrödinger equations describing their propagation. Here we examine loss mechanisms that exist even in lossless media and are caused by shedding of energy away from the self-trapping beam making it to relax to an exact solution of lower energy. Using the conservative NLS equations with absorbing boundary conditions we show that energy shedding not only occurs during the initial reshaping process but also during oscillatory propagation induced by saturation of the nonlinear effect. For pulsed input we also show that, depending on the sign and magnitude of dispersion, pulse splitting, energy shedding, collapse or stable self-focusing may result. PMID:24104260

Travis, C; Norris, G; McConnell, G; Oppo, G-L

2013-10-01

94

An energy-preserving description of nonlinear beam vibrations in modal coordinates  

NASA Astrophysics Data System (ADS)

Conserved quantities are identified in the equations describing large-amplitude free vibrations of beams projected onto their linear normal modes. This is achieved by writing the geometrically exact equations of motion in their intrinsic, or Hamiltonian, form before the modal transformation. For nonlinear free vibrations about a zero-force equilibrium, it is shown that the finite-dimensional equations of motion in modal coordinates are energy preserving, even though they only approximate the total energy of the infinite-dimensional system. For beams with constant follower forces, energy-like conserved quantities are also obtained in the finite-dimensional equations of motion via Casimir functions. The duality between space and time variables in the intrinsic description is finally carried over to the definition of a conserved quantity in space, which is identified as the local cross-sectional power. Numerical examples are used to illustrate the main results.

Wynn, Andrew; Wang, Yinan; Palacios, Rafael; Goulart, Paul J.

2013-10-01

95

Geometric nonlinear diffusion filter and its application to X-ray imaging  

PubMed Central

Background Denoising with edge preservation is very important in digital x-ray imaging since it may allow us to reduce x-ray dose in human subjects without noticeable degradation of the image quality. In denoising filter design for x-ray imaging, edge preservation as well as noise reduction is of great concern not to lose detailed spatial information for accurate diagnosis. In addition to this, fast computation is also important since digital x-ray images are mostly comprised of large sized matrices. Methods We have developed a new denoising filter based on the nonlinear diffusion filter model. Rather than employing four directional gradients around the pixel of interest, we use geometric parameters derived from the local pixel intensity distribution in calculating the diffusion coefficients in the horizontal and vertical directions. We have tested the filter performance, including edge preservation and noise reduction, using low dose digital radiography and micro-CT images. Results The proposed denoising filter shows performance similar to those of nonlinear anisotropic diffusion filters (ADFs), one Perona-Malik ADF and the other Weickert's ADF in terms of edge preservation and noise reduction. However, the computation time has been greatly reduced. Conclusions We expect the proposed denoising filter can be greatly used for fast noise reduction particularly in low-dose x-ray imaging.

2011-01-01

96

Improvements to a method for the geometrically nonlinear analysis of compressively loaded stiffened composite panels  

NASA Astrophysics Data System (ADS)

The NLPAN computer code uses a finite-strip approach to the analysis of thin-walled prismatic composite structures such as stiffened panels. The code can model in-plane axial loading, transverse pressure loading, and constant through-the-thickness thermal loading, and can account for shape imperfections. The NLPAN code represents an attempt to extend the buckling analysis of the VIPASA computer code into the geometrically nonlinear regime. Buckling mode shapes generated using VIPASA are used in NLPAN as global functions for representing displacements in the nonlinear regime. While the NLPAN analysis is approximate in nature, it is computationally economical in comparison with finite-element analysis, and is thus suitable for use in preliminary design and design optimization. A comprehensive description of the theoretical approach of NLPAN is provided. A discussion of some operational considerations for the NLPAN code is included. NLPAN is applied to several test problems in order to demonstrate new program capabilities, and to assess the accuracy of the code in modeling various types of loading and response. User instructions for the NLPAN computer program are provided, including a detailed description of the input requirements and example input files for two stiffened-panel configurations.

Stoll, Frederick

97

An analytical geometric calibration method for circular cone-beam geometry.  

PubMed

This work is a continuation of our previous work on geometric calibration in the circular cone-beam geometry. It is well known that seven parameters completely describe such a geometry in either flat-panel X-ray computed tomography or single pinhole SPECT imaging. Previously we developed a graphical procedure to determine the detector in-plane rotation angle independently of the other six parameters. Using the discovered geometrical relationships, in this paper we determine the remaining six parameters using the cone-beam projections of a minimum of three point objects. Our method is analytical. It makes use of the parameters of the fitted ellipse from the calibration data. The parameter estimation is accurate in the noise-free case or when there is moderate projection data truncation or shorter calibration scan range ( ? 360°). We perform numerical evaluations to study the robustness of the proposed method under different projection noise levels and using different data acquisition ranges. Using a full 360° scan range, the estimation accuracy and precision of our method are comparable or superior to previous methods. Using a shorter acquisition range, there may be bias in the ellipse parameters obtained by simple algebraic fitting methods. This bias will propagate to the estimated geometric parameters. Such bias can be mostly eliminated by using a more sophisticated fitting algorithm. At the same noise level, the geometric parameter estimation accuracies are comparable, but the estimation precision degrades, as the acquisition range becomes shorter. PMID:23771316

Xu, Jingyan; Tsui, Benjamin M W

2013-06-12

98

Geometrically Nonlinear Parametric Vibrations of a Transversely Straightened Cylindrical Shell in the Process of Its Dynamic Interaction with a Medium  

NASA Astrophysics Data System (ADS)

The problem on the parametric vibrations of a transversely straightened cylindrical shell contacting with a viscoelastic medium under the action of the internal pressure was solved on the basis of the variation principle in the geometrical nonlinear formulation. The influence of the environment on the indicated vibrations was estimated with the use of the Pasternak dynamic model.

Latifov, F. S.; Seifullaev, F. A.; Yuzbashieva, A. O.

2013-03-01

99

Active constrained layer damping of geometrically nonlinear vibrations of functionally graded plates using piezoelectric fiber-reinforced composites  

Microsoft Academic Search

In this paper, a geometrically nonlinear dynamic analysis has been presented for functionally graded (FG) plates integrated with a patch of active constrained layer damping (ACLD) treatment and subjected to a temperature field. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber-reinforced composite (PFRC) material. The temperature field is assumed to be spatially

Satyajit Panda; M. C. Ray

2008-01-01

100

A geometric nonlinear triangular finite element with an embedded discontinuity for the simulation of quasi-brittle fracture  

Microsoft Academic Search

This paper is aimed to model the appearance and evolution of discrete cracks in quasi-brittle materials using triangular finite elements with an embedded interface in a geometric nonlinear setting. The kinematics for the discontinuous displacement field is presented and the standard variational formulation with respect to the reference configuration is extended to a body with an internal discontinuity. Special attention

J. Schröder; J. Löblien

2005-01-01

101

Nonlinear transmission line based electron beam driver  

SciTech Connect

Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique.

French, David M.; Hoff, Brad W.; Tang Wilkin; Heidger, Susan; Shiffler, Don [Directed Energy Directorate, Air Force Research Laboratory, Kirtland AFB, New Mexico 87117 (United States); Allen-Flowers, Jordan [Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721 (United States)

2012-12-15

102

Nonlinear transmission line based electron beam driver.  

PubMed

Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique. PMID:23277977

French, David M; Hoff, Brad W; Tang, Wilkin; Heidger, Susan; Allen-Flowers, Jordan; Shiffler, Don

2012-12-01

103

Special two-dimensional and three-dimensional geometrically nonlinear finite elements for analysis of adhesively bonded joints  

NASA Astrophysics Data System (ADS)

Finite element models have been successfully used to analyze adhesive bonds in actual structures, but this takes a considerable amount of time and a high computational cost. The objective of this study is to develop a simple and cost-effective finite element model for adhesively bonded joints which could be used in industry. Stress and durability analyses of crack patch geometries are possible applications of this finite element model. For example, the lifetime of aging aircraft can be economically extended by the application of patches bonded over the flaws located in the wings or the fuselage. Special two- and three-dimensional adhesive elements have been developed for stress and displacement analyses in adhesively bonded joints. Both the 2-D and 3-D elements are used to model the whole adhesive system: adherends and adhesive layer. In the 2-D elements, adherends are represented by Bernoulli beam elements with axial deformation and the adhesive layer by plane stress or plane strain elements. The nodes of the plane stress-strain elements that lie in the adherend-adhesive interface are rigidly linked with the nodes of the beam elements. The 3-D elements consist of shell elements that represent the adherends and solid brick elements to model the adhesive. This technique results in smaller models with faster convergence than ordinary finite element models. The resulting mesh can represent arbitrary geometries of the adhesive layer and include cracks. Since large displacements are often observed in adhesively bonded joints, geometric nonlinearity is modeled. 2-D and 3-D stress analyses of single lap joints are presented. Important 3-D effects can be appreciated. Fracture mechanics parameters are computed for both cases. A stress analysis of a crack patch geometry is presented. A numerical simulation of the debonding of the patch is also included.

Andruet, Raul Horacio

104

Modulation instability of broad optical beams in nonlinear media with general nonlinearity  

Microsoft Academic Search

The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schrodinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate. The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in

Hongcheng Wang; Weilong She

2006-01-01

105

Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities  

NASA Astrophysics Data System (ADS)

This paper presents nonlinear vibration analysis of a curved beam subject to uniform base harmonic excitation with both quadratic and cubic nonlinearities. The Galerkin method is employed to discretize the governing equations. A high-dimensional model that can take nonlinear model coupling into account is derived, and the incremental harmonic balance (IHB) method is employed to obtain the steady-state response of the curved beam. The cases investigated include softening stiffness, hardening stiffness and modal energy transfer. The stability of the periodic solutions for given parameters is determined by the multi-variable Floquet theory using Hsu's method. Particular attention is paid to the anti-symmetric response with and without excitation, as the excitation frequency is close to the first and third natural frequencies of the system. The results obtained with the IHB method compare very well with those obtained via numerical integration.

Huang, J. L.; Su, R. K. L.; Lee, Y. Y.; Chen, S. H.

2011-10-01

106

Beam loading by electrons in nonlinear plasma wakes  

SciTech Connect

An analytical theory for the interaction of an electron bunch with a nonlinear plasma wave is developed to make it possible to design efficient laser- and/or beam-driven accelerators that generate high quality monoenergetic electron beams. This theory shows how to choose the charge, the shape, and the placing of the bunch so that the conversion efficiency from the fields of the bubble to the accelerating electrons reaches nearly 100% and the beam quality is optimized. For intense drivers the nonlinear wake is described by the shape of the bubble and beam loading arises when the radial space-charge force of the beam acts back on the electron sheath surrounding the ion channel. The modification of the wake due to the presence of flat-top electron bunches is studied and it is shown that the energy spread of an externally injected flat-top electron bunch can be kept low. The bunch profile that leads to zero energy spread is also derived.

Tzoufras, M. [Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Lu, W. [Department of Electrical Engineering, University of California, Los Angeles, California 90095 (United States); Tsung, F. S.; Huang, C. [Department of Physics and Astronomy, University of California, Los Angeles, California 90095 (United States); Mori, W. B. [Department of Electrical Engineering, University of California, Los Angeles, California 90095 (United States); Department of Physics and Astronomy, University of California, Los Angeles, California 90095 (United States); Katsouleas, T. [Pratt School of Engineering, Duke University, Durham, North Carolina 27708 (United States); Vieira, J.; Fonseca, R. A.; Silva, L. O. [GoLP/Instituto de Plasmas e Fusao Nuclear, Instituto Superior Tecnico, 1049-001 Lisboa (Portugal)

2009-05-15

107

Analysis and simulations of a nonlinear elastic dynamic beam  

NASA Astrophysics Data System (ADS)

A model for the dynamics of a Gao elastic nonlinear beam, which is subject to a horizontal traction at one end, is studied. In particular, the buckling behavior of the beam is investigated. Existence and uniqueness of the local weak solution is established using truncation, approximations, a priori estimates, and results for evolution problems. An explicit finite differences numerical algorithm for the problem is presented. Results of representative simulations are depicted in the cases when the oscillations are about a buckled state, and when the horizontal traction oscillates between compression and tension. The numerical results exhibit a buckling behavior with a complicated dependence on the amplitude and frequency of oscillating horizontal tractions.

Andrews, K. T.; Dumont, Y.; M'Bengue, M. F.; Purcell, J.; Shillor, M.

2012-12-01

108

Frequency conversion of Bessel light beams in nonlinear crystals  

SciTech Connect

The properties of frequency conversion of Bessel light beams (BLBs) in nonlinear crystals are studied theoretically and experimentally. New possibilities and prospects of the development of methods for nonlinear optical frequency conversion using BLBs are discussed. The second harmonic generation (SHG) is studied under the conditions of critical and noncritical phase matching. The longitudinal and transverse phase matching is analysed in detail upon SHG and sum frequency generation in BLBs. The concept of azimuthal width of phase matching caused by the longitudinal and transverse wave detuning is introduced, and its value is calculated for collinear and {pi}-vector interactions. The regime of azimuthally matched interactions is selected, which is realised when the azimuthal phase matching width is small. A correlation of the azimuthal BLB components caused by these interactions is predicted. It is shown that azimuthally matched BLBs are characterised by a significant increase in the overlap integral and by nonlinear interactions that do not destroy their spatial structure. (invited paper)

Belyi, V N; Kazak, N S [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus); Khilo, N A [Division of Optical problems in Informatics, National Academy of Sciences of Belarus, Minsk (Belarus)

2000-09-30

109

Investigation of the Geometric Accuracy of Proton Beam Irradiation in the Liver  

SciTech Connect

Purpose: To investigate the geometric accuracy of proton beam irradiation to the liver by measuring the change in Hounsfield units (HUs) after irradiation. Methods and Materials: We examined 21 patients with liver tumors who were treated with respiratory-gated proton beam therapy (PBT). The radiation dose was 66 GyE in 12 patients and 72.6 GyE in 9 patients. Image registration and reslicing of the computed tomography (CT) results obtained within 1 month before and 3 months after PBT was performed, referring to the planning CT image. The resliced CT images obtained after PBT were subtracted from the images obtained before PBT. We investigated whether the area of the large HU change was consistent with the high-dose distribution area using the location of the largest change in HU around the tumor (peak) on the subtracted CT image and the 90% dose distribution area of the planning CT image. Results: The number of patients (n = 20) whose left-right peaks were within the 90% dose distribution area was significantly larger than the number of patients whose anterior-posterior peaks and superior-inferior peaks were within the 90% dose distribution area (n = 14, n = 13, p = 0.034, and p = 0.02, respectively). Twelve patients exhibited a peak within the 90% dose distribution area in all directions. Nine of the 11 patients with smaller 90% confidence intervals of the percent normalization of the beam cycle (BC; 90% BC) showed a peak within the 90% dose distribution area in six directions, and this percentage was higher than that among the patients with larger 90% BC (3/10, p = 0.03). Conclusion: The geometric accuracy of proton beam irradiation to the liver was higher in the left-right direction than in the other directions. Patients with an irregular respiratory rhythm have a greater risk of a reduced geometric accuracy of PBT in the liver.

Fukumitsu, Nobuyoshi, E-mail: fukumitsun@yahoo.co.jp [Proton Medical Research Center, University of Tsukuba, Tsukuba (Japan); Hashimoto, Takayuki; Okumura, Toshiyuki; Mizumoto, Masashi [Proton Medical Research Center, University of Tsukuba, Tsukuba (Japan); Tohno, Eriko [Department of Radiology, Graduate School of Comprehensive Human Sciences, University of Tsukuba, Tsukuba (Japan); Fukuda, Kuniaki; Abei, Masato [Department of Gastroenterology, Graduate School of Comprehensive Human Sciences, University of Tsukuba, Tsukuba (Japan); Sakae, Takeji; Sakurai, Hideyuki [Proton Medical Research Center, University of Tsukuba, Tsukuba (Japan)

2012-02-01

110

Nonlinear development of weak beam--plasma instability  

SciTech Connect

Nonlinear interactions of tenuous electron beam, background, unmagnetized plasma, and self-consistently generated Langmuir and ion-sound waves are analyzed in the framework of plasma weak turbulence kinetic theory. Full numerical solutions of the complete weak turbulence equations are obtained for the first time, which show the familiar plateau formation in the electron beam distribution and concomitant quasi-saturation of primary Langmuir waves, followed by fully nonlinear processes which include three-wave decay and induced-scattering processes. A detailed analysis reveals that the scattering off ions is an important nonlinear process which leads to prominent backscattered and long-wavelength Langmuir wave components. However, it is found that the decay process is also important, and that the nonlinear development of weak Langmuir turbulence critically depends on the initial conditions. Special attention is paid to the electron-to-ion temperature ratio, T{sub e}/T{sub i}, and the initial perturbation level. It is found that higher values of T{sub e}/T{sub i} promote the generation of backscattered Langmuir wave component, and that a higher initial wave intensity suppresses the backscattered component while significantly enhancing the long-wavelength Langmuir wave component.

Ziebell, L. F.; Gaelzer, R.; Yoon, Peter H.

2001-09-01

111

Phase controlled beam combining with nonlinear frequency conversion.  

PubMed

A phase controlled beam combining via nonlinear optical conversion is proposed and demonstrated. This process involves the combining of the fields at the second harmonic frequency generated by non-collinear input fields. The arrangement of the excitation configuration allows the generated second-harmonic light waves to propagate collinearly, with phases coherently correlated. The manipulation of the conversion efficiency is then possible with the phase control of the input fields. The combined second-harmonic fields are shown to be conveniently and robustly variable from zero to a maximum value that greatly exceeds the second-harmonic field generated by a single laser beam. By using a self-adaptive control algorithm, it is possible to optimize the output without prior knowledge on each beamlet property. Either the second-harmonic output beam profile or the total second-harmonic output power can be optimized with the control algorithm. PMID:20174128

Zhang, Peiqing; Guan, Yefeng; Xie, Xiangsheng; Zhou, Jianying; Yan, Li; Wong, Kam Sing

2010-02-01

112

A Nonlinear Elastic Beam System with Inelastic Contact Constraints  

SciTech Connect

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

Russell, D.L. [Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-123 (United States)], E-mail: russell@calvin.math.vt.edu; White, L.W. [Department of Mathematics, University of Oklahoma, Norman, Norman, OK 73019 (United States)

2002-12-19

113

Non-linear vibration of composite beams with an arbitrary delamination  

NASA Astrophysics Data System (ADS)

In this paper, the non-linear vibration, including the transverse shear, is investigated for composite beams with an arbitrary delamination through the width. The effects of different positions and sizes of the delamination on non-linear vibration of beams are considered. The amplitude-frequency curves of non-linear free vibration are obtained.

Luo, Song-Nan; Yi-Ming, Fu; Zhi-Yuan, Cao

2004-04-01

114

The wave energy flux of high frequency diffracting beams in complex geometrical optics  

NASA Astrophysics Data System (ADS)

We consider the construction of asymptotic solutions of Maxwell's equations for a diffracting wave beam in the high frequency limit and address the description of the wave energy flux transported by the beam. With this aim, the complex eikonal method is applied. That is a generalization of the standard geometrical optics method in which the phase function is assumed to be complex valued, with the non-negative imaginary part accounting for the finite width of the beam cross section. In this framework, we propose an argument which simplifies significantly the analysis of the transport equation for the wave field amplitude and allows us to derive the wave energy flux. The theoretical analysis is illustrated numerically for the case of electron cyclotron beams in tokamak plasmas by using the GRAY code [D. Farina, Fusion Sci. Technol. 52, 154 (2007)], which is based upon the complex eikonal theory. The results are compared to those of the paraxial beam tracing code TORBEAM [E. Poli et al., Comput. Phys. Commun. 136, 90 (2001)], which provides an independent calculation of the energy flow.

Maj, Omar; Mariani, Alberto; Poli, Emanuele; Farina, Daniela

2013-04-01

115

Focused ion beam techniques for fabricating geometrically-complex components and devices.  

SciTech Connect

We have researched several new focused ion beam (FIB) micro-fabrication techniques that offer control of feature shape and the ability to accurately define features onto nonplanar substrates. These FIB-based processes are considered useful for prototyping, reverse engineering, and small-lot manufacturing. Ion beam-based techniques have been developed for defining features in miniature, nonplanar substrates. We demonstrate helices in cylindrical substrates having diameters from 100 {micro}m to 3 mm. Ion beam lathe processes sputter-define 10-{micro}m wide features in cylindrical substrates and tubes. For larger substrates, we combine focused ion beam milling with ultra-precision lathe turning techniques to accurately define 25-100 {micro}m features over many meters of path length. In several cases, we combine the feature defining capability of focused ion beam bombardment with additive techniques such as evaporation, sputter deposition and electroplating in order to build geometrically-complex, functionally-simple devices. Damascene methods that fabricate bound, metal microcoils have been developed for cylindrical substrates. Effects of focused ion milling on surface morphology are also highlighted in a study of ion-milled diamond.

Mayer, Thomas Michael; Adams, David Price; Hodges, V. Carter; Vasile, Michael J.

2004-03-01

116

Finite element analysis for geometrically nonlinear deformations of smart functionally graded plates using vertically reinforced 1-3 piezoelectric composite  

Microsoft Academic Search

In this paper, a finite element model has been developed for the geometrically nonlinear static analysis of simply supported\\u000a functionally graded (FG) plates integrated with a patch of vertically reinforced 1-3 piezoelectric composite material acting\\u000a as a distributed actuator. The material properties of the functionally graded substrate plate are assumed to be graded only\\u000a in the thickness direction according to

Satyajit Panda; M. C. Ray

2008-01-01

117

Geometrically non-linear analysis of arbitrary elastic supported plates and shells using an element-based Lagrangian shell element  

Microsoft Academic Search

In the present paper, the ELF (element-based Lagrangian formulation) 9-node ANS (assumed natural strain) shell element was combined with the spring element for geometrically non-linear analysis of plates and shells sustained by arbitrary elastic edge supports that are subjected to variation in loading.This particular spring element serves as tool for modeling an arbitrary elastic edge support with 6 DOF (degrees

Sung-Cheon Han; Heung-Don Ham; Worsak Kanok-Nukulchai

2008-01-01

118

Nonlinear vibration of edged cracked FGM beams using differential quadrature method  

NASA Astrophysics Data System (ADS)

This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory. The cracked section is modeled by a massless elastic rotational spring. It is assumed that material properties follow exponential distributions through the beam thickness. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of beams with different boundary conditions. The effects of the material gradient, crack depth and boundary conditions on nonlinear free vibration characteristics of the cracked FGM beams are studied in detail.

Ke, LiaoLiang; Wang, YueSheng; Yang, Jie; Kitipornchai, Sritawat; Alam, Firoz

2012-11-01

119

Nonlinear modeling of pulsed and CW HIFU beams for dual-mode ultrasound arrays  

NASA Astrophysics Data System (ADS)

Nonlinear propagation can have beneficial or detrimental effects on focused ultrasound beams for imaging and therapy. The advent of piezocomposite transducer technology have allowed for the fabrication of new generation of therapeutic arrays with relatively wide bandwidth and low cross coupling between elements (resulting in new dual-mode ultrasound array (DMUA) systems for imaging and therapy). The feedback capabilities of DMUAs offer new opportunities to characterize the HIFU beam in situ, including its spectral components due to harmonic generation. This form of feedback allows for the optimization of the DMUA driving patterns to achieve maximum therapeutic gain, by maximizing the harmonic generation within the focal spot. We present results of full 3D modeling of nonlinear wave propagation from the surface of currently available DMUA prototypes (1 and 3.5 MHz) into the treatment volume, modeled as heterogeneous absorbing medium. For example, a 1 MHz DMUA with f-number of 0.8 when geometrically focused at 100 mm with surface intensity of 2.2 W/c\\mcirc 2 was simulated. For 4-second exposure, accounting for harmonic generation resulted in ~10% increase in peak temperature at the focus. We will present and discuss examples of complex DMUA focus patterns in the context of therapeutic gain.

Almekkawy, Mohamed; Casper, Andrew; Ballard, John; Ebbini, Emad

2012-10-01

120

Active constrained layer damping of geometrically nonlinear vibrations of functionally graded plates using piezoelectric fiber-reinforced composites  

NASA Astrophysics Data System (ADS)

In this paper, a geometrically nonlinear dynamic analysis has been presented for functionally graded (FG) plates integrated with a patch of active constrained layer damping (ACLD) treatment and subjected to a temperature field. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber-reinforced composite (PFRC) material. The temperature field is assumed to be spatially uniform over the substrate plate surfaces and varied through the thickness of the host FG plates. The temperature-dependent material properties of the FG substrate plates are assumed to be graded in the thickness direction of the plates according to a power-law distribution while the Poisson's ratio is assumed to be a constant over the domain of the plate. The constrained viscoelastic layer of the ACLD treatment is modeled using the Golla-Hughes-McTavish (GHM) method. Based on the first-order shear deformation theory, a three-dimensional finite element model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG substrate plates under the thermal environment. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the PFRC material for active control of geometrically nonlinear vibrations of FG plates in the absence or the presence of the temperature gradient across the thickness of the plates. It is found that the ACLD treatment is more effective in controlling the geometrically nonlinear vibrations of FG plates than in controlling their linear vibrations. The analysis also reveals that the ACLD patch is more effective for controlling the nonlinear vibrations of FG plates when it is attached to the softest surface of the FG plates than when it is bonded to the stiffest surface of the plates. The effect of piezoelectric fiber orientation in the active constraining PFRC layer on the damping characteristics of the overall FG plates is also discussed.

Panda, Satyajit; Ray, M. C.

2008-04-01

121

NONLINEAR EVOLUTION OF BEAM-PLASMA INSTABILITY IN INHOMOGENEOUS MEDIUM  

SciTech Connect

The problem of electron-beam propagation in inhomogeneous solar wind is intimately related to the solar type II and/or type III radio bursts. Many scientists have addressed this issue in the past by means of quasi-linear theory, but in order to fully characterize the nonlinear dynamics, one must employ weak-turbulence theory. Available numerical solutions of the weak-turbulence theory either rely on only one nonlinear process (either decay or scattering), or when both nonlinear terms are included, the inhomogeneity effect is generally ignored. The present paper reports the full solution of weak-turbulence theory that includes both decay and scattering processes, and also incorporating the effects of density gradient. It is found that the quasi-linear effect sufficiently accounts for the primary Langmuir waves, but to properly characterize the back-scattered Langmuir wave, which is important for eventual radiation generation, it is found that both nonlinear decay and scattering processes make comparable contributions. Such a finding may be important in the quantitative analysis of the plasma emission process with application to solar type II and/or type III radio bursts.

Ziebell, L. F.; Pavan, J. [Instituto de Fisica, UFRGS, Porto Alegre, RS (Brazil); Yoon, P. H. [IPST, University of Maryland, College Park (United States); Gaelzer, R. [Instituto de Fisica e Matematica, UFPel, Pelotas, RS (Brazil)

2011-01-20

122

Nonlinear vibration of an elastically restrained tapered beam  

NASA Astrophysics Data System (ADS)

This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method (EBM) and the iteration perturbation method (IPM). To assess the accuracy of solutions, we compare the results with the harmonic balance method (HBM). The obtained results from EBM and IPM are in excellent agreement with HBM results. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.

Karimpour, S.; Ganji, S. S.; Barari, A.; Ibsen, L. B.; Domairry, G.

2012-10-01

123

Using the nonlinear geometrical acoustics method in the problem of moreton and EUV wave propagation in the solar corona  

NASA Astrophysics Data System (ADS)

Propagation of shock related Moreton and EUV waves in the solar atmosphere is simulated by the nonlinear geometrical acoustics method. This method is based on the ray approximation and takes account of nonlinear wave features: dependence of the wave velocity on its amplitude, nonlinear dissipation of wave energy in the shock front, and the increase in its duration with time. The paper describes ways of applying this method to solve the propagation problem of a blast magnetohydrodynamic shock wave. Results of analytical modeling of EUV and Moreton waves in the spherically symmetric and isothermal solar corona are also presented. The calculations demonstrate deceleration of these waves and an increase in their duration. The calculation results of the kinematics of the EUV wave observed on the Sun on January 17, 2010 are presented as an example.

Afanasyev, An. N.; Uralov, A. M.; Grechnev, V. V.

2011-12-01

124

Nonlinear Finite Element Analysis of FRP Strengthened Reinforced Concrete Beams  

NASA Astrophysics Data System (ADS)

This paper focuses on nonlinear analysis of parent and fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beam using general purpose finite element software, ANSYS. Further, it is aimed to investigate the suitability of different elements available in ANSYS library to represent FRP, epoxy and interface. 3-D structural RC solid element has been used to model concrete and truss element is employed for modeling the reinforcements. FRP has been modelled using 3-D membrane element and layered element with number of layers, epoxy is modelled using eight node brick element, and eight node layered solid shell is used to mathematically represent the concrete-FRP interface behavior. Initially, the validation of the numerical model for the efficacy of different elements (SOLID65 for concrete and LINK8 for reinforcement) and material models is carried out on the experimental beam reported in literature. The validated model, elements and material properties is used to evaluate the load-displacement and load-strain response behavior and crack patterns of the FRP strengthened RC beams. The numerical results indicated that significant improvement in the displacement in the strengthened RC beams with the advancement of cracks. The study shows that FRP with shell elements is recommended when single layer of FRP is used. When multi layered FRP is used, solid layered element can be a reasonably good choice whereas the epoxy matrix with linear solid element does not need further complicated model. Interfacial element makes the analysis minimally improved at the cost of complicated modeling issues and considerable computation time. Hence, for nonlinear analysis of usual strengthened structures, unless it is specifically required for, interface element may not be required and a full contact can be assumed at interface.

Sasmal, S.; Kalidoss, S.; Srinivas, V.

2012-12-01

125

Geometric and Material Nonlinear Analysis of Structures Comprising Rectangular Hollow Sections.  

National Technical Information Service (NTIS)

A nonlinear finite element analysis is presented of structures comprising thin walled rectangular hollow sections. Nonlinearities due to both the change of geometry and material yielding are included, incorporating also the effects of strain unloading. Th...

S. Kitipornchai F. G. A. Al-Bermani S. L. Chan

1987-01-01

126

ELF\\/VLF wave generation via ionospheric HF heating: Experimental comparison of amplitude modulation, beam painting, and geometric modulation  

Microsoft Academic Search

Generation of ELF\\/VLF radio waves (300 Hz to 10 kHz) is achievable via modulation of natural currents in the lower ionosphere with high-power HF (2-10 MHz) heating. Recently, Cohen et al. (2008b) put forth an alternative to conventional amplitude HF power modulation, therein referred to as geometric modulation, in which the HF ionospheric heating beam is geometrically steered at the

M. B. Cohen; M. Golkowski; M. J. McCarrick

2010-01-01

127

ELF\\/VLF wave generation via ionospheric HF heating: Experimental comparison of amplitude modulation, beam painting, and geometric modulation  

Microsoft Academic Search

Generation of ELF\\/VLF radio waves (300 Hz to 10 kHz) is achievable via modulation of natural currents in the lower ionosphere with high-power HF (2–10 MHz) heating. Recently, Cohen et al. (2008b) put forth an alternative to conventional amplitude HF power modulation, therein referred to as geometric modulation, in which the HF ionospheric heating beam is geometrically steered at the

M. B. Cohen; M. Go?kowski; M. J. McCarrick

2010-01-01

128

Active twist rotor blade modelling using particle-wake aerodynamics and geometrically exact beam structural dynamics  

NASA Astrophysics Data System (ADS)

An active aeroelastic and aeroacoustic analysis of helicopter rotor systems is presented in this paper. It is a tightly coupled computational aeroelastic code that interfaces a particle-wake panel method code with an active nonlinear mixed variational intrinsic beam element code. In addition, a Ffowcs-Williams-Hawkings equation-based acoustic component is incorporated to complete the numerical implementation. The theory behind each component is summarized here as well as the method for coupling the aerodynamic and structural components. Sample acoustic and aeroelastic results are given for different model-scale rotors. Comparisons with available (passive) results show very good agreement. Preliminary study with an active twist rotor is also shown.

Cesnik, C. E. S.; Opoku, D. G.; Nitzsche, F.; Cheng, T.

2004-06-01

129

Generation of linear and nonlinear propagation of three-Airy beams.  

PubMed

We report the first experimental demonstration of the so-called three-Airy beams. Such beams represent a two-dimensional field that is a product (rather than simple superposition) of three Airy beams. Our experiments show that, in contrast to conventional Airy beams, this new family of Airy beams can be realized even without the use of truncation by finite apertures. Furthermore, we study linear and nonlinear propagation of the three-Airy beams in a photorefractive medium. It is found that a three-Airy beam tends to linearly diffract into a super-Gaussian-like beam, while under nonlinear propagation it either turns into three intensity spots with a self-defocusing nonlinearity or evolves into a self-trapped channel with a self-focusing nonlinearity. PMID:23389146

Liang, Yi; Ye, Zhuoyi; Song, Daohong; Lou, Cibo; Zhang, Xinzheng; Xu, Jingjun; Chen, Zhigang

2013-01-28

130

Evaluation and Correction of the Non-linear Distortion of CEBAF Beam Position Monitors  

SciTech Connect

The beam position monitors at CEBAF have four antenna style pickups that are used to measure the location of the beam. There is a strong nonlinear response when the beam is far from the electrical center of the device. In order to conduct beam experiments at large orbit excitation we need to correct for this nonlinearity. The correction algorithm is presented and compared to measurements from our stretched wire BPM test stand.

M. Spata, T.L. Allison, K.E. Cole, J. Musson, J. Yan

2011-09-01

131

Geometrical Non-Linear Steady State, Forced, Periodic Vibration of Plates, Part i: Model and Convergence Studies  

NASA Astrophysics Data System (ADS)

A model for the steady state, geometrically non-linear, periodic vibration of thin rectangular plates under harmonic external excitation is presented. The equations of motion in the time domain are derived by applying the principle of virtual work and the hierarchical finite element method (HFEM). These equations are transformed into the frequency domain by the harmonic balance method (HBM) and are solved by a continuation method. The convergence properties of the model are discussed by applying it to isotropic and to composite laminated plates.

Ribeiro, P.; Petyt, M.

1999-10-01

132

Vehicle Frontal Crashworthiness Analysis by Simplified Structure Modeling using Nonlinear Spring and Beam Elements  

Microsoft Academic Search

In this paper modeling and crashworthiness analyses of simplified vehicle structures are carried out using beam elements and nonlinear springs to which axial and bending collapse are applied. In our initial analysis we use a full car model of which 30% of the structures are modeled with nonlinear springs and beam elements while in the second analysis 75% are modeled

Heung-Soo Kim; Shin-You Kang; In-Hyuk Lee; Shin-Hee Park; Dong-Chul Han

1996-01-01

133

Reflected beam parameters during excitation of a waveguide with cubic nonlinearity through a prism coupler  

SciTech Connect

The problem of the field of TE-polarized light beam reflected from the prism during excitation of an optical waveguide possessing cubic nonlinearity is solved. The effect of nonlinear switching is studied taking into account the amplitude distribution of the exciting beam and nonlinear absorption. New possibilities of determining the nonlinear constants of waveguide layers form the intensity distribution of the reflected beam are found. The results of experimental study of the As{sub 2}S{sub 3} film waveguide are presented. 20 refs., 4 figs.

Sotskii, A.B.; Khomchenko, A.V.; Sotskaya, L.I. [Inst. of Applied Optics, Mogilev (Belarus)

1995-03-01

134

EFFECT OF LINEARLY VARYING NORMAL FORCE UPON THE NONLINEAR MODAL ANALYSIS OF SLENDER BEAMS  

Microsoft Academic Search

An improved solution to the nonlinear normal modes of a slender beam, subjected to a linearly varying normal force and end thrust, is determined, by means of an extended method of multiple time and space scales; The nonlinear free vibrations of a straight offshore riser is considered as an example. The vibration frequency of a nonlinear mode is not constant

Carlos E. N. Mazzilli

135

Numerical investigation of the effects of structural geometric and material nonlinearities on limit-cycle oscillation of a cropped delta wing  

NASA Astrophysics Data System (ADS)

This article presents numerical simulations of the limit-cycle oscillation (LCO) of a cropped delta wing in order to investigate the effects of structural geometric and material nonlinearities on aeroelastic behavior. In the computational model, the structural part included both the geometric nonlinearity that arises from large deflections, and the material nonlinearity that originates from plasticity. The Euler equations were employed in the fluid part to describe the transonic aerodynamics. Moreover, the load transfer was conducted using a 3-D interpolating procedure, and the interfaces between the structural and aerodynamic domains were constructed in the form of an exact match. The flutter and LCO behaviors of the cropped delta wing were simulated using the coupling model, and the results were compared with existing experimental measurements. For lower dynamic pressures, the geometric nonlinearity provided the proper mechanism for the development of the LCO, and the numerical results correlated with the experimental values. For higher dynamic pressures, the material nonlinearity led to a rapid rise in the LCO amplitude, and the simulated varying trend was consistent with the experimental observation. This study demonstrated that the LCO of the cropped delta wing was not only closely related to geometric nonlinearity, but was also remarkably affected by material nonlinearity.

Peng, Cui; Han, Jinglong

2011-05-01

136

Integrability and chaos in nonlinearly coupled optical beams  

SciTech Connect

This paper presents a study, using dynamical systems methods, of the equations describing the polarization behavior of two nonlinearly coupled optical beams counterpropagating in a nonlinear medium. In the travelling-wave regime assumption, this system possesses a Lie-Poisson structure on the manifold C{sup 2} {times} C{sup 2}. In the case where the medium is assumed to be isotropic, this system exhibits invariance under the Hamiltonian action of two copies of the rotation group, S{sup 1}, and actually reduces to a lower-dimensional system on the two-sphere, S{sup 2}. We study the dynamics on the reduced space and examine the structure of the phase portrait by determining the fixed points and infinite-period homoclinic and heteroclinic orbits; we concentrate on presenting some exotic behaviour that occurs when some parameters are varied, and we also show special solutions associated with some of the above-mentioned orbits. Last, we demonstrate the existence of complex dynamics when the system is subject to certain classes of Hamiltonian perturbations. To this end, we make use of the Melnikov method to analytically show the occurrence of either horseshoe chaos, or Arnold diffusion. 19 refs.

David, D.

1989-01-01

137

Coupled axial\\/torsional vibrations of drill-strings by means of non-linear model  

Microsoft Academic Search

In the present work a geometrically non-linear model is presented to study the coupling of axial and torsional vibrations on a drill-string, which is described as a vertical slender beam under axial rotation. It is known that the geometrical non-linearities play an important role in the stiffening of a beam. Here, the geometrical stiffening is analyzed using a non-linear finite

R. Sampaio; M. T. Piovan; G. Venero Lozano

2007-01-01

138

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

Microsoft Academic Search

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

Hong Qin

2003-01-01

139

Nonlinear delta f simulations of collective effects in intense charged particle beams  

Microsoft Academic Search

A nonlinear deltaf 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, Phys. Rev. ST

Hong Qin

2003-01-01

140

Implications of the Electrostatic Approximation in the Beam Frame on the Nonlinear Vlasov-Maxwell Equations for Intense Beam Propagation  

SciTech Connect

This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.

Ronald C. Davidson; W. Wei-li Lee; Hong Qin; Edward Startsev

2001-11-08

141

An optimization-based method for geometrical calibration in cone-beam CT without dedicated phantoms.  

PubMed

In this paper we present a new method for the determination of geometrical misalignments in cone-beam CT scanners, from the analysis of the projection data of a generic object. No a priori knowledge of the object shape and positioning is required. We show that a cost function, which depends on the misalignment parameters, can be defined using the projection data and that such a cost function has a local minimum in correspondence to the actual parameters of the system. Hence, the calibration of the scanner can be carried out by minimizing the cost function using standard optimization techniques. The method is developed for a particular class of 3D object functions, for which the redundancy of the fan beam sinogram in the transaxial midplane can be extended to cone-beam projection data, even at wide cone angles. The method has an approximated validity for objects which do not belong to that class; in that case, a suitable subset of the projection data can be selected in order to compute the cost function. We show by numerical simulations that our method is capable to determine with high accuracy the most critical misalignment parameters of the scanner, i.e., the transversal shift and the skew of the detector. Additionally, the detector slant can be determined. Other parameters such as the detector tilt, the longitudinal shift and the error in the source-detector distance cannot be determined with our method, as the proposed cost function has a very weak dependence on them. However, due to the negligible influence of these latter parameters in the reconstructed image quality, they can be kept fixed at estimated values in both calibration and reconstruction processes without compromising the final result. A trade-off between computational cost and calibration accuracy must be considered when choosing the data subset used for the computation of the cost function. Results on real data of a mouse femur as obtained with a small animal micro-CT are shown as well, proving the capability of the proposed calibration method. In principle, the method can be adapted to other cone-beam imaging modalities (e.g., single photon emission computed tomography). PMID:18583729

Panetta, D; Belcari, N; Del Guerra, A; Moehrs, S

2008-06-26

142

An optimization-based method for geometrical calibration in cone-beam CT without dedicated phantoms  

NASA Astrophysics Data System (ADS)

In this paper we present a new method for the determination of geometrical misalignments in cone-beam CT scanners, from the analysis of the projection data of a generic object. No a priori knowledge of the object shape and positioning is required. We show that a cost function, which depends on the misalignment parameters, can be defined using the projection data and that such a cost function has a local minimum in correspondence to the actual parameters of the system. Hence, the calibration of the scanner can be carried out by minimizing the cost function using standard optimization techniques. The method is developed for a particular class of 3D object functions, for which the redundancy of the fan beam sinogram in the transaxial midplane can be extended to cone-beam projection data, even at wide cone angles. The method has an approximated validity for objects which do not belong to that class; in that case, a suitable subset of the projection data can be selected in order to compute the cost function. We show by numerical simulations that our method is capable to determine with high accuracy the most critical misalignment parameters of the scanner, i.e., the transversal shift and the skew of the detector. Additionally, the detector slant can be determined. Other parameters such as the detector tilt, the longitudinal shift and the error in the source-detector distance cannot be determined with our method, as the proposed cost function has a very weak dependence on them. However, due to the negligible influence of these latter parameters in the reconstructed image quality, they can be kept fixed at estimated values in both calibration and reconstruction processes without compromising the final result. A trade-off between computational cost and calibration accuracy must be considered when choosing the data subset used for the computation of the cost function. Results on real data of a mouse femur as obtained with a small animal micro-CT are shown as well, proving the capability of the proposed calibration method. In principle, the method can be adapted to other cone-beam imaging modalities (e.g., single photon emission computed tomography).

Panetta, D.; Belcari, N.; DelGuerra, A.; Moehrs, S.

2008-07-01

143

Nonlinear beam shaper for femtosecond laser pulses, from Gaussian to flat-top profile  

Microsoft Academic Search

We present a straightforward method to transform a spatially Gaussian femtosecond laser beam into a flat-top shaped beam. The proposed technique takes advantage of a nonlinear phase induced in positive Kerr medium followed by a simple optical system. The variation of the refractive index with the laser intensity creates a phase plate which induces changes in the beam profile after

B. Mercier; J. P. Rousseau; A. Jullien; L. Antonucci

2010-01-01

144

Improvements to a method for the geometrically nonlinear analysis of compressively loaded stiffened composite panels  

Microsoft Academic Search

The NLPAN computer code uses a finite-strip approach to the analysis of thin-walled prismatic composite structures such as stiffened panels. The code can model in-plane axial loading, transverse pressure loading, and constant through-the-thickness thermal loading, and can account for shape imperfections. The NLPAN code represents an attempt to extend the buckling analysis of the VIPASA computer code into the geometrically

Frederick Stoll

1993-01-01

145

Observation of Nonlinear Self-Trapping of Broad Beams in Defocusing Waveguide Arrays  

SciTech Connect

We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity.

Bennet, Francis H.; Haslinger, Franz; Neshev, Dragomir N.; Kivshar, Yuri S. [Nonlinear Physics Centre, Centre for Ultrahigh-Bandwidth Devices for Optical Systems (CUDOS), Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 (Australia); Alexander, Tristram J. [Nonlinear Physics Centre, Centre for Ultrahigh-Bandwidth Devices for Optical Systems (CUDOS), Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 (Australia)] [School of Physical, Environmental and Mathematical Sciences, UNSW-ADFA, Canberra ACT 2600 (Australia); Mitchell, Arnan [CUDOS, School of Electrical and Computer Engineering, RMIT University, Melbourne Vic 3001 (Australia)

2011-03-04

146

Nonlinear realizations of the (super)diffeomorphism groups, geometrical objects and integral invariants in the superspace  

Microsoft Academic Search

It is shown that vielbeins and connections of any (super)space are naturally described in terms of nonlinear realizations of infinite - dimensional diffeomorphism groups of the corresponding (super)space. The method of construction of integral invariants from the invariant Cartan's differential $\\\\Omega$ - forms is generalized to the case of superspace.

A. Pashnev

1997-01-01

147

Development of a global/local approach and a geometrically nonlinear local panel analysis for structural design  

NASA Astrophysics Data System (ADS)

A computationally efficient analysis capability for the geometrically non-linear response of compressively loaded prismatic plate structures was developed. Both a "full" finite strip solution procedure and a "reduced" solution procedure were implemented in a FORTRAN 90 computer code, and comparisons were made with results available in the technical literature. Both the full and reduced solution procedures were demonstrated to provide accurate results for displacement and strain quantities through moderately large post-buckling loads. The full method is a non-linear finite strip analysis of the semi-analytical, multi-term type. Individual finite strips are modeled as balanced and symmetric laminated composite materials which are assumed to behave orthotropically in bending, and the structure is loaded in uniaxial or biaxial compression. The loaded ends of the structure are assumed to be simply supported, and geometric shape imperfections may be modeled. The reduced solution method makes use of a reduced basis technique in conjunction with the full finite strip analysis. Here, the potentially large set of non-linear algebraic equations produced by the finite strip method are replaced by a small set of system equations. In the present implementation, the basis vectors consist of successive derivatives of the non-linear solution vector with respect to a loading parameter. Depending on the nature of the problem, the reduced solution procedure is capable of computational savings of up to 60%+ compared to the full finite strip method. The reduced method is most effective in reducing the computational cost of the full method when the most significant portion of the cost of the full method is factorization of the assembled system matrices. The robustness and efficiency of the reduced solution procedure was found to be sensitive to the user specified error norm which is used during the reduced solution procedure to determine when to generate new sets of basis vectors. In parallel with this effort, a new method for performing global/local design optimization of large complex structures (such as aircraft wings or fuselages) was developed. A simple and flexible interface between the global and local design levels was constructed using response surface methodology. The interface is constructed so as to minimize the changes required in either the global design code or the local design codes(s). Proper coupling is maintained between the global and local design levels via a "weight constraint" and the transfer of global stiffness information to the local level. The method was verified using a simple isotropic global wing model and the local panel design code PASCO .

Ragon, Scott Alan, II

148

Description of the Nonlinear and Collective Behavior of Charged-Particle Beams by means of a Nonlinear Schroedinger Equation  

SciTech Connect

Charged-particle beams are employed for a number of scientific and technological applications. The conventional description of their collective behavior is usually given in terms of the Vlasov equation. In the last 15 years some alternative descriptions have been developed in terms of a nonlinear Schroedinger equation governing the collective dynamics of the beam while interacting with the surrounding medium. This approach gives new insights, providing an alternative 'key of reading' of the charged-particle beam dynamics, and have been applied to a number of physical problems concerning conventional particle accelerating machines as well as plasma-based accelerator schemes. Remarkably, it is based on a mathematical formalism fully similar to those used for the propagation of e.m. radiation beams in nonlinear media a well as the nonlinear dynamics of the Bose-Einsten condensates.In this paper, a presentation of some significant nonlinear collective effects of a charged-particle beam in particle accelerators, that have been recently investigated in the framework of the above Schroedinger-like descriptions, is given.

Fedele, Renato [Dipartimento di Scienze Fisiche, Universita Federico II, Napoli Complesso Universitario di M.S. Angelo, via Cintia, I-80126 Naples (Italy); INFN, Napoli Complesso Universitario di M.S. Angelo, via Cintia, I-80126 Naples (Italy); Jovanovic, Dusan [Institute of Physics, P.O. Box 57, Yu-11001 Belgrade (Serbia and Montenegro)

2004-12-01

149

Geometric scaling in ultrahigh-energy neutrino scattering and nonlinear perturbative QCD  

SciTech Connect

It is shown that in ultrahigh-energy inelastic neutrino-nucleon(nucleus) scattering the cross sections for the boson-hadron(nucleus) reactions should exhibit geometric scaling on the single variable {tau}{sub A}=Q{sup 2}/Q{sub sat,A}{sup 2}. The dependence on energy and atomic number of the charged/neutral current cross sections are encoded in the saturation momentum Q{sub sat,A}. This fact allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization based on the scaling property.

Machado, Magno V.T. [Departamento de Fisica de Particulas. 15706 Universidade de Santiago de Compostela (Spain); Universidade Estadual do Rio Grande do Sul, Unidade de Bento Goncalves. CEP 95700-000 (Brazil)

2005-06-01

150

Non-conventional non-linear two-node hybrid stress-strain curved beam elements  

Microsoft Academic Search

This paper presents a family of two-node hybrid stress–strain curved beam elements with four displacement degrees of freedom (dof) per node for the finite deformation 2D Timoshenko beam theory, which can be readily generalized on the two-node curved beam elements with six displacement dof for the 3D beam theory. The developed formulation is based on the principally new non-linear strain–displacement

G. M. Kulikov; S. V. Plotnikova

2004-01-01

151

Effects of geometrical order on the linear and nonlinear optical properties of metal nanoparticles  

NASA Astrophysics Data System (ADS)

This dissertation describes experimental and computational studies of the effects of ordered arrangement on the linear and nonlinear optical properties of metal nanoparticles. The principal result is that second-harmonic light may be generated and observed from nanoparticle gratings having maximum in-plane symmetry, provided that one looks at non-normal observation angles. These measurements are made possible by a custom-built variable-angle microscope, and enable a variety of studies of the second-order nonlinear response of nanoparticles that were not previously feasible. In addition, the surface plasmon resonance of metal nanoparticles is studied by linear spectroscopy. A comparison of experimental data with computational modeling shows that under normal ambient conditions, Ag nanoparticles tarnish by a sulfidation reaction more readily than bulk silver, and that even a very thin surface layer of corroded material (Ag2S) considerably redshifts and weakens the localized surface plasmon resonance of a nanoparticle.

McMahon, Matthew David

152

Genuinely resultant shell finite elements accounting for geometric and material non-linearity  

Microsoft Academic Search

A general theoretical and numerical framework for the fully nonlinear analysis of shells is presented. It is shown how to derive 2D governing equations for shells and the corresponding finite element discretizations from basic laws of classical continuum mechanics. The finite elements for shells avoid time-consuming through-the-thickness integration to evaluate element matrices typical for the degenerated shell element concept. Drilling

J. Chroscielewski; J. Makowski; H. Stumpf

1992-01-01

153

Numerical simulations of the nonlinear evolution of the magnetron instability for several geometric configurations  

Microsoft Academic Search

Summary form only given. We present the theory of the magnetron instability, which is developed using a fluid plasma description. A 1-D non-linear steady-state model is developed for relativistic and non-relativistic planar and cylindrical smooth-bore magnetron geometries. To this steady-state background, 1-D and 2-D linear perturbation analyses are applied to determine the modes and growth rates for the magnetron instability

C. Lenyk; T. Fleming; K. Cartwright

2004-01-01

154

Geometrically nonlinear design sensitivity analysis on parallel-vector high-performance computers  

SciTech Connect

Parallel-vector solution strategies for generation and assembly of element matrices, solution of the resulted system of linear equations, calculations of the unbalanced loads, displacements, stresses, and design sensitivity analysis (DSA) are all incorporated into the Newton Raphson (NR) procedure for nonlinear finite element analysis and DSA. Numerical results are included to show the performance of the proposed method for structural analysis and DSA in a parallel-vector computer environment. 10 refs.

Baddourah, M.A.; Nguyen, D.T.

1993-01-01

155

The effects of nonlinear phase for the generation and propagation of finite energy Airy beams  

NASA Astrophysics Data System (ADS)

The generation of a high-power finite-energy Airy beam (FEAB) needs a high-power source laser which leads a nonlinear phase into the generation and propagation of the FEAB. We theoretically and numerically investigate how the nonlinear phase affects the generation and propagation of FEAB. The nonlinear phase is associated with the B-integral of the laser system. The second-order term of the nonlinear phase’s Taylor series can theoretically represent the impacts of nonlinear phase with small B-integral. The nonlinear phase significantly changes the peak intensity and the beam shape during the generation and propagation of FEAB. The variation becomes larger with increasing B-integral, and the bigger the truncation coefficient of FEAB, the smaller the B-integral domain.

Wu, Yifang; Fu, Xiquan; Wang, Wenlong; Yu, Wenlong; Wu, Hao

2013-10-01

156

Nonlinear stationary waves and solitons in ion beam-plasma configuration  

Microsoft Academic Search

A fully nonlinear treatment for stationary waves in a cold plasma with an ion beam propagating parallel to the magnetic field is carried out in the framework of Hall MHD. It is shown that the linearly unstable system can evolve into a steady nonlinear configuration in which both ion populations undergo a coherent helical motion guided by the magnetic field.

E. Dubinin; K. Sauer; J. F. McKenzie

2004-01-01

157

Relativistic electron beam acceleration by nonlinear Landau damping of electrostatic waves in a magnetized plasma  

SciTech Connect

Acceleration and heating of a relativistic electron beam due to nonlinear electron Landau and cyclotron damping of electrostatic waves in a magnetized plasma are investigated theoretically and numerically on the basis of the relativistic kinetic wave and transport equations derived from the relativistic Vlasov-Maxwell equations. Two electrostatic waves interact nonlinearly with the relativistic electron beam satisfying the resonance condition for nonlinear electron Landau and cyclotron damping of {omega}{sub k}-{omega}{sub k{sup '}}-(k{sub perpendicular}-k{sub perpendicula=} r{sup '})v{sub d}-(k{sub parallel}-k{sub parallel}{sup '})v{sub b}{approx_equal}m{omega}{sub ce} where v{sub b} and v{sub d} are the parallel and perpendicular velocities of the relativistic electron beam, respectively, and {omega}{sub ce} is the relativistic electron cyclotron frequency. The beat waves produced by two electrostatic waves resonate with the relativistic electron beam. The relativistic transport equations using the relativistic drifted Maxwellian momentum distribution function of the relativistic electron beam were derived and analyzed. They show obviously its acceleration and heating (deceleration or cooling). Nonlinear electron Landau damping of the two lower-hybrid waves has been studied by the numerical analysis of relativistic nonlinear wave-particle coupling coefficients and it was clarified that the highly relativistic electron beam can be accelerated efficiently via the Compton scattering due to nonlinear electron Landau damping of the lower-hybrid waves.

Sugaya, R. [Department of Physics, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577 (Japan)

2004-12-01

158

A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches  

NASA Astrophysics Data System (ADS)

This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.

Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.

2013-10-01

159

Nonlinear finite element analysis of reinforced concrete beams strengthened by fiber-reinforced plastics  

Microsoft Academic Search

Numerical analyses are performed using the ABAQUS finite element program to predict the ultimate loading capacity of rectangular reinforced concrete beams strengthened by fiber-reinforced plastics applied at the bottom or on both sides of these beams. Nonlinear material behavior, as it relates to steel reinforcing bars, plain concrete, and fiber-reinforced plastics is simulated using appropriate constitutive models. The influences of

Hsuan-Teh Hu; Fu-Ming Lin; Yih-Yuan Jan

2004-01-01

160

Waveguide propagation of laser beams in media with saturating non-linearity  

Microsoft Academic Search

The waveguide propagation of Gaussian laser beams in dielectric media with saturating non-linearity has been investigated analytically, using two profiles for the dependence of the dielectric constant on intensity. An expression for the radius of the uniform wave-guide, corresponding to a given power of the beam, has been obtained and the existence of a minimum radius, corresponding to an optimum

D. P. Tewari; V. K. Tripathi; J. Kamal; M. S. Sodha

1971-01-01

161

Nonlinear micromechanics-based finite element analysis of the interfacial behaviour of FRP-strengthened reinforced concrete beams  

NASA Astrophysics Data System (ADS)

This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be exploited to bridge the existing gaps in the development of analysis and modelling approaches that can predict the behaviour of FRP-strengthened concrete beams. The research effort here begins with the formulation of a concrete model and development of FRP/concrete interface constitutive laws, followed by finite element simulations for beams strengthened in flexure. Finally, a statistical analysis is carried out taking the advantage of the aforesaid numerical tools to propose design guidelines. In this dissertation, an alternative incremental formulation of the M4 microplane model is proposed to overcome the computational complexities associated with the original formulation. Through a number of numerical applications, this incremental formulation is shown to be equivalent to the original M4 model. To assess the computational efficiency of the incremental formulation, the "arc-length" numerical technique is also considered and implemented in the original Bazant et al. [2000] M4 formulation. Finally, the M4 microplane concrete model is coded in FORTRAN and implemented as a user-defined subroutine into the commercial software package ADINA, Version 8.4. Then this subroutine is used with the finite element package to analyze various applications involving FRP strengthening. In the first application a nonlinear micromechanics-based finite element analysis is performed to investigate the interfacial behaviour of FRP/concrete joints subjected to direct shear loadings. The intention of this part is to develop a reliable bond--slip model for the FRP/concrete interface. The bond--slip relation is developed considering the interaction between the interfacial normal and shear stress components along the bonded length. A new approach is proposed to describe the entire tau-s relationship based on three separate models. The first model captures the shear response of an orthotropic FRP laminate. The second model simulates the shear characteristics of an adhesive layer, while the third model represents the shear nonlinearity of a thin layer inside the concrete, referred to as the interfacial layer. The proposed bond--slip model reflects the geometrical and material characteristics of the FRP, concrete, and adhesive layers. Two-dimensional and three-dimensional nonlinear displacement-controlled finite element (FE) models are then developed to investigate the flexural and FRP/concrete interfacial responses of FRP-strengthened reinforced concrete beams. The three-dimensional finite element model is created to accommodate cases of beams having FRP anchorage systems. Discrete interface elements are proposed and used to simulate the FRP/concrete interfacial behaviour before and after cracking. The FE models are capable of simulating the various failure modes, including debonding of the FRP either at the plate end or at intermediate cracks. Particular attention is focused on the effect of crack initiation and propagation on the interfacial behaviour. This study leads to an accurate and refined interpretation of the plate-end and intermediate crack debonding failure mechanisms for FRP-strengthened beams with and without FRP anchorage systems. Finally, the FE models are used to conduct a parametric study to generalize the findings of the FE analysis. The variables under investigation include two material characteristics; namely, the concrete compressive strength and axial stiffness of the FRP laminates as well as three geometric properties; namely, the steel reinforcement ratio, the beam span length and the beam depth. The parametric study is followed by a statistical analysis for 43 strengthened beams involving the five aforementioned variables.

Abd El Baky, Hussien

162

Non-linear analysis of composite beams under positive bending  

Microsoft Academic Search

The structural behaviour of steel–concrete composite beams depends on the interaction between the steel beam and the concrete slab. Therefore, the connection largely influences the global behaviour of the beam and its modelling is a key issue in the analysis of these structures. An effective model requires the introduction of an explicit relationship between slip and interaction force given by

G. Fabbrocino; G. Manfredi; E. Cosenza

1999-01-01

163

Nonlinear analysis of steel–concrete composite beams curved in plan  

Microsoft Academic Search

This paper deals with the behavior of structural steel–concrete composite beams curved in plan. The finite element package ABAQUS has been used to study the nonlinear behavior and ultimate load-carrying capacity of such beams. A three-dimensional finite element model has been adopted. Shell elements have been used to simulate the behavior of concrete slab and steel girder, and rigid beam

V. Thevendran; S. Chen; N. E. Shanmugam; J. Y. Richard Liew

1999-01-01

164

A geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites  

SciTech Connect

A triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads. The nonlinear deformation process is computed using an incremental/iterative approach with the Newton-Raphson Method used to find the incremental displacements in each step. The presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation-independent mechanical loads, deformation-dependent pressure loads, and thermal loads. Unlike elastic structures that have a single critical load value associated with a given snapping of buckling instability phenomenon, viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times. Both creep buckling and snap-through examples are presented here. In some cases, viscoelastic results are also obtained using the quasielastic method in which load-history effects are ignored, and time-varying viscoelastic properties are simply used in a series of elastic problems. The presented numerical examples demonstrate the capability and accuracy of the formulation.

HAMMERAND,DANIEL C.; KAPANIA,RAKESH K.

2000-05-01

165

Simultaneous generation of second to fifth harmonic conical beams in a two dimensional nonlinear photonic crystal.  

PubMed

Broadly tunable multiple high-harmonic conical beams have been generated by means of a multistep ?(2) cascade processes in a two dimensional nonlinear photonic crystal. The nonlinear structure consists of a square lattice of inverted hexagonal domains with diameters and distances between domains as low as 1 ?m. The large number of reciprocal lattice vectors provided by both the square nonlinear structure and the hexagonal shaped domains, along with imperfections on the size and shape of the individual domains make possible the simultaneous generation of second up to fifth harmonic conical beams in a single nonlinear structure by using different types of phase matching geometries. The frequency response can be tuned in an extremely large spectral range, and continuous generation of nonlinear conical beams covering the whole visible spectral region can be achieved. Further, the same photon energy can be generated at different orders, so that concentrically emitted conical beams with angular dispersion as large as ?? = 50° can be observed. The results highlight the significance of highly controlled engineered 2D nonlinear structures to generate advanced multi-photon devices with large spatial and spectral tunable response. PMID:23388820

Mateos, Luis; Molina, Pablo; Galisteo, Juan; López, Cefe; Bausá, Luisa E; Ramírez, Mariola O

2012-12-31

166

Determination of geometrical, spectroscopic, thermal and nonlinear optical parameters of (+)-Varitriol by DFT/ab initio calculations.  

PubMed

Theoretical studies have been carried out on (+)-Varitriol using both the B3LYP/6-311+G and HF/6-311+G methods. The vibrational spectra of the title molecule have been recorded in solid state with FT-IR and Micro-Raman spectrometry. The calculated geometrical parameters of the title molecule, like bond length, bond angle and dihedral angles have been compared with the experimental data. The spectral frequencies have been calculated theoretically using both the above mentioned methods and are compared with the observed spectra. The complete vibrational assignments of wavenumbers have been made on the basis of potential energy distribution (PED). From this analysis, it is seen that the vibrational frequencies obtained from B3LYP method are in good agreement with the experiment, when compared to HF method. Nonlinear optical properties like dipole moment, hyperpolarizabilities and thermal properties like rotational constants, zero point vibrational energies are calculated. The effect of temperature on various thermodynamic properties have been calculated and reported. PMID:23896295

Vasantha Kumar, V; Nagabhushanam, M; Laxmikanth Rao, J

2013-07-11

167

On the nonlinearity of the Langmuir turbulence excited by a weak electron beam-plasma interaction  

SciTech Connect

In the present study, we analyze the data sets produced by a one-dimensional Vlasov-Poisson simulation of the weak electron beam-plasma instability to clarify the nonlinearity of the Langmuir turbulence excited by the weak-beam interaction. The growth of wave number modes is analyzed by using the momentum equation of the whole electrons. The analysis shows that the primary Langmuir wave mode is almost linear, while the nonlinear terms play important roles in the growth of the lower harmonic mode and the secondary higher harmonic mode. After the linear growth saturates, while the wave power of the primary mode is much larger than the other modes, linear and nonlinear interactions occurring in both lower harmonic and secondary higher harmonic modes are more active than those in the primary mode. Nonlinearity in the system comes from the advection rather than the ponderomotive forces.

Nariyuki, Y. [Department of Electrical Engineering and Information Science, Kochi National College of Technology, Kochi 783-8508 (Japan); Umeda, T. [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8601 (Japan)

2010-05-15

168

Terahertz vector beam generation using segmented nonlinear optical crystals with threefold rotational symmetry.  

PubMed

We propose and demonstrate a simple method for cylindrical vector beam generation in the terahertz frequency region using optical rectification in segmented nonlinear crystals with threefold rotational symmetry. We used segmented GaP(111) plates to generate the terahertz cylindrical vector beam, and obtained clear evidence of the beam generation with a terahertz camera. By this method, a broadband terahertz cylindrical vector beam can be generated, and the radial and azimuth modes can be easily switched. We also report on the direct observation of the longitudinal electric field components at the focal point using a terahertz time-domain spectroscopy technique. PMID:23037339

Imai, Ryo; Kanda, Natsuki; Higuchi, Takuya; Zheng, Zhu; Konishi, Kuniaki; Kuwata-Gonokami, Makoto

2012-09-24

169

Strong self-focusing of laser beam in a medium with quadratic nonlinear response  

NASA Astrophysics Data System (ADS)

We compare self-focusing of laser beam with Gaussian, super-Gaussian and ring profile in a medium with quadratic nonlinear response due to cascading SHG. The duration of the light pulse under consideration is about microsecond. Nevertheless, the dispersion of group velocity is also taken into account. We demonstrate a possibility of strong growth for intensity of the laser radiation without changing the pulse shape and Gaussian profile of the beam. For initial super- Gaussian and ring profile the Gaussian profile appears due to the diffraction of laser beam at certain section of nonlinear medium. Then, the optical radiation undergoes self-focusing without changing the Gaussian intensity distribution till appearance of the first nonlinear focus. This phenomenon has various practical applications. For example, it can be used for developing the laser system in microsecond range of pulse duration which operates in the regime similar to KLM regime for femtosecond laser system.

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2012-10-01

170

Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction.  

PubMed

We modify the well-known photothermal beam deflection technique to study ultrafast nonlinearities. Using phase-sensitive detection we directly measure the temporal and polarization dynamics of nonlinear refraction (NLR) with sensitivity to optically induced phase changes of approximately ?/20,000. We use the relative polarization dependence of excitation and probe to separate the isotropic and reorientational components of the NLR. PMID:24104803

Ferdinandus, Manuel R; Hu, Honghua; Reichert, Matthew; Hagan, David J; Van Stryland, Eric W

2013-09-15

171

C exp 0 finite element geometrically non-linear analysis of fibre reinforced composite and sandwich laminates based on a higher-order theory  

NASA Astrophysics Data System (ADS)

This paper presents a refined higher-order shear deformation theory for the linear and geometrically nonlinear finite element analysis of fiber-reinforced composite and sandwich laminates. Laminae material is assumed to be linearly elastic, homogeneous and isotropic/orthotropic. This theory accounts for parabolic distribution of the transverse shear strains through the thickness of the laminate and higher-order terms in Green's strain vector in the sense of von Karman. A simple C exp 0 finite element formulation is presented with a total Lagrangian approach and a nine-node Lagrangian quadrilateral element is chosen with nine degrees of freedom per node. Numerical results are presented for linear and geometric nonlinear analysis of multilayer cross-ply laminates and sandwich plates. The present theory predicts displacements and stresses more accurately than the first-order shear deformation theory. The results are compared with available closed-form and numerical solutions of both three-dimensional elasticity and plate theories.

Kant, T.; Kommineni, J. R.

1992-10-01

172

BEAM-BASED NON-LINEAR OPTICS CORRECTIONS IN COLLIDERS.  

SciTech Connect

A method has been developed to measure and correct operationally the non-linear effects of the final focusing magnets in colliders, that gives access to the effects of multi-pole errors by applying closed orbit bumps, and analyzing the resulting tune and orbit shifts. This technique has been tested and used during 4 years of RHIC (the Relativistic Heavy Ion Collider at BNL) operations. I will discuss here the theoretical basis of the method, the experimental set-up, the correction results, the present understanding of the machine model, the potential and limitations of the method itself as compared with other non-linear correction techniques.

PILAT, R.; LUO, Y.; MALITSKY, N.; PTITSYN, V.

2005-05-16

173

Nonlinear Longitudinal Space Charge Oscillations in Relativistic Electron Beams  

SciTech Connect

In this Letter we study the evolution of an initial periodic modulation in the temporal profile of a relativistic electron beam under the effect of longitudinal space-charge forces. Linear theory predicts a periodic exchange of the modulation between the density and the energy profiles at the beam plasma frequency. For large enough initial modulations, wave breaking occurs after 1/2 period of plasma oscillation leading to the formation of short current spikes. We confirm this effect by direct measurements on a ps-modulated electron beam from an rf photoinjector. These results are useful for the generation of intense electron pulse trains for advanced accelerator applications.

Musumeci, P.; Li, R. K.; Marinelli, A. [Department of Physics and Astronomy, UCLA, Los Angeles, California, 90095 (United States)

2011-05-06

174

Nonlinear effects in the radiation force generated by amplitude-modulated focused beams  

NASA Astrophysics Data System (ADS)

Harmonic Motion Imaging (HMI) uses an amplitude-modulated (AM) beam to induce an oscillatory radiation force before, during and after ablation. In this paper, the findings from a numerical analysis of the effects related with the nonlinear propagation of AM focused ultrasonic beams in water on the radiation force and the location of its maxima will be presented. The numerical modeling is performed using the KZK nonlinear parabolic equation. The radiation force is generated by a focused transducer with a gain of 18, a carrier frequency of 1 MHz and a modulation frequency of 25 kHz. The modulated excitation generates a spatially-invariant force proportional to the intensity. Regarding the nonlinear wave propagation, the force is no longer proportional to the intensity, reaching a factor of eight between the nonlinear and linear estimations. Also, a 9 mm shift in the on-axis force peak occurs when the initial pressure increased from 1 to 300 kPa. This spatial shift, due to the nonlinear effects, becomes dynamic in AM focused beams, as the different signal periods have different amplitudes. This study shows that both the value and the spatial position of the force peak are affected by the nonlinear propagation of the ultrasonic waves.

González, Nuria; Jiménez, Noé; Redondo, Javier; Roig, Bernardino; Picó, Rubén; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.; Camarena, Francisco

2012-10-01

175

Nonlinear d--ta-f Simulation Studies of Intense Charged Particle Beams with Large Temperature Anisotropy  

SciTech Connect

In this paper, a 3-D nonlinear perturbative particle simulation code (BEST) [H. Qin, R.C. Davidson and W.W. Lee, Physical Review Special Topics on Accelerators and Beams 3 (2000) 084401] is used to systematically study the stability properties of intense nonneutral charged particle beams with large temperature anisotropy (T{sub {perpendicular}b} >> T{sub {parallel}b}). The most unstable modes are identified, and their eigen frequencies, radial mode structure, and nonlinear dynamics are determined for axisymmetric perturbations with {partial_derivative}/{partial_derivative}{theta} = 0.

Edward A. Startsev; Ronald C. Davidson; Hong Qin

2002-05-07

176

Nonlinear evolution of the Weibel instability of relativistic electron beams  

SciTech Connect

Physics of the long-term evolution of the Weibel instability (WI) of an electron beam propagating through the plasma is described. Several phenomena occurring during the WI are identified: (i) the exponential growth stage resulting in beam breakup into small current filaments; (ii) merger of the small filaments and beam particles' trapping inside them; (iii) filaments' compression and expulsion of the ambient plasma from the filaments; (iv) formation of high-current filaments and their merger. It is shown that during the final stage these beam filaments can carry super-Alfvenic currents and form hollow current density profiles similar to the Hammer-Rostoker equilibrium. This explains why the initially increasing magnetic field energy eventually decreases during the late stage of the instability. Different computational approaches to modeling both collisionless and collisional WI are also described.

Shvets, Gennady; Khudik, Vladimir; Siemon, Carl [Department of Physics and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712 (United States); Polomarov, Oleg [Fusion Science Center, Laboratory for Laser Energetics, University of Rochester, New York 14623 (United States); Kaganovich, Igor [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)

2009-05-15

177

Non-Linear Stability of Magnetically Focused Particle Beams.  

National Technical Information Service (NTIS)

The subject of our project supported by the AFOSR is the dynamics of intense charged beams focused by magnetic fields. There are several applications for this kind system, ranging from microwaves to controlled nuclear fusion. Our group is currently formed...

F. B. Rizzato R. Pakter Y. Levin

2012-01-01

178

Nonlinear response of a beam under distributed moving contact load  

Microsoft Academic Search

In this paper, the nonlinear behavior of a one-dimensional model of the disc brake pad is examined. The contact normal force between the disc brake pad lining and rotor is represented by a second order polynomial of the relative displacement between the two elastic bodies. The frictional force due to the sliding motion of the rotor against the stationary pad

B. Kang; C. A. Tan

2006-01-01

179

Application of nonlinear finite strip technique to concrete deep beams  

Microsoft Academic Search

The salient features of an alternative version of the nonlinear finite strip method for analysing reinforced concrete elements is presented. Unlike the conventional finite strip models which can only handle structures whose geometry does not change in one direction, the newly developed finite strip model can analyse certain structures whose geometry (although still fairly simple) can change along their length

Mohammed Raoof

1995-01-01

180

Study of Intense Laser Beam Propagation in AXIALLY Inhomogeneous and Relativistic Nonlinear Plasma  

Microsoft Academic Search

The relativistic oscillation of the electron mass in the field of intense laser beam affect the dynamics of the propagation in plasma. This paper presents an investigation of steady-state self-focusing and self-trapping of the intense Gaussian laser beam incident normally on a plane interface of linear and nonlinear nonabsorbing axially inhomogeneous plasma. Nonparaxial technique has been used for the analysis

R. K. Khanna; R. C. Chouhan

2002-01-01

181

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

SciTech Connect

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, et al., in Proc. of the Particle Accelerator Conference, Chicago, 2001 (IEEE, Piscataway, NJ, 2001), Vol. 1, p. 688.] at the Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very-high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles.

Hong Qin

2003-01-21

182

A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam  

Microsoft Academic Search

A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall

Han S. Uhm

1994-01-01

183

Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres  

NASA Astrophysics Data System (ADS)

Various researchers have predicted situations where the acoustical or optical radiation force on a sphere centered on a Bessel beam is opposite the direction of beam propagation. We develop the analogy between acoustical and optical radiation forces of arbitrary-order helicoidal and ordinary Bessel beams to gain insight into negative radiation forces. The radiation force is expressed in terms of the asymmetry of the scattered field, the scattered power, the absorbed power, and the conic angle of the Bessel beam and is related to the partial-wave coefficients for the scattering. Negative forces only occur when the scattering into the backward hemisphere is suppressed relative to the scattering into the forward hemisphere. Absorbed power degrades negative radiation forces.

Zhang, Likun; Marston, Philip L.

2011-09-01

184

Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation  

NASA Astrophysics Data System (ADS)

The present paper investigates the dynamic response of finite Timoshenko beams resting on a sixparameter foundation subjected to a moving load. It is for the first time that the Galerkin method and its convergence are studied for the response of a Timoshenko beam supported by a nonlinear foundation. The nonlinear Pasternak foundation is assumed to be cubic. Therefore, the effects of the shear deformable beams and the shear deformation of foundations are considered at the same time. The Galerkin method is utilized for discretizing the nonlinear partial differential governing equations of the forced vibration. The dynamic responses of Timoshenko beams are determined via the fourth-order Runge-Kutta method. Moreover, the effects of different truncation terms on the dynamic responses of a Timoshenko beam resting on a complex foundation are discussed. The numerical investigations shows that the dynamic response of Timoshenko beams supported by elastic foundations needs super high-order modes. Furthermore, the system parameters are compared to determine the dependence of the convergences of the Galerkin method.

Yang, Yan; Ding, Hu; Chen, Li-Qun

2013-09-01

185

Optical bistability based on nonlinear oblique reflection of light beams from a screen with an aperture on its axis  

SciTech Connect

It is shown that, in principle, optical bistability can be based on a nonlinear interaction of noncollinearly propagating beams when one of them is reflected from a plane screen with an aperture on its axis. The requirements to be satisfied by the interacting beams are discussed and estimates are obtained of the shortest response time of such an optically bistable system. (nonlinear optical phenomena)

Nikitenko, K Yu; Trofimov, V A [Department of Computing Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, Moscow (Russian Federation)

1999-02-28

186

Study of nonlinear interaction between bunched beam and intermediate cavities in a relativistic klystron amplifier  

SciTech Connect

In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.

Wu, Y. [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China); Institute of Applied Electronics, China Academy of Engineering Physics, Mianyang 621900 (China); Science and Technology on High Power Microwave Laboratory, Mianyang 621900 (China); Xu, Z.; Li, Z. H. [Institute of Applied Electronics, China Academy of Engineering Physics, Mianyang 621900 (China); Tang, C. X. [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China)

2012-07-15

187

Study of nonlinear interaction between bunched beam and intermediate cavities in a relativistic klystron amplifier  

NASA Astrophysics Data System (ADS)

In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.

Wu, Y.; Xu, Z.; Li, Z. H.; Tang, C. X.

2012-07-01

188

Effects of laser and particle beams on the synthesis and nonlinear optical response of nanostructures  

NASA Astrophysics Data System (ADS)

Nonlinear optical materials comprising metal nanocrystallites embedded in linear and nonlinear dielectrics are of wide current interest for use in all-optical switching devices. We have investigated several ways in which laser- and ion-beam processing can be used to create vertically and/or laterally patterned nanostructured composite materials. Pulsed laser deposition using both metal and dielectric targets can be used to create layered structures in which some layers contain quantum dots as a nonlinear element. Ion beams can also be used to induce the formation of deep waveguides in soda-lime glass subjected first to Ag ion exchange. When these Ag quantum-dot composites are irradiated by high-intensity laser light, a photochemical reaction generates Ag2O nanoclusters, changing the sign of the nonlinear index of refraction. This phenomenon offers unusual possibilities for spatially modulating a nonlinear waveguide with very high lateral resolution. Finally, we consider the use of lasers in conjunction with laser- or particle-beam-created surface defects to serve as distributed nucleation sites for quantum- dot growth. Atomic-force microscopy on planar versus offcut surfaces shows that substrate orientation, temperature and deposition pressure can be used to control the size distribution and two-dimensional growth pattern of Au nanoclusters on strontium titanate substrates.

Haglund, Richard F.; Afonso, Carmen N.; Battaglin, Giancarlo; Godbole, Mukund; Gonella, Francesco; Hamilton, John D.; Lowndes, Douglas H.; Magruder, Robert H.; Mazzoldi, Paolo; Osborne, Dannie H.; Solis, J.

1997-05-01

189

Nonlinear Optical Effects on ISI-Smoothed Beams in KrF Fusion Drivers  

NASA Astrophysics Data System (ADS)

Induced Spatial Incoherence (ISI) allows rapid and effective smoothing of speckle structure in the focal beam, but its application to fusion drivers may be complicated by nonlinear refraction in the optical components that can significantly distort the beam's envelope profile. Nonlinear refraction can introduce curvature over the entire profile and scatter ~ 15% of the light into a low intensity halo. These effects arise because the transient hot spots in the ISI speckle begin to self-focus as they propagate through the laser optics, and thus pass through focus before they reach the target. We report the first experimental confirmation of this distortion using a 4 ns 248 nm ISI beam at intensities ~ 0.5 GW/cm^2 propagating through KrF-grade fused silica, giving an average nonlinear phase perturbation B ~ 0.5 radian. We also present measurements of the nonlinear refractive index and two-photon absorption coefficient in fused silica at 4 ns, and discuss the impact of nonlinear optical effects on the design of future KrF fusion drivers.

Lehmberg, R. H.; Pawley, C. J.; Deniz, A. V.

2000-10-01

190

Nonlinear vibration and stability of a beam subjected to planar excitations  

NASA Astrophysics Data System (ADS)

The dynamic response of a beam subjected to an axial acceleration and transverse, planar impulsive loading has been investigated to characterize the nonlinear vibration and stability. The equations of motion were derived using Hamilton's principle. After applying Galerkin's procedure they were reduced to a system of nonlinear coupled ordinary differential equations, which in turn were solved numerically for numerous loading and boundary conditions. Determining the oscillatory motion of a beam in an axial acceleration field has applications in the micromechanics area, where resonating beams are used as accelerometers. Here the frequency response is of interest and the equations of motion reduce to a special eigenvalue problem. Both linear and nonlinear analyses were performed and the corresponding frequencies were identified. Transverse, planar excitation of the beam has applications in the design of fusion reaction chambers. Here the beams are used as cooling tubes inside the chamber as part of the first wall protection scheme. The external loading of these tubes (beams) consists of a series of impulsive pressures that occur at the repetition rate of the reactor. The dynamic response of the tubes, both planar and nonplanar, is necessary to aid in the design of the tube bank and the supporting constraints. The equations of motion were coded to simulate the response numerically. Amplitude-frequency curves were determined, from which the nonlinear jump phenomena could easily be observed. The conditions under which nonplanar motion could occur were also identified. Calculations were performed for both inextensional and extensional beams. Comparison of the responses for both cases were presented for the transient and steady state displacements.

Lee, Yung-Ming

1994-01-01

191

Influence of nonadiabaticity and nonlinearity on the operation of cold-atom beam splitters  

NASA Astrophysics Data System (ADS)

The operation of cold-atom beam splitters is analyzed in the context of Bose-Einstein condensate interferometry. We introduce two representative geometries of the splitting region and study influence of nonlinearity and nonadiabaticity on the splitting and the recombination of the condensate for both geometries.

Stickney, James; Zozulya, Alex

2003-07-01

192

DQM large amplitude vibration of composite beams on nonlinear elastic foundations with restrained edges  

NASA Astrophysics Data System (ADS)

This paper presents an efficient and accurate differential quadrature (DQ) large amplitude free vibration analysis of laminated composite thin beams on nonlinear elastic foundation. Beams under consideration have elastically restrained against rotation and in-plane immovable edges. Elastic foundation has cubic nonlinearity with shearing layer. We impose the boundary conditions directly into the governing equations in spite of the conventional DQ method and without any extra efforts. A direct iterative method is used to solve the nonlinear eigenvalue system of equations after transforming the governing equations into the frequency domain. The fast rate of convergence of the method is shown and their accuracy is demonstrated by comparing the results with those for limit cases, i.e. beams with classical boundary conditions, available in the literature. Besides, we develop a finite element program to verify the results of the presented DQ approach and to show its high computational efficiency. The effects of different parameters on the ratio of nonlinear to linear natural frequency of beams are studied.

Malekzadeh, P.; Vosoughi, A. R.

2009-03-01

193

Nonlinear Saturation of Cyclotron Maser Instability Associated with Energetic Ring-Beam Electrons  

Microsoft Academic Search

We study the cyclotron maser instability (CMI) driven by an energetic ring-beam distribution by a particle simulation to explain possible generation mechanisms of intense radiation phenomena observed in space. The main objective is to understand the nonlinear processes that control saturation of the emission process. Our study reveals new issues that have been overlooked in past literature. It is found

K. H. Lee; Y. Omura; L. C. Lee; C. S. Wu

2009-01-01

194

Optical spatial soliton supported by photoisomerization nonlinearity in a polymer with a background beam  

SciTech Connect

We present detailed theoretical studies of optical spatial solitons (SSs) supported by photoisomerization nonlinearity in a polymer sample. One-dimensional dark and bright SSs and their existence curves are presented. Several combinations of polarizations of the signal and background beams can be used to form the SSs.

Wang Xiaosheng; She Weilong; Lee Wingkee [State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen (Zhongshan) University, Guangzhou 510275 (China); Department of Physics, Chinese University of Hong Kong, Shatin, Hong Kong (China)

2006-10-15

195

Nonlinear stationary waves and solitons in ion beam-plasma configuration  

NASA Astrophysics Data System (ADS)

A fully nonlinear treatment for stationary waves in a cold plasma with an ion beam propagating parallel to the magnetic field is carried out in the framework of Hall MHD. It is shown that the linearly unstable system can evolve into a steady nonlinear configuration in which both ion populations undergo a coherent helical motion guided by the magnetic field. The complete system of equations can be reduced to two coupled differential equations for the transverse proton (or beam ion) speed and the phase difference between the wave motion of both ion fluids. In the case of a weak beam these equations possess a phase-portrait integral which describes the main dynamical features of the system. A soliton-type solution with a core filled by smaller-scale oscillations is found for the transverse components of the ion velocities and magnetic field. It is suggested that gyrophased bunched ion beams associated with large-amplitude quasi-monochromatic ULF waves often observed in the ion foreshock are a manifestation of these fully nonlinear structures. A driver for such oscilliton-like structures is provided by a linear instability in which the wave is exponentially growing. The momentum exchange between two different ion populations, mediated by the magnetic field stresses, leads to the formation of a steady nonlinear wave-oscilliton.

Dubinin, E.; Sauer, K.; McKenzie, J. F.

2004-02-01

196

Magnetic design and measurement of nonlinear multipole magnets for the APT beam expander system  

SciTech Connect

Two prototype nonlinear multipole magnets have been designed for use in the 800-MeV beam test of the APT beam-expansion concept at LANSCE. The iron-dominated magnets each consist of three independent coils, two for producing a predominantly octupole field with a tunable duodecapole component, and one for canceling the residual quadrupole field. Two such magnets, one for shaping each transverse plane, are required to produce a rectangular, uniform beam current density distribution with sharp edges on the APT target. This report will describe the magnetic design of these magnets, along with field measurements, and a comparison to the magnetic design.

Barlow, D.B.; Shafer, R.E.; Martinez, R.P. [Los Alamos National Lab., NM (United States); Walstrom, P.L. [Northrop Grumman Corp., Princeton, NJ (United States); Kahn, S.; Jain, A.; Wanderer, P. [Brookhaven National Lab., Upton, NY (United States)

1997-10-01

197

Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams  

SciTech Connect

This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (TllT? < 1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in accelerated particle beams, including Harris-type electrostatic instabilities, known to limit the luminosity and minimum spot size attainable in experiments. The thermodynamic bound on the field perturbation energy of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an arbitrary initial distribution function, including the effects of intense self-fields, finite geometry and nonlinear processes. This paper also includes analytical estimates of the nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic bi-Maxwellian distributions.

Nikolas C. Logan and Ronald C. Davidson

2012-07-18

198

Thermodynamic bounds on nonlinear electrostatic perturbations in intense charged particle beams  

NASA Astrophysics Data System (ADS)

This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (T?/T?<1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in accelerated particle beams, including Harris-type electrostatic instabilities, known to limit the luminosity and minimum spot size attainable in experiments. The thermodynamic bound on the field perturbation energy of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an arbitrary initial distribution function, including the effects of intense self-fields, finite geometry, and nonlinear processes. This paper also includes analytical estimates of the nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic bi-Maxwellian distributions.

Logan, Nikolas C.; Davidson, Ronald C.

2012-07-01

199

A geometrically exact beam element based on the absolute nodal coordinate formulation  

Microsoft Academic Search

In this study, Reissner’s classical nonlinear rod formulation, as implemented by Simo and Vu-Quoc by means of the large rotation\\u000a vector approach, is implemented into the framework of the absolute nodal coordinate formulation. The implementation is accomplished\\u000a in the planar case accounting for coupled axial, bending, and shear deformation. By employing the virtual work of elastic\\u000a forces similarly to Simo

Johannes Gerstmayr; Marko K. Matikainen; Aki M. Mikkola

2008-01-01

200

Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect  

SciTech Connect

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.

Bliokh, Konstantin Yu. [Institute of Radio Astronomy, Kharkov, 61002 (Ukraine); A.Ya. Usikov Institute of Radiophysics and Electronics, Kharkov, 61085 (Ukraine); Department of Physics, Bar-Ilan University, Ramat Gan, 52900 (Israel)

2006-07-28

201

Implementation and efficiency of two geometric stiffening approaches  

Microsoft Academic Search

When the modeling of flexible bodies is required in multibody systems, the floating frame of reference formulations are probably\\u000a the most efficient methods available. In the case of beams undergoing high speed rotations, the geometric stiffening effect\\u000a can appear due to geometric nonlinearities, and it is often not captured by the aforementioned methods, since it is common\\u000a to linearize the

Urbano Lugrís; Miguel A. Naya; José A. Pérez; Javier Cuadrado

2008-01-01

202

Analytical and computational study of nonlinear collisionless filamentation of a relativistic electron beam in plasma  

NASA Astrophysics Data System (ADS)

The nonlinear stage of Weibel instability of a relativistic beam propagating through ambient plasma is studied analytically and through computationally efficient hybrid simulations. In our hybrid approach [1], beam electrons are modeled using numerical macroparticles while plasma electrons are modeled as a passive fluid instantaneously responding to the beam evolution. But in contrast to [1], present numerical analysis captures the effects of violation of the charge quasi-neutrality near the boundaries of high-current filaments. Assuming for analytical tractability that the beam density is small, we find the self-similarity law for nonlinear dynamics of the Weibel instability. It is found that the electron energy distribution of the beam particles trapped in the filaments is close to Maxwellian. Using the Boltzmann distribution of the electron density in transverse plane, we derive a closed equation describing filament structure. This analytical model of fully thermalized filament allows us to evaluate the fraction of initial beam energy transferred to transverse particle beam motion, to plasma electron motion, and to the magnetic field. The analytical results are compared with those from hybrid simulations. [1] Oleg Polomarov et al., Phys. Plasmas 14,043103 (2007). Supported by the US DOE grant DE-FG02-05ER54840.

Khudik, Vladimir; Shvets, Gennady; Kaganovich, Igor

2010-11-01

203

Nonlinear analysis of a curved sandwich beam joined with a straight sandwich beam  

Microsoft Academic Search

The buckling behaviour of straight sandwich beams joined with curved sandwich beams loaded in pure bending is investigated using two different models. One is based on a high order sandwich beam theory and the other model is based on finite element analysis. The analyses are applied to a numerical example and the results are compared with experimental results.

Anders Lyckegaard; Ole Thybo Thomsen

2005-01-01

204

Geometrical study on two tilting arcs based exact cone-beam CT for breast imaging  

NASA Astrophysics Data System (ADS)

Breast cancer is the second leading cause of cancer death in women in the United States. Currently, X-ray mammography is the method of choice for screening and diagnosing breast cancer. However, this 2D projective modality is far from perfect; with up to 17% breast cancer going unidentified. Over past several years, there has been an increasing interest in cone-beam CT for breast imaging. However, previous methods utilizing cone-beam CT only produce approximate reconstructions. Following Katsevich's recent work, we propose a new scanning mode and associated exact cone-beam CT method for breast imaging. In our design, cone-beam scans are performed along two tilting arcs for collection of a sufficient amount of data for exact reconstruction. In our Katsevich-type algorithm, conebeam data is filtered in a shift-invariant fashion and then backprojected in 3D for the final reconstruction. This approach has several desirable features. First, it allows data truncation unavoidable in practice. Second, it optimizes image quality for quantitative analysis. Third, it is efficient for sequential/parallel computation. Furthermore, we analyze the reconstruction region and the detection window in detail, which are important for numerical implementation.

Zeng, Kai; Yu, Hengyong; Fajardo, Laurie L.; Wang, Ge

2006-08-01

205

Laser beam propagation through bulk nonlinear media: Numerical simulation and experiment  

NASA Astrophysics Data System (ADS)

This dissertation describes our efforts in modeling the propagation of high intensity laser pulses through optical systems consisting of one or multiple nonlinear elements. These nonlinear elements can be up to 103 times thicker than the depth of focus of the laser beam, so that the beam size changes drastically within the medium. The set of computer codes developed are organized in a software package (NLO_BPM). The ultrafast nonlinearities of the bound-electronic n2 and two-photon absorption as well as time dependent excited-state, free-carrier and thermal nonlinearities are included in the codes for modeling propagation of picosecond to nanosecond pulses and pulse trains. Various cylindrically symmetric spatial distributions of the input beam are modeled. We use the cylindrical symmetry typical of laser outputs to reduce the CPU and memory requirements making modeling a real- time task on PC's. The hydrodynamic equations describing the rarefaction of the medium due to heating and electrostriction are solved in the transient regime to determine refractive index changes on a nanosecond time scale. This effect can be simplified in some cases by an approximation that assumes an instantaneous expansion. We also find that the index change obtained from the photo-acoustic equation overshoots its steady-state value once the ratio between the pulse width and the acoustic transit time is greater than unity. We numerically study the sensitivity of the closed- aperture Z-scan experiment to nonlinear refraction for various input beam profiles. If the beam has a ring structure with a minimum (or zero) on axis in the far field, the sensitivity of Z-scan measurements can be increased by up to one order of magnitude. The linear propagation module integrated with the nonlinear beam propagation codes allows the simulation of typical experiments such as Z-scan and optical limiting experiments. We have used these codes to model the performance of optical limiters. We study two of the most promising limiter designs: the monolithic self-protective semiconductor limiter (MONOPOL) and a multi-cell tandem limiter based on a liquid solution of reverse saturable absorbing organic dye. The numerical outputs show good agreement with experimental results up to input energies where nonlinear scattering becomes significant.

Kovsh, Dmitriy I.

206

Differential Polarization Nonlinear Optical Microscopy with Adaptive Optics Controlled Multiplexed Beams  

PubMed Central

Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red), which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures.

Samim, Masood; Sandkuijl, Daaf; Tretyakov, Ian; Cisek, Richard; Barzda, Virginijus

2013-01-01

207

Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma  

NASA Astrophysics Data System (ADS)

We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schrödinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.

Wang, Yunliang; Shukla, P. K.; Eliasson, B.

2013-01-01

208

Modelling the Propagation of a Weak Fast-Mode MHD Shock Wave near a 2D Magnetic Null Point Using Nonlinear Geometrical Acoustics  

NASA Astrophysics Data System (ADS)

We present the results of analytical modelling of fast-mode magnetohydrodynamic wave propagation near a 2D magnetic null point. We consider both a linear wave and a weak shock and analyse their behaviour in cold and warm plasmas. We apply the nonlinear geometrical acoustics method based on the Wentzel-Kramers-Brillouin approximation. We calculate the wave amplitude, using the ray approximation and the laws of solitary shock wave damping. We find that a complex caustic is formed around the null point. Plasma heating is distributed in space and occurs at a caustic as well as near the null point due to substantial nonlinear damping of the shock wave. The shock wave passes through the null point even in a cold plasma. The complex shape of the wave front can be explained by the caustic pattern.

Afanasyev, A. N.; Uralov, A. M.

2012-10-01

209

Geometrically non-linear analysis of symmetrically laminated composite and sandwich shells with a higher-order theory and C deg finite elements  

NASA Astrophysics Data System (ADS)

A C(sub 0) continuous displacement based finite element formulation of a higher-order theory for linear and geometrically non-linear analysis (which accounts for large displacements in the sense of von Karman) of symmetrically laminated composite and sandwich shells under transverse loads is presented. The displacement model accounts for non-linear and constant variation of tangential and transverse displacement components respectively, through the shell thickness. The assumed displacement model eliminates the use of shear correction coefficients. The discrete element chosen is nine-node quadrilateral element with nine degrees of freedom per node. The accuracy of the present formulation is then established by comparing the present results with the available analytical closed-form two-dimensional solutions, three-dimensional elasticity solutions and other finite element solutions. Some new results are generated for future comparisons to and evaluations of sandwich shells.

Kant, T.; Kommineni, J. R.

210

Geometric Mechanics  

NASA Astrophysics Data System (ADS)

Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.

Talman, Richard

1999-10-01

211

Self consistent nonlinear transverse quantum dynamics of a cold relativistic electron beam in a magnetized plasma  

NASA Astrophysics Data System (ADS)

A relativistic electron/positron beam travelling in a cold plasma in the overdense regime n0>>nb is the driver of large amplitude plasma oscillations that are generated by the Plasma Wake Field excitation. The beam experiences the 3D effects of the wake field that it has produced by itself (self interaction). In the long beam limit, the transverse effects due to the self interaction (f.i., self focusing/defocusing) are dominant compared to the longitudinal ones. Here, ignoring the longitudinal beam dynamics, a theoretical investigation of the quantum transverse beam motion is carried out when a relativistic electron/positron beam is travelling along an external magnetic field. This is done by adopting a fluid model of a magnetized plasma describing the Plasma Wake Field excitation driven by the beam density and current. On the other hand, taking into account the quantum nature of the single particle of the beam, it is shown that the transverse electron/positron dynamics is governed by a 2D Schrödinger equation in the form of the Gross-Pitaevskii equation. The latter accounts for the collective effects due to both the plasma wake field and the external magnetic field. The above set of equations governing the beam-plasma system (i.e., fluid plus 2D Schrödinger equations), is then reduced to a pair of coupled equations that can be thought as a quantum Zakharov system, leading in general to a 2D nonlocal and nonlinear Schrödinger equation. In the weakly focussed regime, the analysis of this equation is carried out, both analytically and numerically. Remarkably, the existence of quantum beam vortices is shown and the conditions for the self focusing and collapse that include the quantum nature of the beam particles are discussed.

Fedele, R.; Tanjia, F.; de Nicola, S.; Jovanovi?, D.; Shukla, P. K.

2012-02-01

212

Geometrically nonlinear analysis of antisymmetric angle-ply smart composite plates integrated with a layer of piezoelectric fiber reinforced composite  

NASA Astrophysics Data System (ADS)

This paper is concerned with static analysis of simply supported antisymmetric angle-ply plates integrated with a layer of piezoelectric fiber reinforced composite (PFRC) material undergoing nonlinear deformations. The Von Kàrmàn type nonlinear strain displacement relations and first-order shear deformation theory are used to formulate the variational model of this electromechanical coupled problem. Subsequently, the Galerkin method is employed to derive the nonlinear algebraic governing equations which are solved by employing the Newton-Raphson method. The results suggest the potential use of PFRC material for distributed control of nonlinear deformations of smart antisymmetric angle-ply composite plates. Particular emphasis has been placed on investigating the effect of variation of piezoelectric fiber orientation on the actuating capability of the PFRC layer for counteracting the nonlinear deformations of the smart antisymmetric angle-ply composite plates.

Shivakumar, J.; Ray, M. C.

2007-06-01

213

Linear, nonlinear and mixed-regime analysis of electrostatic MEMS  

Microsoft Academic Search

Electrostatically actuated microstructures can undergo large deformations for certain geometric configurations and applied voltages. The use of linear theories in such cases can produce inaccurate results. By selecting a range of geometric parameters (such as beam lengths, thicknesses and gaps), we identify the regimes, where linear theories become inaccurate and necessitate the use of nonlinear theories. In cases where linear

Gang Li; N. R. Aluru

2001-01-01

214

Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets  

NASA Astrophysics Data System (ADS)

Controlling the propagation of intense optical wavepackets in transparent media is not a trivial task. During propagation, low- and high-order non-linear effects, including the Kerr effect, multiphoton absorption and ionization, lead to an uncontrolled complex reshaping of the optical wavepacket that involves pulse splitting, refocusing cycles in space and significant variations of the focus. Here we demonstrate both numerically and experimentally that intense, abruptly autofocusing beams in the form of accelerating ring-Airy beams are able to reshape into non-linear intense light-bullet wavepackets propagating over extended distances, while their positioning in space is extremely well defined. These unique wavepackets can offer significant advantages in numerous fields such as the generation of high harmonics and attosecond physics or the precise micro-engineering of materials.

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

2013-10-01

215

A comparison between nonlinear cantilever and buckled beam for energy harvesting  

NASA Astrophysics Data System (ADS)

Nonlinear dynamics has become one of the key aspect to improve the efficiency of kinetic energy harvesters working in the real environment. Different methods based on the exploitation of the dynamical features of stochastic nonlinear oscillators using bi-stable piezoelectric cantilevers or buckled beams have been proposed in the past years. Such methods are shown to outperform standard linear oscillators and to overcome some of the most severe limitations of present approaches once applied to ambient vibrations. This work presents simulation results comparing the two methods. The same piezoelectric element subjected to a fixed vibrating body in a cantilever or bridge configuration has been simulated. The kinetic excitation considered is a zero mean exponentially correlated gaussian noise with different amplitudes. The piezoelectric oscillator output response has been obtained as a function of a nonlinear parameter. This work is intended to help designing the most performing energy harvester for real world applications starting from the same piezoelectric element.

Vocca, H.; Cottone, F.; Neri, I.; Gammaitoni, L.

2013-09-01

216

Terahertz and Infrared Surface Wave Beams and Pulses on Gyrotropic, Nonlinear and Metamaterial Interfaces  

NASA Astrophysics Data System (ADS)

This work is devoted to theoretical study of surface plasmon polariton propagation on metal or metamaterial - dielectric interfaces where media can possess optical or magnetooptical activity or cubic nonlinearity. On the interface of gyrotropic media surface wave changes its polarization and profile as well as in case of interface of media with cubic nonlinearity. Surface wave propagation constant can be modified by magnetization leading to magnetooptical intensity effect. The properties of plasmons in gratings are also considered including excitation, dispersion and existence of various types of modes. The theory of surface wave and pulsed beam diffraction in gyrotropic, nonlinear and layered media is developed. We also present waveguide for surface waves based on layered metamaterial - dielectric interfaces suppressing diffraction spreading.

Sukhorukov, A. P.; Ignatyeva, D. O.; Kalish, A. N.

2011-10-01

217

Nonlinear gyrofluid models of shear Alfven instabilities in ignited and beam heated toroidal plasmas  

SciTech Connect

Shear Alfven instabilities driven by energetic beams and alpha populations are investigated using a reduced MHD-gyrofluid model with Landau closure. The moment equations for the fast ions are truncated in a way which incorporates the wave particle resonances that are required to destabilize the shear Alfven mode. These are coupled to an Ohm`s law and vorticity equations which have been generalized to include ion FLR, electron and ion Landau damping. This model has been applied to experimentally observed regimes in a number of tokamak and stellarator devices. Both linearized growth rates and the nonlinear evolution are obtained. The saturated nonlinear regimes indicate mode number and frequency spectra which are generally consistent with experiment. A detailed examination of one typical nonlinear state has allowed identification of the dominant saturation mechanisms. This indicates that generation of n = 0, m = 0 sheared poloidal velocity flows and quasi linear modification of the q(r) profile can be important factors in reaching saturation.

Spong, D.A.; Hedrick, C.L.; Carreras, B.A.

1993-07-01

218

Experimental validation of the orthogonalised reverse path method using a nonlinear beam  

NASA Astrophysics Data System (ADS)

The Orthogonalised Reverse Path (ORP) method is a new algorithm of the 'reverse path' class but developed in the time-domain. Like the Conditioned Reverse Path (CRP) method, the ORP approach is capable of identifying the underlying linear FRF of a system or structure in the presence of nonlinearities and may well also lead to simplifications in the estimation of coefficients of nonlinear terms. The method has shown itself to be numerically robust not only for simple simulated SDOF systems but also for simulated MDOF systems. The aim of this paper is to discuss an application of the ORP method to an experimental test set-up based on a nonlinear beam rig.

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

2012-08-01

219

Observation Nonlinear Effects Of A Laser Beam Interaction With Waveguide Photosensitive Agcl-Ag Films  

Microsoft Academic Search

\\u000a Nowadays a great attention is spared between various nonlinear optical effects to the spatio-temporal transformation of the\\u000a laser beams such as: self-focusing, self- diffraction, bistability, optical turbulence and other transversal instabilities\\u000a [1, 2]. The main part of experiments was accomplished in Kerr media placed in the resonator with a positive feedback. Comparatively\\u000a a new object of the study of such

E. I. Larionova; L. A. Ageev; V. K. Miloslavsky

220

Nonparaxial propagation of soliton-like laser beams-pulses in media with saturable nonlinearity  

Microsoft Academic Search

The theoretical analysis of manifestations of nonparaxiality of propagation (in the plane transverse to the direction of propagation\\u000a of radiation) of soliton-like beams-pulses in self-focusing media with electronic saturable nonlinearity is carried out. It\\u000a is shown that, in formation of such structures by pulses of a comparatively small duration, a modulation of the radiation\\u000a intensity arises, which can result in

N. V. Vysotina; N. N. Rozanov; V. E. Semenov; V. A. Smirnov; S. V. Fedorov

2004-01-01

221

Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams  

Microsoft Academic Search

Most existing formulations for structural elements such as beams, plates and shells do not allow for the use of general nonlinear\\u000a constitutive models in a straightforward manner. Furthermore, such structural element models, due to the nature of the generalized\\u000a coordinates used, do not capture some Poisson modes such as the ones that couple the deformation of the cross section of

Luis G. Maqueda; Ahmed A. Shabana

2007-01-01

222

Three-dimensional nonlinear vibrations of composite beams — I. Equations of motion  

Microsoft Academic Search

Newton's second law is used to develop the nonlinear equations describing the extensional-flexural-flexural-torsional vibrations of slewing or rotating metallic and composite beams. Three consecutive Euler angles are used to relate the deformed and undeformed states. Because the twisting-related Euler angle ? is not an independent Lagrangian coordinate, twisting curvature is used to define the twist angle, and the resulting equations

Perngjin F. Pai; Ali H. Nayfeh

1990-01-01

223

Nonlinear dynamics of an inclined beam subjected to a moving load  

Microsoft Academic Search

In this paper, the nonlinear dynamic response of an inclined pinned-pinned beam with a constant cross section, finite length\\u000a subjected to a concentrated vertical force traveling with a constant velocity is investigated. The study is focused on the\\u000a mode summation method and also on frequency analysis of the governing PDEs equations of motion. Furthermore, the steady-state\\u000a response is studied by

Ahmad Mamandi; Mohammad H. Kargarnovin; Davood Younesian

2010-01-01

224

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation  

Microsoft Academic Search

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary\\u000a doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations\\u000a under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted\\u000a to the theoretical developments and their numerical

E. J. Sapountzakis; J. A. Dourakopoulos

2009-01-01

225

Beam optics modeling at CPS extraction throughout a non-linear fringe field  

Microsoft Academic Search

An accurate optics model of the CPS ring in the extraction region, where the lateral fringe field is highly non-linear, is of importance for transverse emittance preservation of beams for the future LHC. For that reason, the measured field map at 26 GeV\\/c of the CPS magnets has been converted into a two-dimensional polynomial to get a functional form appropriate

Django Manglunki; M. MARTINI

1997-01-01

226

Frequency-domain subspace identification for nonlinear mechanical systems  

NASA Astrophysics Data System (ADS)

This paper introduces a new frequency-domain subspace-based method for the identification of nonlinear mechanical systems. The technique exploits frequency-domain data and interprets nonlinearities as feedback forces exciting the underlying linear system. It is first demonstrated using two academic examples, namely a Duffing oscillator and a five-degree-of-freedom system comprising two nonlinearities. The identification of an experimental beam exhibiting geometrically nonlinear behaviour is then addressed.

Noël, J. P.; Kerschen, G.

2013-11-01

227

Radiation force on a nonlinear microsphere by a tightly focused Gaussian beam.  

PubMed

We determine the characteristics of the radiation force that is exerted on a nonresonant nonlinear (Kerr-effect) rigid microsphere by a strongly focused Gaussian beam when diffraction and interference effects are significant (sphere radius a < or = illumination wavelength lambda). The average force is calculated from the surface integral of the energy-momentum tensor consisting of incident, scattered, and internal electromagnetic field vectors, which are expressed as multipole spherical-wave expansions. The refractive index of a Kerr microsphere is proportional to the internal field intensity, which is computed iteratively by the Rytov approximation (residual error of solution, 10(-30). The expansion coefficients for the field vectors are calculated from the approximated index value. Compared with that obtained in a dielectric (linear) microsphere in the same illumination conditions, we find that the force magnitude on the Kerr microsphere is larger and increases more rapidly with both a and the numerical aperture of the focusing objective. It also increases nonlinearly with the beam power unlike that of a linear sphere. The Kerr nonlinearity also leads to possible reversals of the force direction. The proposed technique is applicable to other types of weak optical nonlinearity. PMID:12510940

Pobre, Romeric; Saloma, Caesar

2002-12-20

228

Effects of initial geometric imperfections on the non-linear response of the Space Shuttle superlightweight liquid-oxygen tank  

Microsoft Academic Search

The results of an analytical study of the elastic buckling and non-linear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a

Michael P. Nemeth; Richard D. Young; Timothy J. Collins; James H. Starnes Jr.

2002-01-01

229

LEADS-DC: A computer code for intense dc beam nonlinear transport simulation  

NASA Astrophysics Data System (ADS)

An intense dc beam nonlinear transport code has been developed. The code is written in Visual FORTRAN 6.6 and has ˜13000 lines. The particle distribution in the transverse cross section is uniform or Gaussian. The space charge forces are calculated by the PIC (particle in cell) scheme, and the effects of the applied fields on the particle motion are calculated with the Lie algebraic method through the third order approximation. Obviously, the solutions to the equations of particle motion are self-consistent. The results obtained from the theoretical analysis have been put in the computer code. Many optical beam elements are contained in the code. So, the code can simulate the intense dc particle motions in the beam transport lines, high voltage dc accelerators and ion implanters.

Lü, JianQin; Zhao, XiaoSong

2011-12-01

230

Ultraslow solitons due to large quintic nonlinearity in coupled quantum well structures driven by two control laser beams  

NASA Astrophysics Data System (ADS)

In this paper, we have shown the existence of large amounts of quintic nonlinearity in asymmetric three-coupled quantum wells, which arise due to a probe pulse and two controlling laser beams. The possibilities of generation and propagation of ultraslow bright optical solitons in these systems have been examined in situations of both Kerr and quintic nonlinearities. We have also demonstrated numerically that these solitons are stable. The modulation instability of a continuous or quasi-continuous wave probe beam has been also investigated and the role of quintic nonlinearity in suppressing this instability has been addressed.

Shwetanshumala, S.; Konar, S.; Biswas, Anjan

2013-04-01

231

A Beam Finite Element for Nonlinear Analysis of Masonry Elements With or Without Fiber-Reinforced Plastic (FRP) Reinforcements  

Microsoft Academic Search

This study addresses the development of a simple beam finite element for the nonlinear analysis of masonry structures, eventually strengthened with fiber-reinforced plastic (FRP) materials, in the context of the “equivalent frame model”. The proposed beam finite element comprises three parts: two rigid offsets, able to simulate the very stiff behavior of the masonry pier-lintel intersections, and a flexible central

Ernesto Grande; Maura Imbimbo; Elio Sacco

2011-01-01

232

Near-critical reflection of nonlinear obliquely incident internal wave beam from a slope  

NASA Astrophysics Data System (ADS)

The reflection of internal gravity waves from sloping boundaries is believed to contribute significantly to vertical mixing in the ocean. This mechanism is likely to be enhanced when a wave is incident at an angle to the horizontal that is close to the slope of the boundary, given that the amplitude of the reflected wave becomes infinite according to linear inviscid theory if the angle of incidence exactly matches the slope. To clarify the role of nonlinear effects in this resonance, the reflection of a nonlinear wave beam of finite cross-section is analyzed by a matched-asymptotics approach, exploiting the fact that, near the critical angle, the reflected disturbance is confined to a thin boundary layer in an "inner" region close to the slope. Unlike prior studies, which assume that incident waves approach the boundary in a plane normal to the isobaths, here the oncoming wave is oblique. This gives rise to an alongslope mean flow component that is equally strong to the upslope induced mean flow, and the evolution of the reflected wave is fully nonlinear, in sharp contrast to the case of normal incidence where nonlinear effects are minor. The theoretical predictions are discussed in connection with related numerical and experimental results.

Akylas, Triantaphyllos

2010-11-01

233

Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations  

Microsoft Academic Search

CONTENTS Introduction Chapter I. Reduction of Abelian integrals and theta functions § 1. Abelian integrals and Riemann theta functions § 2. Reduction of Abelian integrals and theta functions of genus 2 § 3. Normal coverings and the reduction of theta functions Chapter II. Multiphase (finite-zone) solutions, expressed by Jacobi theta functions, of non-linear equations of KdV-type of genus g ?

E D Belokolos; Alexander I Bobenko; V B Matveev; V Z Enolskii

1986-01-01

234

Nonlinear Delta-f Particle Simulations of Collective Effects in High Intensity Charged Particle Beams  

NASA Astrophysics Data System (ADS)

A wide range of collective effects in high intensity charged particle beams have been numerically studied using the nonlinear delta-f particle simulation method implemented in the Beam Equilibrium Stability and Transport (BEST) code. For the electron-ion two-stream instability in high intensity accelerators and storage rings, the secondary electron yield effects are self-consistently studied by coupling the secondary electron yield library CMEE with the instability simulations. Progress has also been made in applying the delta-f particle simulation method to bunched beams, and a three-dimensional equilibrium solver has been implemented. With the help of recently developed parallel diagnostic techniques, we are able to characterize the chaotic particle dynamics under the influences of collective instabilities as well as three-dimensional equilibrium fields. To further extend the application areas of the delta-f particle simulation method, 2D domain decomposition is being developed using the Message Passing Interface, and three-dimensional equilibria with anisotropic temperature in the transverse and longitudinal directions are being investigated. References: [1] R. C. Davidson and H. Qin, An Introduction to the Physics of Intense Charged Particle Beams in High Energy Accelerators, World Scientific (2001). [2] H. Qin, Physics of Plasmas 10, 2078 (2003). [3] H. Qin, E. A. Startsev, and R. C. Davidson, Physical Review Special Topics on Accelerators and Beams 6, 014401 (2003).

Qin, Hong; Davidson, Ronald C.; Startsev, Edward A.

2004-11-01

235

Polarization effect on the relativistic nonlinear dynamics of an intense laser beam propagating in a hot magnetoactive plasma  

NASA Astrophysics Data System (ADS)

Nonlinear dynamics of an intense circularly polarized laser beam interacting with a hot magnetized plasma is investigated. Using a relativistic fluid model, a modified nonlinear Schrödinger equation is derived based on a quasineutral approximation, which is valid for hot plasma. Using a three-dimensional model, spatial-temporal development of the laser pulse is investigated. The occurrence of some nonlinear phenomena such as self-focusing, self-modulation, light trapping, and filamentation of the laser pulse is discussed. Also the effect of polarization and external magnetic field on the nonlinear evolution of these phenomena is studied.

Sepehri Javan, N.; Adli, F.

2013-10-01

236

Nonlinear backward stimulated Raman scattering from electron beam acoustic modes in the kinetic regime  

SciTech Connect

The backward stimulated Raman scattering (BSRS) of a laser from electron beam acoustic modes (BAM) in the presence of self-consistent non-Maxwellian velocity distributions is examined by linear theory and particle-in-cell (PIC) simulations in one and two dimensions (1D and 2D). The BAM evolve from Langmuir waves (LW) as electron trapping modifies the distribution to a non-Maxwellian form that exhibits a beam component. Linear dispersion relations using the nonlinearly modified distribution from simulations are solved for the electrostatic modes involved in the parametric coupling. Results from linear analysis agree well with electrostatic spectra from simulations. It is shown that the intersection of the Stokes root with BAM (instead of LW) determines the matching conditions for BSRS at a nonlinear stage. As the frequency of the unstable Stokes mode decreases with increasing wave number, the damping rate and the phase velocity of BAM decreases with the phase velocity of the Stokes mode, providing a self-consistently evolving plasma linear response that favors continuation of the nonlinear frequency shift. Coincident with the emergence of BAM is a rapid increase in BSRS reflectivity. The details of the wave-particle interaction region in the electron velocity distribution determine the growth/damping rate of these electrostatic modes and the nonlinear frequency shift; in modeling this behavior, the use of sufficiently large numbers of particles in the simulations is crucial. Both the reflectivity scaling with laser intensity and the spectral features from simulations are discussed and are consistent with recent Trident experiments.

Yin, L.; Daughton, W.; Albright, B. J.; Bowers, K. J.; Montgomery, D. S.; Kline, J. L.; Fernandez, J. C.; Roper, Q. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

2006-07-15

237

Calculation of non-linear vibration of rotating beams by using tetrahedral and solid finite elements  

NASA Astrophysics Data System (ADS)

A development is presented of the non-linear dynamic equations that govern the motion of the tetrahedral and solid finite elements that undergo large displacements. The development presented is exemplified by using the four-node, 12-degree-of-freedom tetrahedral element and the eight-node, 24-degree-of-freedom solid element. It is shown that the element shape functions used in this investigation can be used to describe large translations and finite rigid body rotations. Accordingly, the non-linear formulation presented in this paper can be used in the analysis of small as well as large deformation. The element configuration is identified by using four co-ordinate systems. These co-ordinate systems are the global, body, element and intermediate element co-ordinate systems. The large displacement of the tetrahedral and solid elements is described by using a set of absolute co-ordinates that define the location and orientation of the deformable body co-ordinate systems. The non-linear differential equations of motion of the tetrahedral and solid finite elements are developed by using the principle of virtual work in dynamics. The use of the non-linear dynamic formulation presented in this investigation is demonstrated by using a flexible single robotic arm manipulator that undergoes large displacements. The results obtained by using the four-node tetrahedral elements and the eight-node solid elements are compared with the results obtained by using the three-dimensional beam element. This comparison shows that the discrepancy between the results obtained by using the solid and tetrahedral elements in beam problems is more significant in the dynamic analysis as compared to the discrepancy of 10% reported in the literature for the static analysis.

Jiang, J. J.; Hsiao, C. L.; Shabana, A. A.

1991-07-01

238

Excitation of Langmuir Wave by Transversal Nonlinear Wave in the Electron-Positron Inhomogeneous Plasma in the Presence of Positron Beam.  

National Technical Information Service (NTIS)

The elliptically polarized transversal nonlinear wave propagation with the small angle to the magnetic field in the electron-positron and electron-proton plasma in the presence of positron beam is investigated. The nonlinear Langmuir wave propagating with...

A. D. Pataraya T. A. Pataraya M. Z. Zedginidze

1990-01-01

239

Model for nonlinear evolution of localized ion ring beam in magnetoplasma  

SciTech Connect

An electrostatic hybrid model, which investigates the nonlinear evolution of a localized ion ring beam in a magnetoplasma, is described and applied to the generation and evolution of turbulence in the very low frequency (VLF) ({Omega}{sub ci}<{omega}<{Omega}{sub ce}) range, where {Omega}{sub ci(e)} is the ion (electron) gyro frequency. Electrons are treated as a fluid and the ions with the particle-in-cell method. Although the model is electrostatic, it includes the effects of energy loss by convection of electromagnetic VLF waves out of the instability region by utilizing a phenomenological model for effective collisions with the fluid electrons. In comparison with a more conventional electrostatic hybrid model, the new model shows much more efficient extraction of energy from the ion ring beam and reduced background plasma heating over a range of parameters.

Scales, W. A. [Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia 24061-0111 (United States); Ganguli, G.; Mithaiwala, M. [Plasma Physics Division, Naval Research Laboratory, Washington D.C. 20375 (United States); Rudakov, L. [Icarus Research, Inc., P.O. Box 30780, Bethesda, Maryland 20824-0780 (United States)

2012-06-15

240

Electron beam instabilities in unmagnetized plasmas via the Stieltjes transform (linear theory and nonlinear mode coupling)  

SciTech Connect

The Stieltjes transform has been used in place of a more common Laplace transform to determine the time evolution of the self-consistent field (SCF) of an unmagnetized semi-infinite plasma, where the plasma electrons together with a primary and a low-density secondary electron beam move perpendicular to the boundary surface. The secondary beam is produced when the primary beam strikes the grid. Such a plasma system has been investigated by Griskey and Stanzel [M. C. Grisky and R. L. Stenzel, Phys. Rev. Lett. 82, 556 (1999)]. The physical phenomenon, observed in their experiment, has been named by them as ''secondary beam instability.'' The character of the instability observed in the experiment is not the same as predicted by the conventional treatments--the field amplitude does not grow with time. In the frequency spectrum, the theory predicts peak values in the amplitude of SCF at the plasma frequency of plasma and secondary beam electrons, decreasing above and below it. The Stieltjes transform for functions, growing exponentially in the long time limit, does not exist, while the Laplace transform technique gives only exponentially growing solutions. Therefore, it should be interesting to know the kind of solutions that an otherwise physically unstable plasma will yield. In the high-frequency limit, the plasma has been found to respond to any arbitrary frequency of the initial field differentiated only by the strength of the resulting SCF. The condition required for exponential growth in the conventional treatments, and the condition for maximum amplitude (with respect to frequency) in the present treatment, have been found to be the same. Nonlinear mode coupling between the modes excited by the plasma electrons and the low-density secondary beam gives rise to two frequency-dependent peaks in the field amplitude, symmetrically located about the much stronger peak due to the plasma electrons, as predicted by the experiment.

Krishan, S. [Department of Physics, Indian Institute of Science, Bangalore 560 012 (India)

2007-11-15

241

Relativistic nonlinear dynamics of an intense laser beam propagating in a hot electron-positron magnetoactive plasma  

NASA Astrophysics Data System (ADS)

The present study is devoted to investigation of the nonlinear dynamics of an intense laser beam interacting with a hot magnetized electron-positron plasma. Propagation of the intense circularly polarized laser beam along an external magnetic field is studied using a relativistic two-fluid model. A modified nonlinear Schrödinger equation is derived based on the quasi-neutral approximation, which is valid for hot plasma. Light envelope solitary waves and modulation instability are studied, for one-dimensional case. Using a three-dimensional model, spatial-temporal development of laser pulse is investigated. Occurrence of some nonlinear phenomena such as self-focusing, self-modulation, light trapping, and filamentation of laser pulse is discussed. Also the effect of external magnetic field and plasma temperature on the nonlinear evolution of these phenomena is studied.

Sepehri Javan, N.; Adli, F.

2013-06-01

242

Nonlinear analysis of short concrete-filled steel tubular beam–columns under axial load and biaxial bending  

Microsoft Academic Search

This paper presents a nonlinear fiber element analysis method for determining the axial load–moment strength interaction diagrams for short concrete-filled steel tubular (CFST) beam–columns under axial load and biaxial bending. Nonlinear constitutive models for confined concrete and structural steel are considered in the fiber element analysis. Efficient secant algorithms are developed to iterate the depth and orientation of the neutral

Qing Quan Liang

2008-01-01

243

Nonlinear beam generated plasma waves as a source for enhanced plasma and ion acoustic lines  

SciTech Connect

Observations by, for instance, the EISCAT Svalbard Radar (ESR) demonstrate that the symmetry of the naturally occurring ion line in the polar ionosphere can be broken by an enhanced, nonthermal, level of fluctuations (naturally enhanced ion-acoustic lines, NEIALs). It was in many cases found that the entire ion spectrum can be distorted, also with the appearance of a third line, corresponding to a propagation velocity significantly slower than the ion acoustic sound speed. It has been argued that selective decay of beam excited primary Langmuir waves can explain some phenomena similar to those observed. We consider a related model, suggesting that a primary nonlinear process can be an oscillating two-stream instability, generating a forced low frequency mode that does not obey any ion sound dispersion relation. At later times, the decay of Langmuir waves can give rise also to enhanced asymmetric ion lines. The analysis is based on numerical results, where the initial Langmuir waves are excited by a cold dilute electron beam. By this numerical approach, we can detect fine details of the physical processes, in particular, demonstrate a strong space-time intermittency of the electron waves in agreement with observations. Our code solves the full Vlasov equation for electrons and ions, with the dynamics coupled through the electrostatic field derived from Poisson's equation. The analysis distinguishes the dynamics of the background and beam electrons. This distinction simplifies the analysis for the formulation of the weakly nonlinear analytical model for the oscillating two-stream instability. The results have general applications beyond their relevance for the ionospheric observations.

Daldorff, L. K. S. [University of Michigan, Space Research Building, 2455 Hayward Street, Ann Arbor, Michigan 48109-2143 (United States); Pecseli, H. L. [Department of Physics, University of Oslo, Box 1048 Blindern, N-0316 Oslo (Norway); Trulsen, J. K. [Institute of Theoretical Astrophysics, University of Oslo, Box 1029 Blindern, N-0315 Oslo (Norway); Ulriksen, M. I. [Norwegian Water Resources and Energy Directorate, Drammensveien 211, Postboks 5091 Majorstua, N-0301 Oslo (Norway); Eliasson, B. [Fakultaet fuer Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany); Stenflo, L. [Department of Physics, Linkoeping University, SE-58183 Linkoeping (Sweden)

2011-05-15

244

Nonlinear coupling between breathing and quadrupole-like oscillations in the transport of mismatched beams in continuous magnetic focusing fields  

SciTech Connect

A nonlinear analysis of the transport of breathing beams considering nonaxisymmetric perturbations is performed. It is shown that large-amplitude breathing oscillations of an initially round beam may couple nonlinearly to quadrupole-like oscillations, such that the excess energy initially constrained to the axisymmetric breathing oscillations is allowed to flow back and forth between breathing and quadrupole-like oscillations. In this case, the beam develops an elliptical shape with a possible increase in its size along one direction as the beam is transported. This is a highly nonlinear phenomenon that occurs for large mismatch amplitudes on the order of 100% and is found to be particularly relevant for space-charge-dominated beams with K > or approx. k{sub 0}{epsilon}, where K is the beam perveance, k{sub 0} is the vacuum phase advance per unit axial length, and {epsilon} is the emittance of the beam. A simple model based on mapping techniques is used to clarify the mechanism that leads to the energy exchange between the modes and is tested against results from direct integration of the envelope equations.

Simeoni, W. Jr.; Rizzato, F.B.; Pakter, R. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS (Brazil)

2006-06-15

245

Determination of turbulent vorticity by the nonlinear scattering of crossed ultrasonic beams  

NASA Astrophysics Data System (ADS)

The nonlinear interaction of two, mutually perpendicular crossed ultrasonic beams, overlapping in the presence of turbulence, generates a scattered sum frequency component that radiates outside the interaction region. In the absence of turbulence, virtually no scattered sum frequency component exists (outside the interaction region). A theoretical investigation is reported which relates the angular dependence of the time-dependent Doppler shift (of the scattered sum frequency) to the time-dependent velocity fluctuations of the turbulent eddies. When a second set of focused crossed beams is operated with an overlap region slightly displaced from the first set (by 1.27 mm), one can measure the vorticity using Doppler shift information from four distinct combination frequencies obtained at two different scattering angles. Experimental results are presented using continuous wave (CW) focused primary beams of frequencies f1=1.8, f2=2.0, f3=2.2 and f4=2.3 MHz (generated by concave transducer units with 15 cm focal lengths). The turbulence is generated by a submerged water jet with nozzle diameter D=0.635 cm and exit velocity ~7 m/s. Here the interaction region is located 37D from the nozzle exit. A 4 MHz circular plane array receiving transducer detects four distinct scattered sum frequency components (at specific angles) using a spectrum analyzer to demonstrate the effect. The receiver is located 14D from the interaction region. .

Korman, Murray S.

2000-07-01

246

Kapitza-Dirac effect and nonresonant nonlinear quantum interaction of laser and electron beams  

NASA Astrophysics Data System (ADS)

When crossing an electron beam in vacuum with an optical (laser) beam with standing waves, an interaction was redicted known as Kapitz-Dirac effect where the electrons are diffracted at the nodes of the optical field. After the final success of an experiment was reported (Freimund et al. 2001) confirming this classical kind of laser interaction with free electrons, the generalization of this effect (Schwarz-Hora effect) in the presence of a target or medium in the crossing area of the beams is re-considered as a basic non-resonance nonlinear quantum interaction process. The proof is based on a discovery of Peierls and of repeated later measurements agreeing with a quantum threshold for which the theory was elaborated initially. This is confirmed also in connectnion with the quantum theory of 1/f noise. Other aspects for electron acceleration of electrons by lasers may be interesting up to PeV energy using laser pulses of femtosecond (fs) duration and powers from Petawatt (PW) to Exawatt and Zetawatt.

Hora, Heinrich; Handel, Peter H.

2013-05-01

247

On a Possibility of Laser Beam Control in LOTV Mission by Means of Nonlinear and Coherent Optics Techniques  

NASA Astrophysics Data System (ADS)

In the context of LOTV Mission (Laser Orbital Transfer Vehicle) the analysis of laser beam delivery efficiency has been carried out for power beaming with a 200-kW-solid-state laser from an aircraft to a space ``tugboat'' having a beam receiving collector of 10-meter-size. Application of nonlinear-optics and adaptive optics techniques of laser beam control for correction of optical distortions in the propagation path caused by vibration and thermal deformation of optical elements as well as by atmospheric turbulence is discussed. Possible architecture of laser beam transport systems including a laser beacon on the receiver, a repetitively pulsed solid-state laser in MOPA-PCM configuration and a beam director telescope of 1-meter size is considered. The results of computer simulation of a MOPA-PCM system as well as the system as a whole are presented. The requirements to optical elements of the system are discussed.

Sherstobitov, V. E.; Kaliteevskiy, N. A.; Kuprenyuk, V. I.; Rodionov, A. Yu.; Romanov, N. A.; Semenov, V. E.; Soms, L. N.; Vysotina, N. V.

2004-03-01

248

High Optical Quality Organic Thin Films for Nonlinear Photonics Fabricated by Molecular Beam Deposition  

NASA Astrophysics Data System (ADS)

We use small donor-acceptor substituted organic molecules that sublimate without decomposition to fabricate organic thin films by organic molecular beam deposition. These thin films have thicknesses of the order of micrometers and are well adapted for integrated nonlinear optics. These films are essentially amorphous, without the formation of microcrystals. They combine a high third-order susceptibility of the order of 1000 times that of fused silica with a high optical quality. Surface roughness is below +/- 5 nm for micrometer thick films. The films have been shown to be durable and robust, with a long shelf life (>2 years). We successfully integrated such films with silicon-on-oxide waveguides which have been used to demonstrate ultrafast all-optical switching on the silicon photonics platform, successfully demultiplexing a 170 GBit/s signal to 42 GBit/s.

Beels, Marten

2012-02-01

249

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.  

PubMed

We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law. PMID:16715163

Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

2006-06-01

250

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions  

Microsoft Academic Search

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which

Carlos E. N. Mazzilli; César T. Sanches; Odulpho G. P. Baracho Neto; Marian Wiercigroch; Marko Keber

2008-01-01

251

Phase mixing of transverse oscillations in the linear and nonlinear regimes for IFR relativistic electron beam propagation  

NASA Astrophysics Data System (ADS)

Phase mixing of transverse oscillations changes the nature of the ion hose instability from an absolute to a convective instability. The stronger the phase mixing, the faster an electron beam reaches equilibrium with the guiding ion channel. This is important for long distance propagation of relativistic electron beams where it is desired that transverse oscillations phase mix within a few betatron wavelengths of injection and subsequently an equilibrium is reached with no further beam emittance growth. In the linear regime phase mixing is well understood and results in asymptotic decay of transverse oscillations as 1/Z(exp 2) for a Gaussian beam and channel system, Z being the axial distance measured in betatron wavelengths. In the nonlinear regime (which is likely mode of propagation for long pulse beams) results of the spread mass model indicate that phase mixing is considerably weaker than in the regime. In this paper we consider this problem of phase mixing in the nonlinear regime. Results of the spread mass model will be shown along with a simple analysis of phase mixing for multiple oscillator models. Particle simulations also indicate that phase mixing is weaker in nonlinear regime than in the linear regime. These results will also be shown.

Shokair, I. R.

252

Nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in a dielectric medium  

SciTech Connect

A nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in an isotropic dielectric medium is presented. A quantum model based on the Klein-Gordon equation is used. The growth rates of beam instabilities caused by the effect of stimulated Cherenkov radiation have been determined in the linear approximation. Mechanisms of the nonlinear saturation of relativistic quantum Cherenkov beam instabilities have been analyzed and the corresponding analytical solutions have been obtained.

Bobylev, Yu. B.; Kuzelev, M. V. [Moscow State University, Faculty of Physics (Russian Federation)

2012-06-15

253

Analytical and nonlinear perturbative simulation studies of the equilibrium and stability properties of intense charged particle beams for heavy ion fusion  

Microsoft Academic Search

This paper presents an overview of recent analytical and numerical investigations of collective processes in intense ion beams at the Plasma Physics Laboratory based on the nonlinear Vlasov–Maxwell equations. The topics covered include: (a) nonlinear stability theorem for quiescent beam propagation at high space-charge intensities; (b) development and application of Hamiltonian averaging techniques for intense beam propagation through alternating-gradient field

Ronald C. Davidson; Hong Qin; W. Wei-li Lee; Sean Strasburg

2001-01-01

254

Finite element modeling of concrete beams prestressed with external tendons  

Microsoft Academic Search

In this study, a numerical model based on the finite element method incorporating an arc-length solution algorithm for materially and geometrically nonlinear analysis of concrete beams prestressed with external tendons is established. The second-order effects are taken into account. The effects of external tendons are expressed by equivalent nodal loads of the beam element and therefore analysis of externally prestressed

Tie-jiong Lou; Yi-qiang Xiang

2006-01-01

255

Nonlinear ?f particle simulations of collective excitations and energy-anisotropy instabilities in high-intensity bunched beams  

NASA Astrophysics Data System (ADS)

Collective effects with strong coupling between the longitudinal and transverse dynamics are of fundamental importance for applications of high-intensity bunched beams. The self-consistent Vlasov-Maxwell equations are applied to high-intensity finite-length charge bunches, and a generalized ?f particle simulation algorithm is developed for bunched beams with or without energy anisotropy. The nonlinear ?f method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. Systematic studies are carried out under conditions corresponding to strong 3D nonlinear space-charge forces in the beam frame. For charge bunches with isotropic energy, finite bunch-length effects are clearly evident by the fact that the spectra for an infinitely long coasting beam and a nearly spherical charge bunch have strong similarities, whereas the spectra have distinctly different features when the bunch length is varied between these two limiting cases. For bunched beams with anisotropic energy, there exists no exact kinetic equilibrium because the particle dynamics do not conserve transverse energy and longitudinal energy separately. A reference state in approximate dynamic equilibrium has been constructed theoretically, and a quasi-steady state has been established in the simulations for the anisotropic case. Collective excitations relative to the reference state have been simulated using the generalized ?f algorithm. In particular, the electrostatic Harris instability driven by strong energy anisotropy is investigated for a finite-length charge bunch. The observed growth rates are larger than those obtained for infinitely long coasting beams. However, the growth rate decreases for increasing bunch length to a value similar to the case of a long coasting beam. For long bunches, the instability is axially localized symmetrically relative to the beam center, and the characteristic wavelength in the longitudinal direction is comparable to the transverse dimension of the beam.

Qin, Hong; Davidson, Ronald C.; Startsev, Edward A.

2007-06-01

256

Lateral-torsional buckling analysis of I-beams using shell finite elements and nonlinear computation methods  

NASA Astrophysics Data System (ADS)

The paper deals with the influence of correlation length, of Gauss random field, and of yield strength of a hotrolled I-beam under bending on the ultimate load carrying capacity limit state. Load carrying capacity is an output random quantity depending on input random imperfections. Latin Hypercube Sampling Method is used for sampling simulation. Load carrying capacity is computed by the programme ANSYS using shell finite elements and nonlinear computation methods. The nonlinear FEM computation model takes into consideration the effect of lateral-torsional buckling on the ultimate limit state.

Kala, Zden?k; Kala, Ji?í

2012-09-01

257

Two-Beam Coupling and Phase Conjugation by Resonant Nonlinear Optical Interactions.  

NASA Astrophysics Data System (ADS)

Two-beam-coupling and degenerate-four-wave-mixing interactions are studied for the case of near-resonance excitation of a system of two-level atoms. First, a theoretical and experimental study is made of the gain and absorption experienced by a weak probe beam propagating through a sodium vapor in the presence of an intense pump field that is nearly resonant with the 3^2S _{1/2} to 3^2P_{3/2 } atomic transition. The probe-transmission spectrum includes three distinct resonances that result from the modification of the atomic-level structure by the ac-Stark effect. Two of these resonances can lead to amplification of the probe wave. The larger gain was measured at the Rabi-sideband resonance and corresponds to a 38-fold increase in the probe intensity, while a somewhat smaller gain, leading to a 4-fold increase, was measured at the Rayleigh resonance. For probe-field intensities comparable to the pump-field intensity, a theoretical calculation predicts a vast number of Rabi-subharmonic resonances. However, the highest coupling efficiencies occur at the Rayleigh resonance and persist even when the effects of atomic motion and propagation are included. An experiment was carried out with beams of equal energies using a pulsed alexandrite laser turned near the 4^2S _{1/2} to 4^2P_{3/2} transition in potassium vapor. The transmitted probe wave was observed to contain 85% of total input energy. Finally, a theory of degenerate four-wave mixing is presented that includes the effects of pump-wave propagation in the weak-probe limit. An analytic solution for the intensity distribution of the two counterpropagating pump fields is derived and used to calculate the spatial variation of the nonlinear absorption and coupling coefficients that appear in the coupled-amplitude equations for the probe and conjugate waves. The couples-amplitude equations are then solved numerically to obtain the phase-conjugate reflectivity. A study is made of the effects of laser intensity, absorption path length, and detuning on the phase-conjugate reflectivity. The conditions required to achieve unit reflectivity and oscillation are discussed.

Gruneisen, Mark Tyree

258

Assessment of two analytical methods in solving the linear and nonlinear elastic beam deformation problems  

Microsoft Academic Search

Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general boundary value problems, but also are used as mathematical models in viscoelastic and inelastic flows. The

A. Barari; B. Ganjavi; M. Ghanbari Jeloudar; G. Domairry

2010-01-01

259

A note on the foreshortening effect of a flexible beam under oblique excitation  

Microsoft Academic Search

In Li et al. (Multibody Syst. Dyn. 21:249–260, 2009), we described the geometric nonlinear effects of a pivoted beam under point-surface impact. We used the floating frame of\\u000a reference (FFR) formulation and the ABAQUS\\/Explicit model for comparative studies. The numerical solutions showed that the\\u000a two approaches agree well with each other only if the FFR formulation includes proper geometric nonlinear

Qing Li; Tianshu Wang; Xingrui Ma

2010-01-01

260

Laser Beam Transmission Through the Atmosphere.  

National Technical Information Service (NTIS)

Theoretical evaluation of the transmission of a laser beam at 10.6 microns has been investigated using the techniques of geometric optics. The interaction is non-linear because the refractive index depends through the mechanism of absorption, upon the int...

J. Wallace M. Camac

1970-01-01

261

Non-linear dynamics of flexible multibody systems  

Microsoft Academic Search

In this work we set to examine several important issues pertinent to currently very active research area of the finite element modeling of flexible multibody system dynamics. To that end, we first briefly introduce three different model problems in non-linear dynamics of flexible 3D solid, a rigid body and 3D geometrically exact beam, which covers the vast majority of representative

Adnan Ibrahimbegovic; Robert L. Taylor; H. Lim

2003-01-01

262

Application of the Green's function method to some nonlinear problems of an electron storage ring. Part III. Beam-size enhancement due to the presence of nonlinear magnets in a ring  

Microsoft Academic Search

A perturbation method which allows one to find the distribution function and the beam size for a broad class of storage ring nonlinear problems is described in Part I of this work. In present note I apply this method to a particular problem. Namely, I want to evaluate an enhancement of the vertical beam size of a bunch due to

S. KHEIFETS

1983-01-01

263

Nonlinear theory of power transfer between multiple crossed laser beams in a flowing plasma  

SciTech Connect

Analytic results are obtained for power transfer among crossing, equal frequency, laser beams, each smoothed by a random phase plate, in a flowing homogeneous plasma. For beams with well-separated directions, interbeam coupling transfers power, while intrabeam coupling causes beam deflection. For any pair of such beams, the beam with the largest positive projection on the flow direction will drain power from the other. {copyright} {ital 1998 American Institute of Physics.}

Rose, H.A.; Ghosal, S. [Los Alamos National Laboratory, Los Alamos, New Mexico87545 (United States)

1998-05-01

264

Nonlinear theory of power transfer between multiple crossed laser beams in a flowing plasma  

NASA Astrophysics Data System (ADS)

Analytic results are obtained for power transfer among crossing, equal frequency, laser beams, each smoothed by a random phase plate, in a flowing homogeneous plasma. For beams with well-separated directions, interbeam coupling transfers power, while intrabeam coupling causes beam deflection. For any pair of such beams, the beam with the largest positive projection on the flow direction will drain power from the other.

Rose, Harvey A.; Ghosal, Sandip

1998-05-01

265

Multi-Focus Structure and Moving Nonlinear Foci: Adequate Models of Self-Focusing of Laser Beams in Nonlinear Media  

Microsoft Academic Search

This chapter presents a review of the theory of the multi-focus structure (MFS) and moving nonlinear foci (MNLF) models of\\u000a self-focusing. It also reviews some experimental results on self-focusing of nanosecond-duration-pulses that support these\\u000a models. Some experimental and simulation results of studies of femtosecond self-focusing in air are discussed. It is concluded\\u000a that the main features of MFS-MNLF models can

V. N. Lugovoi; A. A. Manenkov

2009-01-01

266

Estimation of the RBE of mammography-quality beams using a combination of a Monte Carlo code with a B-DNA geometrical model  

NASA Astrophysics Data System (ADS)

The PENELOPE code is used to determine direct strand break yields corresponding to photons from a 60Co source and 28 and 30 kV x-ray beams impacting on a B-DNA geometrical model, which accounts for five organizational levels of the human genetic material. Direct single, double and total strand break probabilities are determined in a liquid water homogeneous medium with 1.06 g cm-3 density. The spectra produced by the x-ray beams at various depths in the phantom have been used to study the dependence of the damage yield on the depth. The relative biological effectiveness (RBE) is also estimated using the 60Co radiation qualities as the reference. According to this work, the damage probabilities and thus the RBE are, within the uncertainties, similar for both x-ray energies and are independent of the depth into the phantom. Furthermore, the total strand break yield is invariant with respect to the energy of the incident photons. The RBE for low-energy x-ray beams determined here (1.3 ± 0.1) is lower than that reported by Kellerer, taking into account that he used a 200 kV radiation as the reference quality. However, our RBE values are consistent with those determined by Kühne et al (2005 Radiat. Res. 164 669-76), which used the same biological endpoint and reference quality as our study. Also, our RBE values are similar to those determined by Verhaegen and Reniers (2004 Radiat. Res. 162 592-9).

Bernal, M. A.; deAlmeida, C. E.; David, M.; Pires, E.

2011-12-01

267

Geometric Solids  

NSDL National Science Digital Library

This math activity exposes early learners to a variety of three-dimensional objects. Learners bring geometric solids (everyday objects) from home. Learners sort and graph the objects on a Floor Graphing Mat. After the activity, learners can explore the geometric shapes in centers (see Extensions).

Lessonplans, Utah

2012-09-18

268

Analytical Solutions for the Nonlinear Longitudinal Drift Compression (Expansion) of Intense Charged Particle Beams  

SciTech Connect

To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.

Edward A. Startsev; Ronald C. Davidson

2004-04-09

269

Large Amplitude Free and Forced Oscillations of Functionally Graded Beams  

Microsoft Academic Search

The free and forced vibration of a functionally graded beam is studied in this paper within the framework of Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. It is assumed that material properties follow either exponential or power law distributions through thickness direction. It is assumed that the beam may be hinged-hinged, or clamped-hinged at its ends. The Galerkin procedure

Mohammad Rafiee; Hamed Kalhori

2012-01-01

270

Direct measurements of non-linear stress-strain curves and elastic properties of metal matrix composite sandwich beams with any core material  

Microsoft Academic Search

A theory for measuring non-linear stress-strain curves and elastic properties of metal matrix composite (MMC) sandwich beams subjected to pure bending loads is discussed. The beam is made from any core material sandwiched between an upper facing of unreinforced metal and a lower facing of MMC with unidirectional fibre reinforcement or vice versa. The model developed shows that the determination

Jacques E. Schoutens; Metal Matrix; Kaman Tempo

1985-01-01

271

Galerkin method for steady-state response of nonlinear forced vibration of axially moving beams at supercritical speeds  

NASA Astrophysics Data System (ADS)

The present paper investigates the steady-state periodic response of an axially moving viscoelastic beam in the supercritical speed range. The straight equilibrium configuration bifurcates in multiple equilibrium positions in the supercritical regime. It is assumed that the excitation of the forced vibration is spatially uniform and temporally harmonic. Under the quasi-static stretch assumption, a nonlinear integro-partial-differential equation governs the transverse motion of the axially moving beam. The equation is cast in the standard form of continuous gyroscopic systems via introducing a coordinate transform for non-trivial equilibrium configuration. For a beam constituted by the Kelvin model, the primary resonance is analyzed via the Galerkin method under the simply supported boundary conditions. Based on the Galerkin truncation, the finite difference schemes are developed to verify the results via the method of multiple scales. Numerical simulations demonstrate that the steady-state periodic responses exist in the transverse vibration and a resonance with a softening-type behavior occurs if the external load frequency approaches the linear natural frequency in the supercritical regime. The effects of the viscoelastic damping, external excitation amplitude, and nonlinearity on the steady-state response amplitude for the first mode are illustrated.

Zhang, Guo-Ce; Ding, Hu; Chen, Li-Qun; Yang, Shao-Pu

2012-03-01

272

Nonlinear optical investigation of Gaussian laser beam propagating in a dye-doped nematic liquid crystal  

Microsoft Academic Search

The laser beam shape and variation of the curvature radius of the wavefront have been simulated when the Gaussian laser beam passes through a dye-doped nematics liquid crystal. The effect of different dyes is investigated in the wavefront distortion as well as the beam shape due to its quality factor. We have reported the dependency of the curvature radius of

S. H. Mousavi; E. Koushki; H. Haratizadeh

2010-01-01

273

Flexural loss factors of sandwich and laminated composite beams using linear and nonlinear dynamic analysis  

Microsoft Academic Search

The purpose of the article presented here is to analyze the flexural loss factors of beams with sandwich or constrained layer damping arrangements and laminated composite beams using a C1 continuous, three-noded beam element. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects, and is applicable for both flexural and

M. Ganapathi; B. P. Patel; P. Boisse; O. Polit

1999-01-01

274

SHORTEST PATHS FOR THE REEDS-SHEPP CAR: A WORKED OUT EXAMPLE OF THE USE OF GEOMETRIC TECHNIQUES IN NONLINEAR OPTIMAL CONTROL. 1  

Microsoft Academic Search

We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed in recent work by Reeds and Shepp who showed, by special methods, (a) that shortest path motion could always be achieved by means of trajectories of

J. Sussmann; Guoqing Tang

1991-01-01

275

Geometrical response of multihole collimators  

NASA Astrophysics Data System (ADS)

A complete theory of camera multihole collimators is presented. The geometrical system response is determined in closed form in frequency space. This closed form accounts for the known efficiency and resolution formulae for parallel beam, fan beam, cone beam and astigmatic collimators as well as for the most frequent hole array patterns and hole shapes. The point spread function in the space domain for a certain collimator and source position can be calculated via a discrete fast Fourier transform. Beside the complete theoretical definition of the response of multihole collimators, this theory allows the definition of accurate models of the geometrical response for SPECT reconstruction and it is suitable for designing new collimators.

Formiconi, Andreas Robert

1998-11-01

276

Higher-order nonlinearity of electron-acoustic solitary waves with vortex-like electron distribution and electron beam  

SciTech Connect

The nonlinear wave structure of small-amplitude electron-acoustic solitary waves (EASWs) is investigated in a four-component plasma consisting of cold electron fluid, hot electrons obeying vortex-like distribution traversed by a warm electron beam and stationary ions. The streaming velocity of the beam, u{sub o}, plays the dominant role in determining the roots of the linear dispersion relation associated with the system. Using the reductive perturbation theory, the basic set of equations is reduced to a modified Korteweg-de Vries (mKdV) equation. With the inclusion of higher-order nonlinearity, a linear inhomogeneous mKdV type equation with fifth-order dispersion term is derived and the higher-order solution is obtained using a renormalization method. However, both mKdV and mKdV-type solutions present a positive potential, which corresponds to a hole (hump) in the cold (hot) electron number density. The mKdV-type solution has a smaller energy amplitude and a wider width than that of mKdV solution. The dependence of the energy amplitude, the width, and the velocity on the system parameters is investigated. The findings of this investigation are used to interpret the electrostatic solitary waves observed by the Geotail spacecraft in the plasma sheet boundary layer of the Earth's magnetosphere.

El-Taibany, W.F.; Moslem, Waleed M. [Department of Physics, Faculty of Science-Damietta, Mansoura University, Damietta El-Gedida 34517 (Egypt); Department of Physics, Faculty of Education, Suez Canal University, Port Said (Egypt)

2005-03-01

277

Nonlinear low-frequency structures in the auroral plasma in the presence of an oxygen beam including charge separation  

SciTech Connect

Observations from the Fast Auroral SnapshoT (FAST) satellite indicate that the parallel and perpendicular (to the Earth's magnetic field) electric field structures exhibit a spiky appearance. In this study, a magnetized plasma system consisting of protons, electrons, and a cold oxygen ion beam is considered. Both background electrons and protons are treated as hot species with Boltzmann density distributions. The dynamics of the oxygen ion beam is governed by the fluid equations. Effect of charge separation is studied on nonlinear fluctuations arising from a coupling of ion cyclotron and ion-acoustic waves. A scan of parameter space reveals a range of solutions for the parallel electric field from sinusoidal to sawtooth to highly spiky waveforms. The inclusion of charge separation effects tends to in most cases increase the frequency of oscillation of the nonlinear structures. In the case of a weakly magnetized plasma, the amplitude of the oscillations are found to be constant while they are modulated for a strongly magnetized plasma. The findings are compared with satellite observations.

Moolla, S. [University of KwaZulu-Natal, Durban 4000 (South Africa); Bharuthram, R. [University of the Western Cape, Modderdam Road, Belville 7535 (South Africa); Singh, S. V.; Lakhina, G. S.; Reddy, R. V. [Indian Institute of Geomagnetism, New Panvel (W), Navi Mumbai 410218 (India)

2010-02-15

278

Nonlinear dynamic processes in the electrostatic plasma lens and their influences on ion beam focusing  

Microsoft Academic Search

Summary form only given, as follows. The plasma lens (PL) is the axial symmetrical plasma-optical system, which transforms longitudinal electric field in to transversal one, the latter focuses and controls ion beams. The plasma lens is useful for fundamental investigations of properties of plasma-optical systems as well as for practical applications for ion beam focusing. Early the static and dynamic

I. Litovko; G. Kirichenko; A. Goncharov

2001-01-01

279

Nonlinear Saturation of Cyclotron Maser Instability Associated With Energetic Ring-beam Electrons  

NASA Astrophysics Data System (ADS)

The cyclotron maser instability (CMI) is a well known mechanism for the generation of radio waves. We present a series of two-dimensional simulation results associated with energetic ring-beam distributions in highly magnetized plasma to discuss the generation of the CMI waves. The results show new issues that we have overlooked in our previous study. First of all, in the presence of a pure or almost pure ring distribution CMI has high efficiency, but only the Z and X modes can be amplified effectively while the O mode is relatively much faint. Second, as the beam velocity of the ring-beam distribution increases, the two-stream instability becomes more active, and there are strong whistler waves with intensive electrostatic energy. Finally, after the settlement of the two stream instability in the ring-beam cases with fast beams, the X mode can still be amplified steadily without the interference of any mode competition.

Lee, K.; Omura, Y.; Lee, L.

2010-12-01

280

Detection and localization of contact-type damages via nonlinear impedance modulation of piezoelectric materials bonded on a beam structure  

NASA Astrophysics Data System (ADS)

In this paper, a nondestructive, in-service structural integrity monitoring methodology that can detect and characterize local structural damages of contact-type, i.e. damages and failures which come along with generation, growth and/or changes of contacting surfaces, such as cracks, debonding, preload-loss in bolted joints, etc., is presented. The presented monitoring system consists of piezoelectric elements bonded on the structural surface, a high-frequency harmonic voltage source, and a current detector. When the structure is subjected to a vibrational load such as operational load at low-frequencies, the scattering conditions for the high-frequency elastic waves in the vicinity of the contact-type damages will change in synchronization with the structural vibration because of the fluctuation of the contact conditions. This nonlinear effects of vibro-acoustic interaction between the low-frequency vibration and the high-frequency wave field causes the change in the driving-point impedance of the structure at the high frequency range, which leads to the significant modulation of the coupled electro-mechanical impedance (or admittance) of the piezoelectric elements. Therefore, if the piezoelectric elements are driven by a fixed amplitude high-frequency harmonic voltage source, the nonlinear fluctuation of the coupled admittance can be observed as the amplitude and phase modulation of the current flowing through the piezoelectric element. A modeling and analytical study of the nonlinear piezoelectric impedance modulation is presented for a beam structure including a crack, utilizing a linear time-varying system theory. A damage evaluation measure is presented based on the dimensionless modal stiffness fluctuation estimated from the instantaneous admittance reconstructed from the demodulated current responses. Furthermore, fundamental strategies and future directions for damage localization based on the nonlinear piezoelectric impedance modulation are briefly discussed.

Masuda, Arata; Aoki, Junsuke; Iba, Daisuke; Sone, Akira

2010-03-01

281

Nonlinear Effects in the Static and Dynamic Behavior of Beams and Rotor Blades,  

National Technical Information Service (NTIS)

Recent conclusions concerning alleged 'effects of transformation sequence' on the static and dynamic behavior of an end-loaded cantilevered, Euler/Bernoulli beam are analyzed and found to be false. The analysis contained in that paper illustrates several ...

D. H. Hodges M. R. M. Crespo Da Silva D. A. Peters

1988-01-01

282

High power amplifiers chain nonlinearity influence on the accelerating beam stability in Free Electron Laser (FLASH)  

Microsoft Academic Search

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

Wojciech Cichalewski; W. Jalmuzna

2009-01-01

283

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

Microsoft Academic Search

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

w Cichalewski; W Ja?mu?na

2010-01-01

284

INTERACTION OF LASER RADIATION WITH MATTER. LASER PLASMA: Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionisation  

NASA Astrophysics Data System (ADS)

The dynamics of a high-power femtosecond tubular pulsed beam in a dielectric medium is numerically analysed upon optically induced ionisation. It is found that the balance between nonlinearities of opposite sign and different magnitude in the case of multiphoton ionisation favours the establishment of a quasi-soliton regime of radiation propagation over a distance exceeding several diffraction lengths. The use of these beams enables attaining high-density light fields and generate high-density plasmas.

Vlasov, R. A.; Khasanov, O. Kh; Smirnova, T. V.

2005-10-01

285

Nonlinear interaction of a beam of finite density with a longitudinal wave  

NASA Astrophysics Data System (ADS)

Quasistationary evolution of a longitudinal wave of finite amplitude in a homogeneous collisionless plasma penetrated by an electron beam is described. The evolution of the wave is accompanied by trapping of the beam electrons in the potential wells of the plasma. For a beam of rather high density with a small longitudinal velocity spread, the contribution of the trapped beam electrons to the total charge described by the right side of the Poisson equation can be comparable to the contribution of nonresonant electrons. As a result, the wave potential profile is distorted in the range of phase oscillations of the beam electrons, whereas outside the range it remains unperturbed throughout the spatial period. The wave becomes a hybrid of two waves whose fragments, alternating, follow one after another. Their amplitudes and spatial periods are different. Analysis of the dispersion equation for such a wave shows that as the wave amplitude increases rather greatly, an anomalously great frequency shift is observed and the frequency halves.

Matveev, A. I.

2012-09-01

286

Proton Beam Fast Ignition Fusion: Nonlinear Generation of B?-Fields by Knock-on Electrons  

NASA Astrophysics Data System (ADS)

The knock-on electrons, generated by the fast proton beamootnotetextM. Roth et al, Phys. Rev. Lett. 86, 436 (2001); M. Tabak et al, Phys. Plasmas 1 (5), 1626 (1994); H. L. Buchanan, F. W. Chambers, E. P. Lee, S. S. Yu, R. J. Briggs, and M. N. Rosenbluth, LLNL , UCRL Report 82586, 1979. in interaction with the free and bound electrons in a precompressed DT fusion pellet, outrun the proton beam, generating the B?-fields ahead of the beam, which may lead to the defocusing of the beam, if B? < 0. The B?-fields are generated due to the magnetic instability, B?/t ˜ (c/?)? x jne, where jne is the knock-on electron current density,? is the background plasma conductivity, and c the speed of light. ootnotetext V. Alexander Stefan, Laser Thermonuclear Fusion: Res. Review, (1984-2008), on Generation of Suprathermal Particles, Laser Radiation Harmonics, and Quasistationary B-Fields. (Stefan University Graduate Courses: ISSN:1543-558X), (S-U-Press, 2008). The instability growth rate compensates for relatively low knock-on generation efficiency by a proton beam. The saturation level,(electron trapping mechanism), of the B-field ahead of the beam, is of the order of 10 MG and is reached on the time scale of 10ps.

Stefan, V. Alexander

2011-11-01

287

Theoretical analysis of SHG conversion efficiency of nonlinear optical crystal with Gaussian beam irradiation  

NASA Astrophysics Data System (ADS)

For the first step of our study, temperature dependence of SHG conversion efficiency has been analyzed theoretically on the supposition of uniform intensity beam. The results are presented in the paper appeared in the same proceedings. In this paper, the analysis was carried out two-dimensionally with an axisymmetrical model based on the previous one-dimensional model, applying the paraxial approximation. Two-dimensional temperature distribution induced by laser absorption and variation of the conversion efficiency of KDP crystals were analyzed quantitatively during repetition irradiation of pulse laser. Main results are summarized as follows: (1) Depending on SHG and its inverse conversion, temperature of the crystal with Gaussian beam irradiation fluctuates remarkably in the axial direction in the central part of crystal. (2) During repetition irradiation of Gaussian beam, heat conduction in the radial direction prevents temperature from rising in the central part of crystal. (3) The conversion efficiency for a Gaussian beam stays relatively high for a long period, compared with that for uniform beam.

Nomura, Kazufumi; Ohmura, Etsuji; Miyamoto, Isamu

2003-02-01

288

(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material  

Microsoft Academic Search

In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized (3+1)-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material (RHM) and left-handed material (LHM) is derived. By the commonly used Drude dispersive model

Yong-Hua Hu; Xi-Quan Fu; Shuang-Chun Wen; Wen-Hua Su; Dian-Yuan Fan

2006-01-01

289

Nonlinear Delta-f Simulation Studies of Intense Charged Particle Beams with Large Temperature Anisotropy  

Microsoft Academic Search

In plasmas with strongly anisotropic distributions (T_|| b\\/T_? b<= 0.4 are linearly unstable to short wavelength perturbations with k_z^2 r_b^2 >= 1, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. In the nonlinear stage, tails develop in the longitudinal momentum distribution and the kinetic instability saturates due to resonant wave-particle interactions. The total distribution

EDWARD A. STARTSEV; Ronald C. Davidson; Hong Qin

2002-01-01

290

On the fully nonlinear acoustic waves in a plasma with positrons beam impact and superthermal electrons  

NASA Astrophysics Data System (ADS)

Arbitrary amplitude ion-acoustic waves in an unmagnetized plasma consisting of cold positive ions, superthermal electrons, and positrons beam are reported. The basic set of fluid equations is reduced to an energy-balance like equation. The latter is numerically analyzed to examine the existence regions for solitary and shock waves. It is found that only solitary waves can propagate, however, the model cannot support shocks. The effects of superthermality and beam parameters (via, positrons concentration and streaming velocity) on the existence region, as well as solitary wave profile have been discussed.

Ali Shan, S.; El-Tantawy, S. A.; Moslem, W. M.

2013-08-01

291

Compensation of nonlinear distortions in photon-counting spectral CT: deadtime loss, spectral response, and beam hardening effects  

NASA Astrophysics Data System (ADS)

Photon counting detectors are an emerging technology for spectral computed tomography. They have the potential to improve tissue contrast and specificity, reduce dose, and enable novel applications for K-edge and functional imaging. In this presentation various non-linear distortions were investigated that affect the image quality in photon-counting spectral CT: deadtime losses and spectral response, inherent to the new technology, and beam hardening artifacts that stem from the use of a polychromatic x-ray source. These effects were corrected or compensated for by performing calibration measurements. Techniques from material decomposition were applied to reconstruct images at a desired energy. Two methods were compared to synthesize a single monoenergetic image from photon counting data with multiple energy bins. The parameters were optimized to maximize a given image quality index. The procedures were evaluated on phantom data acquired on an experimental CT scanner with photon-counting detectors with two energy thresholds.

Cammin, J.; Srivastava, S.; Tang, Q.; Barber, W. C.; Iwanczyk, J. S.; Hartsough, N. E.; Taguchi, K.

2012-02-01

292

NUMERICAL TESTS OF STEEL BEAM-TO-COLUMN SEMI-RIGID CONNECTIONS  

Microsoft Academic Search

This paper presents an analysis of semi-rigid beam-to-column connections in which the beam is connected to column not at 90 degrees angle. Beam-to-column bolted end-plate connections that are subjected to pure bending were modelled by three-dimensional finite elements. Numerical modelling of connection covers the geometrical and material non-linearities as well as contact and separation between various components of connection. Moment-rotation

K?stutis Urbonas; Alfonsas Dani?nas

2003-01-01

293

Analytical solution for nonlinear free vibrations of viscoelastic microcantilevers covered with a piezoelectric layer  

NASA Astrophysics Data System (ADS)

Nonlinear vibrations of viscoelastic microcantilevers with a piezoelectric actuator layer on the top surface are investigated. In this work, the microcantilever follows a classical linear viscoelastic model, i.e., Kelvin-Voigt. In addition, it is assumed that the microcantilever complies with Euler-Bernoulli beam theory. The Hamilton principle is used to obtain the equations of motion for the microcantilever oscillations. Then, the Galerkin approximation is utilized for separation of time and displacement variables, thus the time function is obtained as a second order nonlinear ordinary differential equation with quadratic and cubic nonlinear terms. Nonlinearities appear in stiffness, inertia and damping terms. Using the method of multiple scales, the analytical relations for nonlinear natural frequency and amplitude of the vibration are derived. Using the obtained analytical relations, the effects of geometric factors and material properties on the free nonlinear behavior of this beam are investigated. The results are also verified by numerical analysis of the equations.

Shooshtari, Alireza; Marzieh Hoseini, Seyedeh; Nima Mahmoodi, S.; Kalhori, Hamed

2012-07-01

294

The Measurement of Several Optical Nonlinearities Using Focused Gaussian Laser Beams.  

National Technical Information Service (NTIS)

The twofold purpose of this study was: (1) To analyze optical second-harmonic generation (SHG) in the focus of the lowest order transverse mode of a cw gas laser beam; (2) to utilize the power enhancement available from focusing to measure smaller nonline...

J. E. Bjorkholm

1966-01-01

295

Nonlinear wave interactions and evolution of a ring-beam distribution of energetic electrons  

Microsoft Academic Search

A ring-beam distribution function of moderately relativistic electrons is unstable to electromagnetic and electrostatic waves. The results obtained in numerical simulations show that electromagnetic radiation corresponding to the normal modes of the background plasma is observed to grow even in the presence of a strong electrostatic instability and becomes very strong when the growth of the electrostatic Langmuir waves is

S. Kainer; J. D. Gaffey; C. P. Price; X. W. Hu; G. C. Zhou

1988-01-01

296

Parametric superfluorescence excited in a nonlinear crystal by two uncorrelated pump beams  

NASA Astrophysics Data System (ADS)

Experimental results of parametric superfluorescence excited in a single-pass KDP-based optical parametric generator (OPG) pumped by two intersecting uncorrelated beams (second and third harmonics of Nd:YAG laser) are presented. The observed angular structure of OPG output radiation is typical for cumulative action of pump waves when the parametric gain does not depend on their phases.

Marcinkevi? Ius, A.; Piskarskas, A.; Smilgevi? Ius, V.; Stabinis, A.

1998-12-01

297

Ion-acoustic waves in a plasma consisting of adiabatic warm ions, nonisothermal electrons, and a weakly relativistic electron beam: Linear and higher-order nonlinear effects  

NASA Astrophysics Data System (ADS)

The nonlinear propagation of finite amplitude ion acoustic solitary waves in a plasma consisting of adiabatic warm ions, nonisothermal electrons, and a weakly relativistic electron beam is studied via a two-fluid model. A multiple scales technique is employed to investigate the nonlinear regime. The existence of the electron beam gives rise to four linear ion acoustic modes, which propagate at different phase speeds. The numerical analysis shows that the propagation speed of two of these modes may become complex-valued (i.e., waves cannot occur) under conditions which depend on values of the beam-to-background-electron density ratio ?, the ion-to-free-electron temperature ratio ?, and the electron beam velocity v0; the remaining two modes remain real in all cases. The basic set of fluid equations are reduced to a Schamel-type equation and a linear inhomogeneous equation for the first and second-order potential perturbations, respectively. Stationary solutions of the coupled equations are derived using a renormalization method. Higher-order nonlinearity is thus shown to modify the solitary wave amplitude and may also deform its shape, even possibly transforming a simple pulse into a W-type curve for one of the modes. The dependence of the excitation amplitude and of the higher-order nonlinearity potential correction on the parameters ?, ?, and v0 is numerically investigated.

Esfandyari-Kalejahi, A.; Kourakis, I.; Shukla, P. K.

2008-02-01

298

Traveling Wave Evolutions of a Cosh-Gaussian Laser Beam in Both Kerr and Cubic Quintic Nonlinear Media Based on Mathematica  

NASA Astrophysics Data System (ADS)

With the aid of Mathematica, three auxiliary equations, i.e. the Riccati equation, the Lenard equation and the Hyperbolic equation, are employed to investigate traveling wave solutions of a cosh-Gaussian laser beam in both Kerr and cubic quintic nonlinear media. As a result, many traveling wave solutions are obtained, including soliton-like solutions, hyperbolic function solutions and trigonometric function solutions.

Wang, Jun-Min

2011-03-01

299

Nonlinear correction to the bending stiffness of a damaged composite beam  

Microsoft Academic Search

When studying damage in composite materials, the classic beam theory is sometimes used in a modified manner to calculate the bending response of a damaged composite laminate. The longitudinal stiffness E0 is then replaced by a field variable E(x,y)=E0×[1?D(x,y)]. The damage distribution D(x,y) affects the calculation of stresses and strains, and requires a modified calculation of the neutral fibre y0(x)

W. Van Paepegem; R. Dechaene; J. Degrieck

2005-01-01

300

Non-Linear Beam Dynamics in High Resolution Multi-Pass Time of Flight Mass Separator  

Microsoft Academic Search

A multi-pass time-of-flight mass separator (MTOF-MS) is under development by the University Radioactive Ion Beam (UNIRIB) collaboration. The MTOF consists of two coaxial electrostatic mirrors, focusing lenses and auxiliary injection, extraction and separation elements. The injected ions having almost the same energy but different masses undergo hundreds or thousands of reflections between the mirrors. In the course of this periodic

V. A. Shchepunov; H. Wollnik

2005-01-01

301

Analytical theory and nonlinear deltaf perturbative simulations of temperature anisotropy instability in intense charged particle beams  

Microsoft Academic Search

In plasmas with strongly anisotropic distribution functions (T||b\\/T?b≪1) a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9,

Edward A. Startsev; Ronald C. Davidson; Hong Qin

2003-01-01

302

Linear and nonlinear properties of the ULF waves driven by ring-beam distribution functions  

Microsoft Academic Search

The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam

K. Killen; N. Omidi; D. Krauss-Varban; H. Karimabadi

1995-01-01

303

Nonlinear Theory of Elastic Shells.  

National Technical Information Service (NTIS)

Nonlinear theory of elastic shells is developed which incorporates both geometric and physical nonlinearities and which does not make use of the well known Love-Kirchhoff hypothesis. The resulting equations are formulated in tensorial notation and are red...

J. A. Costa

1979-01-01

304

Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations  

SciTech Connect

A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.

Davidson, R.C. [Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.; Chen, C. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Plasma Science and Fusion Center

1997-08-01

305

Discrete Surface Modeling using Geometric Flows  

Microsoft Academic Search

We use various nonlinear geometric partial dieren tial equations to ecien tly solve several surface modelling problems, including surface blending, N-sided hole lling and free-form surface tting. The nonlinear equations used include two second order o ws (mean curvature o w and average mean curvature o w), one fourth order o w (surface diusion o w) and a sixth order

Guoliang Xu; Qing Pan; Chandrajit L. Bajaj

2003-01-01

306

Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena  

NASA Astrophysics Data System (ADS)

The Euler-Bernoulli kinematic model as well as the von Kármán geometric non-linearity are used to derive the PDEs governing flexible beam vibrations. The beam is embedded into a 2D temperature field, and its surface is subjected to action of the electric potential. We report how an increase of the exciting load amplitude yields the beam turbulent behavior, and how the temperature changes a scenario from a regular/laminar to spatio-temporal/turbulent dynamics. Both classical Fourier analysis and Morlet wavelets are used to monitor a strong influence of temperature on regular and chaotic beam dynamics.

Krysko, V. A.; Awrejcewicz, J.; Kutepov, I. E.; Zagniboroda, N. A.; Papkova, I. V.; Serebryakov, A. V.; Krysko, A. V.

2013-11-01

307

Dynamic analysis of very flexible beams  

NASA Astrophysics Data System (ADS)

The dynamic analysis of flexible beams with large deformations is difficult and few studies have been performed. In this paper, the vibration analysis of several very flexible beams with large deflections using the finite element approach is studied. The examples were a cantilever beam and rotating flexible robot arms. The results were compared with the results available in the published literature. Several successful checks on the finite element results were performed to ensure the accuracy of the solutions. Due to the geometrical nonlinearity, several static equilibrium shapes can exist for large deflections of a cantilever beam for a given load. Nonlinear dynamic finite element analysis was implemented to investigate the stability of these shapes.

Fotouhi, R.

2007-08-01

308

Nonlinear thermally induced distortions of a laser beam in a cryogenic disk amplifier  

SciTech Connect

Taking into account the temperature dependences of the heat conductivity, the refractive index, and the thermal expansion coefficient, we calculated the temperature, elastic stresses, a thermally induced lens and depolarisation of a beam in a cryogenic disk amplifier (an Yb:YAG disk placed between a copper cylinder and a sapphire disk cooled by liquid nitrogen). When the active element (the thickness is 0.6 mm, the orientation is [001], the atomic concentration of Yb is 10%) is pumped by radiation from a diode laser (the beam diameter is 6 mm), the temperature does not exceed 140 K for the heat release power of 100 W. In this case, elastic stresses in the active element are six times lower than the maximum permissible value. The focal distance of the thermally induced lens is 5.5 m and the depolarisation rate is 0.038% per two passes through the active element. Although the heat conductivity of the active element rapidly decreases with temperature, the thermal load can be increased by 1.5-2 times when the dimensions of the active element remain constant. (active media)

Vyatkin, A G; Khazanov, Efim A [Institute of Applied Physics, Russian Academy of Sciences, Nizhnii Novgorod (Russian Federation)

2009-09-30

309

Statistically-averaged rate equations for intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations  

SciTech Connect

This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.

Davidson, R.C.; Lee, W.W.; Stoltz, P.

1997-08-01

310

Geometrically exact analysis of structures: a meshless alternative  

Microsoft Academic Search

In the last two decades a new class of geometrically nonlinear formulations has emerged. The so-called geometrically exact models give rise to nonlinear problems which demand numerical methods that, on one hand, have excellent approximation properties and, on other hand, ro- bust procedures to capture complicated structural behaviors. Until recently the Finite Element Method (FEM) has systematically been chosen to

Carlos Tiago; Paulo M. Pimenta

311

Geometric optimization  

SciTech Connect

An algorithm is presented which describes an application independent method for reducing the number of polygonal primitives required to faithfully represent an object. Reducing polygon count without a corresponding reduction in object detail is important for: achieving interactive frame rates in scientific visualization, reducing mass storage requirements, and facilitating the transmission of large, multi-timestep geometric data sets. This paper shows how coplanar and nearly coplanar polygons can be merged into larger complex polygons and re-triangulated into fewer simple polygons than originally required. The notable contributions of this paper are: (1) a method for quickly grouping polygons into nearly coplanar sets, (2) a fast approach for merging coplanar polygon sets and, (3) a simple, robust triangulation method for polygons created by 1 and 2. The central idea of the algorithm is the notion of treating polygonal data as a collection of segments and removing redundant segments to quickly form polygon hulls which represent the merged coplanar sets.

Hinker, P.; Hansen, C.

1993-09-01

312

Nonlinearity of the photorefractive response upon two-beam interaction in a bismuth silicon oxide crystal in an alternating electric field  

SciTech Connect

Nonlinearity of the photorefractive response is studied experimentally and theoretically upon two-beam interaction of light waves in a bismuth silicate crystal placed in an external meander electric field. The experimental data are shown to be in good agreement with a model, taking into account the influence of the second harmonic of the space-charge field on a photorefractive grating. The concentration of acceptors in a crystal and a product of the mobility of charge carriers by their recombination time are estimated from a comparison of the experimental and calculated data. (nonlinear optical phenomena)

Kobozev, O V; Mandel', A E; Shandarov, S M; Petrov, S A [Division of Electronic Devices, Tomsk University of Control Systems and Radioelectronics, Tomsk (Russian Federation); Kargin, Yu F [N.S. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Moscow (Russian Federation)

2000-06-30

313

Normal dynamic scaling in the class of the nonlinear molecular-beam-epitaxy equation  

NASA Astrophysics Data System (ADS)

The scaling of local height fluctuations is studied numerically in lattice growth models of the class of the nonlinear stochastic equation of Villain-Lai-Das Sarma (VLDS) in substrate dimensions d=1 and 2. In d=1, the average local slopes of the conserved restricted solid-on-solid (CRSOS) models converge to a finite value in the long-time limit, with power-law corrections in time whose exponents are close to 0.1. Other VLDS models in d=1, such as that of Das Sarma and Tamborenea, show a divergence of local slopes up to 106 monolayers, typical of anomalous roughening, but a comparison of roughness distributions shows that they scale as the linear fourth-order growth equation in those time scales. Normal scaling is also obtained in a modified VLDS equation with instability suppression, in contrast to recent numerical works. In d=2, a CRSOS model and a model with lateral aggregation of diffusing particles show normal scaling of the local slopes, also with small correction exponents. These results consistently show that the VLDS class has normal dynamic scaling in d=1 and 2, in agreement with the theoretical predictions of Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.94.166103 94, 166103 (2005), and they show that the apparently anomalous features observed in previous works are effects of large scaling correction terms or crossover effects.

Aarão Reis, F. D. A.

2013-08-01

314

Nonlinear finite element analyses of FRP-reinforced concrete slabs using a new layered composite plate element  

Microsoft Academic Search

A simple and shear-flexible rectangular composite layered plate element and nonlinear finite element analysis procedures are\\u000a developed in this paper for nonlinear analysis of fiber reinforced plastic (FRP)-reinforced concrete slabs. The composite\\u000a layered plate element is constructed based on Mindlin–Reissner plate theory and Timoshenko’s composite beam functions, and\\u000a transverse shear effects and membrane-bending coupling effects are accounted for. Both geometric

Y. Zhu; Y. X. Zhang

2010-01-01

315

Geometrical camera calibration with diffractive optical elements.  

PubMed

Traditional methods for geometrical camera calibration are based on calibration grids or single pixel illumination by collimated light. A new method for geometrical sensor calibration by means of diffractive optical elements (DOE) in connection with a laser beam equipment is presented. This method can be especially used for 2D-sensor array systems but in principle also for line scanners. PMID:19065162

Bauer, M; Griessbach, D; Hermerschmidt, A; Krüger, S; Scheele, M; Schischmanow, A

2008-12-01

316

Behaviour of steel beam to concrete-filled SHS column frames: Finite element model and verifications  

Microsoft Academic Search

This paper presents the behaviour of the composite frame with concrete-filled square hollow section (SHS) columns to steel beam. Finite element modeling (FEM) was developed to carry out the behaviour of composite frames under a constant axial load on columns and a lateral cyclic load on the frame. Accurate material and geometrical nonlinear for confined concrete and steel were considered

Lin-Hai Han; Wen-Da Wang; Xiao-Ling Zhao

2008-01-01

317

Nonlinear generation of a neat semi-Gaussian laser beam with a transversely varying periodically-poled LiTaO3 crystal.  

PubMed

We experimentally demonstrate a compact, all-solid-state 532 nm semi-Gaussian laser beam (SGB) source based on a 1064 nm laser and a transversely varying periodically-poled LiTaO3 (TPPLT) crystal as the laser beam shaper as well as the nonlinear frequency converter. We have used the designed TPPLT crystal to obtain a neat 532nm SGB with the quality of QSGB=1:17.5 by a single-pass second harmonic generation. The dependence of the generated SGB quality on the designed TPPLT parameter and the potential applications of the neat SGB are also discussed. PMID:21445167

Yin, Yaling; Lv, Xinjie; Zhao, Lina; Cao, Jingxiao; Yuan, Ye; Zhang, Chao; Leng, Hanyang; Xie, Zhenda; Xu, Ping; Zhao, Gang; Zhu, Shining

2011-03-14

318

Externally Prestressed Monolithic and Segmental Concrete Beams under Torsion: a Comparative Finite Element Study  

NASA Astrophysics Data System (ADS)

Externally Prestressed segmental beams are widely used in the construction of bridge structures today. These beams have many attractive advantages for rehabilitation and strengthening of existing structures as well. However, segmental beams experience significant effect under combined stresses at the joint interfaces between segments. This paper presents a finite element study on the effect of torsion on the structural behavior of both external prestressed monolithic and segmental concrete beams. Geometric and material nonlinearities were included in the study. The results show significant difference in the behavior of monolithic and segmental beams under torsion.

Al-Gorafi, M. A.; Ali, A. A. A.; Othman, I.; Jaafar, M. S.; Anwar, M. P.

2011-02-01

319

Geometrical response of multihole collimators.  

PubMed

A complete theory of camera multihole collimators is presented. The geometrical system response is determined in closed form in frequency space. This closed form accounts for the known efficiency and resolution formulae for parallel beam, fan beam, cone beam and astigmatic collimators as well as for the most frequent hole array patterns and hole shapes. The point spread function in the space domain for a certain collimator and source position can be calculated via a discrete fast Fourier transform. Beside the complete theoretical definition of the response of multihole collimators, this theory allows the definition of accurate models of the geometrical response for SPECT reconstruction and it is suitable for designing new collimators. PMID:9832021

Formiconi, A R

1998-11-01

320

Influence of axial loads on the nonplanar vibrations of cantilever beams  

NASA Astrophysics Data System (ADS)

The three-dimensional motions of cantilever beams have been extensively studied in the past. This structural element can be found in several applications, including MEMS and NEMS. In many applications the beam is subjected to axial loads which can play an important role in the dynamics of very slender beams. In this paper a cantilever inextensible beam subject to a concentrated axial load and a lateral harmonic excitation is investigated. Special attention is given to the effect of axial load on the frequency-amplitude relation, bifurcations and instabilities of the beam, a problem not tackled in the previous literature on this subject. To this aim, the nonlinear integro-differential equations describing the flexural-flexural-torsional couplings of the beam are used, together with the Galerkin method, to obtain a set of discretized equations of motion, which are in turn solved by numerical integration using the Runge-Kutta method. Both inertial and geometric nonlinearities are considered in the present analysis. Due to symmetries of the beam cross section, the beam exhibits a 1:1 internal resonance which has an important role on the nonlinear oscillations and bifurcation scenario. The results show that the axial load influences the stiffness of the beam changing its nonlinear behavior from hardening to softening. A detailed parametric analysis using several tools of nonlinear dynamics, unveils the complex dynamics of the beam in the parametric or external resonance regions. Bifurcations leading to multiple coexisting solutions are observed.

Carvalho, Eulher C.; Gonçalves, Paulo B.; Del Prado, Zenón; Rega, Giuseppe

2012-11-01

321

Change in the Polarization State and the Intensity of a Weak Light Beam in a Lossy Isotropic Nonlinear Medium in the Presence of an Intense Co-Propagating Light Beam  

NASA Astrophysics Data System (ADS)

The effect of an intense plane wave on a co-propagating weak plane wave in a lossy isotropic nonlinear medium is studied using the exact solution of H. Prakash et al.1 The presence of a plane-polarized intense beam changes the initial circular polarization of the weak beam to elliptical in general. The plane containing the direction of the major axis and the propagation oscillates about the plane of polarization of the intense beam. At the extreme positions, the elliptical polarization reduces to plane polarization and switches its handedness. For the lossless case, the plane of the major axis remains fixed at 45° to the plane of polarization of the intense beam and the polarization oscillates between circular and plane, switching the handedness when the plane polarization occurs, and there effects are periodic in distance within the medium. The presence of a circularly polarized intense beam changes the initial plane polarization of the weak beam to elliptical, whose major axis rotates in propagation. For the lossless case, the weak beam remains plane-polarized and rotates at a uniform rate in propagation. Suggestions for experimental observations of these effects are given and the values of observable quantities estimated for carbon disulfide.

Prakash, Hari; Singh, Devendra K.

322

Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field  

NASA Astrophysics Data System (ADS)

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.

Kurkin, S. A.; Koronovski, A. A.; Hramov, A. E.

2009-08-01

323

Nonlinear behavior and characterization of a piezoelectric laminated microbeam system  

NASA Astrophysics Data System (ADS)

A methodology of analyzing and characterizing the responses of a piezoelectric laminated microbeam system actuated by AC and DC voltages is developed in this research. The present development is based on the piezoelectric theory, Euler-Bernoulli hypothesis, and a newly developed periodicity-ratio (P-R) approach. The electric excitation loading on the beam is considered to be generated by AC and DC interactions. The control voltage of the piezoelectric layer and the geometric nonlinearity of the beam are also taken into account. The analysis of the nonlinear motion trend of the beam system with multiple parameters is carried out with the employment of the P-R criterion. The findings of the research are significant for the design of microbeam systems and micro-structures.

Chen, Changping; Hu, Haitao; Dai, Liming

2013-05-01

324

Nonlinear dynamic analysis of pipe whip tests. Final report  

SciTech Connect

This is a numerical verification of two groups of pipe whip tests sponsored or cosponsored by EPRI. Experimental data of the two pipe whip tests, one by Tennessee Valley Authority (TVA) and by FRAMATOME/CEA, were provided by EPRI. A nonlinear finite element code, ABAQUS-EPGEN, developed under partial sponsorship by EPRI was used for modeling the pipe whip tests. Beam elements together with an equivalent nonlinear spring element or a partial shell mesh were used to model pipes and elbow in the pipe whip tests. Material nonlinearity due to plasticity, strain rate effects, and temperature, as well as geometric nonlinearity due to large rotation and boundary conditions were included in the study. Effects of strain rate and modeling techniques were assessed. Results by current industry approach were also included as a reference solution. This report can be used as a guideline for numerical simulation of pipe whip phenomena. 74 figs.

Hsu, L.C.; Kuo, A.Y.

1986-05-01

325

Geometrically Nonlinear Analysis of Laminated Elastic Structures.  

National Technical Information Service (NTIS)

The research deals with the analysis of laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many others. The finite element method, a numerical technique for engineeri...

J. N. Reddy

1984-01-01

326

An inverse vibration-based approach towards modelling and damage identification in nonlinearly vibrating structures. Application for delamination detection in a composite beam  

NASA Astrophysics Data System (ADS)

This study explores the possibilities for inverse analysis and modelling from data of a nonlinearly vibrating structure. We are suggesting a statistical approach based on singular spectrum analysis (SSA). The method is based on a free decay response, when the structure is given an initial disturbance and is left to vibrate on its own. The measured vibration response is decomposed into new variables, the principal components, which are used to uncover oscillatory patterns in the structural response. In this study an application of the methodology for the purposes of delamination detection in a composite beam is explored.

Trendafilova, Irina

2012-08-01

327

Finite element modelling of cold-formed steel beams under local buckling or combined local\\/distortional buckling  

Microsoft Academic Search

The finite element (FE) method is capable of solving the complex interactive buckling of cold-formed steel beams allowing for all important governing features such as geometrical imperfections, material nonlinearity, postbuckling, etc.; this is unlikely to be achieved by analytical methods. In this paper, two series of finite element models for buckling behaviour of laterally-restrained cold-formed steel Z-section beams have been

Mohammad Reza Haidarali; David A. Nethercot

2011-01-01

328

Application of hybrid differential transformation\\/finite difference method to nonlinear analysis of micro fixed-fixed beam  

Microsoft Academic Search

Analyzing the dynamic response of electrostatic devices is problematic due to the complexity of the interactions between the\\u000a electrostatic coupling effect, the fringing field effect and the nonlinear electrostatic force. To resolve this problem, this\\u000a study presents an efficient computational scheme in which the nonlinear governing equation of the electrostatic device is\\u000a obtained in accordance with Hamilton’s principle and is

Cha’o-Kuang Chen; H. Y. Lai; Chin-Chia Liu

2009-01-01

329

Geometrical Methods for Equations of Hydrodynamical Type  

NASA Astrophysics Data System (ADS)

We describe some recent results for a class of nonlinear hydrodynamical approximation models where the geometric approach gives insight into a variety of aspects. The main contribution concerns analytical results for Euler equations on the diffeomorphism group of the circle for which the inertia operator is a nonlocal operator.

Escher, Joachim; Kolev, Boris

2012-10-01

330

Nonlinear feedback in robot arm control  

Microsoft Academic Search

Nonlinear feedback control is proposed for implementation of an advanced dynamic control strategy for robot arms. Using differential geometric system theory we obtained necessary and sufficient conditions for the existence of a nonlinear feedback control for a general nonlinear system to be externally linearized and simultaneously output decoupled. An algorithm is given for the construction of the required nonlinear feedback.

T. J. Tarn; A. K. Bejczy; A. Isidori; Y. Chen

1984-01-01

331

Wrinkled flames and geometrical stretch  

NASA Astrophysics Data System (ADS)

Localized wrinkles of thin premixed flames subject to hydrodynamic instability and geometrical stretch of uniform intensity (S) are studied. A stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous Michelson-Sivashinsky equation, is used as a starting point, and pole decompositions are used as a tool. Analytical and numerical descriptions of isolated (centered or multicrested) wrinkles with steady shapes (in a frame) and various amplitudes are provided; their number increases rapidly with 1/S>0. A large constant S>0 weakens or suppresses all localized wrinkles (the larger the wrinkles, the easier the suppression), whereas S<0 strengthens them; oscillations of S further restrict their existence domain. Self-similar evolutions of unstable many-crested patterns are obtained. A link between stretch, nonlinearity, and instability with the cutoff size of the wrinkles in turbulent flames is suggested. Open problems are evoked.

Denet, Bruno; Joulin, Guy

2011-07-01

332

Effect of self-magnetic fields on the nonlinear dynamics of relativistic electron beam with virtual cathode  

SciTech Connect

The report is devoted to the results of the numerical study of the virtual cathode (VC) formation conditions in the relativistic electron beam (REB) under the influence of the self-magnetic and external axial magnetic fields. The azimuthal instability of the relativistic electron beam leading to the formation of the vortex electron structure in the system was found out. This instability is determined by the influence of the self-magnetic fields of the relativistic electron beam, and it leads to the decrease of the critical value of the electron beam current (current when the non-stationary virtual cathode is formed in the drift space). The typical dependencies of the critical current on the external uniform magnetic field value were discovered. The effect of the beam thickness on the virtual cathode formation conditions was also analyzed.

Hramov, A. E.; Koronovskii, A. A. [Saratov State University, Astrakhanskaja 83, Saratov 410012, Russia Saratov State Technical University, Politechnicheskaja 77, Saratov 410028 (Russian Federation); Kurkin, S. A. [Saratov State University, Astrakhanskaja 83, Saratov 410012 (Russian Federation); Filatova, A. E. [Saratov State Technical University, Politechnicheskaja 77, Saratov 410028 (Russian Federation)

2012-11-15

333

Effect of self-magnetic fields on the nonlinear dynamics of relativistic electron beam with virtual cathode  

NASA Astrophysics Data System (ADS)

The report is devoted to the results of the numerical study of the virtual cathode (VC) formation conditions in the relativistic electron beam (REB) under the influence of the self-magnetic and external axial magnetic fields. The azimuthal instability of the relativistic electron beam leading to the formation of the vortex electron structure in the system was found out. This instability is determined by the influence of the self-magnetic fields of the relativistic electron beam, and it leads to the decrease of the critical value of the electron beam current (current when the non-stationary virtual cathode is formed in the drift space). The typical dependencies of the critical current on the external uniform magnetic field value were discovered. The effect of the beam thickness on the virtual cathode formation conditions was also analyzed.

Hramov, A. E.; Kurkin, S. A.; Koronovskii, A. A.; Filatova, A. E.

2012-11-01

334

Intensity modulation under geometrical uncertainty: a deconvolution approach to robust fluence  

Microsoft Academic Search

A deconvolution algorithm has been developed to obtain robust fluence for external beam radiation treatment under geometrical uncertainties. Usually, the geometrical uncertainty is incorporated in the dose optimization process for inverse treatment planning to determine the additional intensity modulation of the beam to counter the geometrical uncertainty. Most of these approaches rely on dose convolution which is subject to the

Yankhua Fan; Ravinder Nath

2010-01-01

335

Calculation of Acceleration and Transport of High Current Laminar Electron Beam in Nonlinear Axial Symmetrical Electric and Magnetic Fields.  

National Technical Information Service (NTIS)

A self-consisting problem is considered for the description of a process of acceleration and transportation of a high current laminar flow of electrons in nonlinear axially symmmetric electric and magnetic fields. It is shown that the redistribution of a ...

L. A. Merkulov

1981-01-01

336

James Clerk Maxwell Prize Talk: Collective Interaction Processes and Nonlinear Dynamics of Nonneutral Plasmas and Intense Charged Particle Beam  

Microsoft Academic Search

A nonneutral plasma is a many-body collection of charged particles in which there is not overall charge neutrality. Such systems are characterized by intense self-electric fields and, in high-current configurations, by intense self-magnetic fields. Nonneutral plasmas, like electrically neutral plasmas, exhibit a broad range of collective properties. This presentation summarizes several recent advances in understanding the collective processes and nonlinear

Ronald Davidson

2008-01-01

337

Geometric Gyrokinetic Theory for Edge Plasma  

SciTech Connect

It turns out that gyrokinetic theory can be geometrically formulated as special cases of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the spacetime is a 7-dimensional fiber bundle P over the 4-dimensional spacetime M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the 7-dimensional phase space determines particles worldlines in the phase space. Through Liouville 6-form {Omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyro-symmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyro-symmetry. The objective is to decouple the gyro-phase dynamics from the rest of particle dynamics by finding the gyro-symmetry in {gamma}. Compared with other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the spacetime coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here can not be achieved using classical methods. What the geometric method offers is a systematic treatment and simplified calculations.

Qin, H; Cohen, R H; Nevins, W M; Xu, X Q

2007-01-18

338

Mechanisms of formation of nonlinear optical light guide structures in metal cluster composites produced by ion beam implantation  

SciTech Connect

Ion implantation has been shown to produce a high density of metal colloids in glasses and crystalline materials. The high-precipitate volume fraction and small size of metal nanoclusters formed leads to values for the third-order susceptibility much greater than those for metal doped solids. This has stimulated interest in use of ion implantation to make nonlinear optical materials. On the other side, LiNbO{sub 3} has proved to be a good material for optical waveguides produced by MeV ion implantation. Light confinement in these waveguides is produced by refractive index step difference between the implanted region and the bulk material. Implantation of LiNbO{sub 3} with MeV metal ions can therefore result into nonlinear optical waveguide structures with great potential in a variety of device applications. The authors describe linear and nonlinear optical properties of a waveguide structure in LiNbO{sub 3}-based composite material produced by silver ion implantation in connection with mechanisms of its formation.

Sarkisov, S.S.; Williams, E.K.; Curley, M.; Smith, C.C.; Ila, D.; Venkateswarlu, P. [Alabama A and M Univ., Normal, AL (United States); Poker, D.B.; Hensley, D.K. [Oak Ridge National Lab., TN (United States). Solid State Div.

1997-11-01

339

Bloch-sphere representation of three-vertex geometric phases  

SciTech Connect

The properties of the geometric phases between three quantum states are investigated in a high-dimensional Hilbert space using the Majorana representation of symmetric quantum states. We found that the geometric phases between the three quantum states in an N-state quantum system can be represented by N-1 spherical triangles on the Bloch sphere. The parameter dependence of the geometric phase was analyzed based on this picture. We found that the geometric phase exhibits rich nonlinear behavior in a high-dimensional Hilbert space.

Tamate, Shuhei; Ogawa, Kazuhisa; Kitano, Masao [Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510 (Japan)

2011-11-15

340

Beam-Bem interactions  

SciTech Connect

In high energy storage-ring colliders, the nonlinear effect arising from beam-beam interactions is a major source that leads to the emittance growth, the reduction of beam life time, and limits the collider luminosity. In this paper, two models of beam-beam interactions are introduced, which are weak-strong and strong-strong beam-beam interactions. In addition, space-charge model is introduced.

Kim, Hyung Jin; /Fermilab

2011-12-01

341

Spatial Evolution of a Strong Field of Few-cycle Light Beam in Dielectric Media with Induced Plasma Nonlinearity  

NASA Astrophysics Data System (ADS)

The paper reports results of computer simulation of strong light beam propagation in dielectric media in case of plasma generation. We investigate an extra-broadening of radiation spectrum to a 'violet' wing of visible range. We show that the resulting pulse spectrum is represented by sequence of well-separated maximums, broadening as propagation distance increases. Experimental data are compared with simulation results, showing a good mutual correspondence of spectral representations.

Stumpf, S. A.; Korolev, A. A.; Kozlov, S. A.

2013-08-01

342

Geometric Algebra for Physicists  

Microsoft Academic Search

As leading experts in geometric algebra, Chris Doran and Anthony Lasenby have led many new developments in the field over the last ten years. This book provides an introduction to the subject, covering applications such as black hole physics and quantum computing. Suitable as a textbook for graduate courses on the physical applications of geometric algebra, the volume is also

Chris Doran; Anthony Lasenby

2003-01-01

343

Geometric Shapes in Architecture  

NSDL National Science Digital Library

A unit designed to improve students' understanding and appreciation of basic geometric shapes used in architecture. It describes various plane geometric figures and discusses in detail the properties of several of these figures. Perimeters and areas of polygons and circles are computed.

Fox, Lauretta J.

2007-02-22

344

Geometric Dimensioning Sentence Structure.  

ERIC Educational Resources Information Center

Explanations of geometric dimensioning symbols are provided to assist in the comprehension of the implied basic sentence structure of modern geometric dimensioning and tolerance. The proper identification and interpretation of the substantive language within several exemplary engineering drawings, otherwise called feature control frames, is…

McCuistion, Patrick J.

1991-01-01

345

Berry phase in nonlinear systems  

SciTech Connect

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

Liu, J.; Fu, L. B. [Institute of Applied Physics and Computational Mathematics, Post Office Box 8009, Beijing 100088 (China) and Center for Applied Physics and Technology, Peking University, Beijing 100084 (China)

2010-05-15

346

Importance of beam-beam tune spread to collective beam-beam instability in hadron colliders.  

PubMed

In hadron colliders, electron-beam compensation of beam-beam tune spread has been explored for a reduction of beam-beam effects. In this paper, effects of the tune-spread compensation on beam-beam instabilities were studied with a self-consistent beam-beam simulation in model lattices of Tevatron and Large Hodron Collider. It was found that the reduction of the tune spread with the electron-beam compensation could induce a coherent beam-beam instability. The merit of the compensation with different degrees of tune-spread reduction was evaluated based on beam-size growth. When two beams have a same betatron tune, the compensation could do more harm than good to the beams when only beam-beam effects are considered. If a tune split between two beams is large enough, the compensation with a small reduction of the tune spread could benefit beams as Landau damping suppresses the coherent beam-beam instability. The result indicates that nonlinear (nonintegrable) beam-beam effects could dominate beam dynamics and a reduction of beam-beam tune spread by introducing additional beam-beam interactions and reducing Landau damping may not improve the stability of beams. PMID:15089423

Jin, Lihui; Shi, Jicong

2004-03-31

347

Image coding with geometric wavelets.  

PubMed

This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image. PMID:17283766

Alani, Dror; Averbuch, Amir; Dekel, Shai

2007-01-01

348

New Beam Theory Using First-Order Warping Functions.  

National Technical Information Service (NTIS)

Due to a certain type of loading and geometrical boundary conditions, each beam will respond differently depending on its geometrical form of the cross section and its material definition. As an example, consider an isotropic rectangular beam under pure b...

C. A. Ie J. B. Kosmatka

1990-01-01

349

Geometric Networks Analysis.  

National Technical Information Service (NTIS)

The main goal of the project was to develop and use algorithmic tools with a geometric underpinning to analyze large networks. For example, the Internet, social networks, connectivity properties between genes or proteins in a biological cell, and other ty...

G. Carlsson M. Mahoney

2012-01-01

350

Geometric ghosts and unitarity  

SciTech Connect

A review is given of the geometrical identification of the renormalization ghosts and the resulting derivation of Unitarity equations (BRST) for various gauges: Yang-Mills, Kalb-Ramond, and Soft-Group-Manifold.

Ne'eman, Y.

1980-09-01

351

AJ Geometric Formulas Calculator  

NSDL National Science Digital Library

Solve various attributes of shapes and solids. Includes calculations for circle, parallelogram, rectangle, square, trapezoid, right circular cone, right circular cylinder, rectangular solid, and sphere geometric formulas. Geometry attributes include volume, area, perimeter, surface area, radius, length and circumference.

Raymond, Jimmy

352

Geometric Retrieval Problems  

Microsoft Academic Search

A large class of geometric retrieval problems has the following form. Given a set X of geometric objects, preprocess to obtain a data structure D(X). Now use D(X) to rapidly answer queries on X. We say an algorithm for such a problem has (worst-case) space-time complexity O(f(n),g(n)) if the space requirement for D(X) is O(f) and the 'locate run-time' required

Richard Cole; Chee-keng Yap

1983-01-01

353

Geometric Algebra for Physicists  

NASA Astrophysics Data System (ADS)

As leading experts in geometric algebra, Chris Doran and Anthony Lasenby have led many new developments in the field over the last ten years. This book provides an introduction to the subject, covering applications such as black hole physics and quantum computing. Suitable as a textbook for graduate courses on the physical applications of geometric algebra, the volume is also a valuable reference for researchers working in the fields of relativity and quantum theory.

Doran, Chris; Lasenby, Anthony

2003-07-01

354

Information Intrinsic Geometric Flows  

NASA Astrophysics Data System (ADS)

Geometric Flow Theory is cross fertilized by diverse elements coming from Pure Mathematic and Mathematical Physic, but its foundation is mainly based on Riemannian Geometry, as explained by M. Berger in a recent panoramic view of this discipline, its extension to complex manifolds, the Erich Kähler's Geometry, vaunted for its unabated vitality by J.P. Bourguignon, and Minimal Surface Theory. This paper would like to initiate seminal studies for applying intrinsic geometric flows in the framework of information geometry theory. More specifically, after having introduced Information metric deduced for Complex Auto-Regressive (CAR) models from Fisher Matrix (Siegel Metric and Hyper-Abelian Metric from Entropic Kähler Potential), we study asymptotic behavior of reflection coefficients of CAR models driven by intrinsic Information geometric Kähler-Ricci and Calabi flows. These Information geometric flows can be used in different contexts to define distance between CAR models interpreted as geodesics of Entropy Manifold. We conclude with potential application of Intrinsic Geometric Flow on Gauss Map to transform Manifold of any dimension by mean of Generalized Weierstrass Formula introduced by Kenmotsu that can represent arbitrary surfaces with non-vanishing mean curvature in terms of the mean curvature function and the Gauss map. One of the advantages of the generalized formulae is that they allow to construct a new class of deformations of surfaces by use of Intrinsic Geometric Flow on Gauss Map. We conclude with the Heat equation interpretation in the framework of Information Geometry.

Barbaresco, Frédéric

2006-11-01

355

Spectrum of Geometric Phases in a Driven Oscillator  

NASA Astrophysics Data System (ADS)

We study geometric phases underlying the time evolution of the quantum wave function of a driven nonlinear oscillator exhibiting periodic, quasiperiodic as well as chaotic dynamics. In the asymptotic limit, irrespective of the classical dynamics, the geometric phases are found to increase linearly with time. However, the fingerprints of classical motion are present in the bounded fluctuations that are superimposed on the monotonically growing phases, as well as in the difference in phases between two neighboring quantum states.

Satija, Indu; Balakrishnan, Radha

2005-03-01

356

Nonlinear formulation for flexible multibody system with large deformation  

NASA Astrophysics Data System (ADS)

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

Liu, Jinyang; Hong, Jiazhen

2007-02-01

357

Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment.  

PubMed

A single-beam implementation of coherent anti-Stokes Raman scattering (CARS) allows experimentally very much simplified and flexible approaches to time-resolved vibrational spectroscopy, with the additional benefit of microscopic spatial resolution. To achieve this, a broadband femtosecond laser is combined with a pulse shaper creating tailored pulse sequences by computer control. We discuss the theoretical foundations and technical issues of the technique in detail and show the successful implementation of different schemes for truly femtosecond time-resolved vibrational spectroscopy. Hereby, we elaborate all the details of the method shown earlier in a proof-of-principle study [Von Vacano and Motzkus, Opt. Comm., 2006, 264, 488] and greatly extend it by novel approaches relying on the use of identical double pulses or additional polarization control for background-free spectroscopy with superior robustness and signal-to-noise ratio. Perspectives and applications of the presented schemes for chemical microanalysis and high-contrast chemical imaging are examined. PMID:19791452

von Vacano, Bernhard; Motzkus, Marcus

2008-02-01

358

Role of nonlinearities and initial prepatterned surfaces in nanobead formation by ion-beam bombardment of Au(001): Experiments and theory  

NASA Astrophysics Data System (ADS)

Au(001) surfaces that have been prepatterned into a rippled morphology develop one-dimensional nanodot arrays (nanobeads) selectively along the ripples when bombarded with energetic ions at an angle that is normal to the average surface orientation. By quantifying the shape and morphology of these arrays, we show experimentally and by numerical simulations of an extended Kuramoto-Sivashinsky equation that the degree of one-dimensional order of the nanobeads can be optimized by considering initial rippled surfaces with various wavelength and roughness values. Our simulations employ physical units and use the experimental topographies as initial conditions. Such nonideal shapes are key to elucidating the influence of nonlinear effects (like conformal interface motion and local redeposition) since the early stages of the dynamics for these prepatterned systems. In spite of the fact that the evolution of the surface morphology becomes far from trivial under these circumstances, our continuum model is able to reproduce the experimental results quantitatively, in contrast to relevant alternative models in the context of surface nanopatterning by ion-beam bombardment.

Kim, J.-H.; Kim, J.-S.; Muñoz-García, J.; Cuerno, R.

2013-02-01

359

Geometrical Monte Carlo simulation of atmospheric turbulence  

NASA Astrophysics Data System (ADS)

Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes intensity scintillation and beam wander from propagation through turbulent eddies of varying sizes and refractive index. This can severely impair the operation of target designation and Free-Space Optical (FSO) communications systems. In addition, experimenting on an FSO communication system is rather tedious and difficult. The interferences of plentiful elements affect the result and cause the experimental outcomes to have bigger error variance margins than they are supposed to have. Especially when we go into the stronger turbulence regimes the simulation and analysis of the turbulence induced beams require delicate attention. We propose a new geometrical model to assess the phase shift of a laser beam propagating through turbulence. The atmosphere along the laser beam propagation path will be modeled as a spatial distribution of spherical bubbles with refractive index discontinuity calculated from a Gaussian distribution with the mean value being the index of air. For each statistical representation of the atmosphere, the path of rays will be analyzed using geometrical optics. These Monte Carlo techniques will assess the phase shift as a summation of the phases that arrive at the same point at the receiver. Accordingly, there would be dark and bright spots at the receiver that give an idea regarding the intensity pattern without having to solve the wave equation. The Monte Carlo analysis will be compared with the predictions of wave theory.

Yuksel, Demet; Yuksel, Heba

2013-09-01

360

Inflation from geometrical tachyons  

SciTech Connect

We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.

Thomas, Steven; Ward, John [Department of Physics, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom)

2005-10-15

361

NONLINEAR MAGNETOTHERMOELASTICITY OF ANISOTROPIC PLATES IMMERSED IN A MAGNETIC FIELD  

Microsoft Academic Search

A geometrically nonlinear theory of magnetothermoelasticity of electroconductive anisotropic plates in a magnetic field is developed. In this context, the Kirchhoff hypothesis is adopted for the plate modeling and the geometrical nonlinearities are considered in the von Kármán sense. In addition, the assumptions related to the distribution of electric and magnetic field disturbances through the plate thickness as proposed by

Liviu Librescu; Davresh Hasanyan; Zhanming Qin; Damodar R. Ambur

2003-01-01

362

SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF S–S AND C–C BEAMS AT LARGE VIBRATION AMPLITUDES PART I: GENERAL THEORY AND APPLICATION TO THE SINGLE MODE APPROACH TO FREE AND FORCED VIBRATION ANALYSIS  

Microsoft Academic Search

In a previous series of papers [1–3], a general model based on Hamilton's principle and spectral analysis was developed for non-linear free vibrations occurring at large displacement amplitudes of fully clamped beams and rectangular homogeneous and composite plates. As an introduction to the present work, concerned with the forced non-linear response of C–C and S–S beams, the above model has

L. Azrar; R. Benamar; R. G. White

1999-01-01

363

Levels of Geometric Understanding.  

ERIC Educational Resources Information Center

Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…

Pegg, John; Davey, Geoff

1991-01-01

364

Geometrical Adventures in Functionland.  

ERIC Educational Resources Information Center

Discussed is an approach in which algebra and geometry are interwoven in a series of problems that develop one from another. The two main concepts are the algebraic concept of function and the geometric concept of the "family of quadrilaterals." (MNS)

Hershkowitz, Rina; And Others

1987-01-01

365

A Geometric Scavenger Hunt  

ERIC Educational Resources Information Center

Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…

Smart, Julie; Marshall, Jeff

2007-01-01

366

Sublinear geometric algorithms  

Microsoft Academic Search

We initiate an investigation of sublinear algorithms for geometric problems in two and three dimensions. We give optimal algorithms for intersection detection of convex polygons and polyhedra, point location in two-dimensional Delaunay triangulations and Voronoi diagrams, and ray shooting in convex polyhedra, all of which run in time O(?n), where n is the size of the input. We also provide

Bernard Chazelle; Ding Liu; Avner Magen

2003-01-01

367

Geometric Series via Probability  

ERIC Educational Resources Information Center

Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…

Tesman, Barry

2012-01-01

368

Levels of Geometric Understanding.  

ERIC Educational Resources Information Center

|Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…

Pegg, John; Davey, Geoff

1991-01-01

369

Meshless geometric subdivision  

Microsoft Academic Search

Point-based surface processing has developed into an attractive alternative to mesh-based process- ing techniques for a number of geometric modeling applications. By working with point clouds directly, any processing is based on the given raw data and its underlying geometry rather than any arbitrary intermediate representations and generally artiflcial connectivity relations. We ex- tend this principle into the area of

C. Moenning; Facundo Mémoli; Guillermo Sapiro; Nira Dyn; Neil A. Dodgson

2007-01-01

370

Geometric Series via Probability  

ERIC Educational Resources Information Center

|Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…

Tesman, Barry

2012-01-01

371

Riemannian Geometrical Optics  

Microsoft Academic Search

The geometrical diffraction theory, in the sense of Keller, is here reconsidered as an obstacle problem in the Riemannian geometry. The first result is the proof of the existence and the analysis of the main properties of the ``diffracted rays'', which follow from the non-uniqueness of the Cauchy problem for geodesics in a Riemannian manifold with boundary. Then, the axial

E. de Micheli; G. Monti Bragadin; G. A. Viano

2000-01-01

372

NONLINEAR MODEL EVALUATION VIA SYSTEM IDENTIFICATION OF A MOORED STRUCTURAL SYSTEM  

Microsoft Academic Search

Complex nonlinear and chaotic responses have been observed and demonstrated in various compliant ocean systems characterized by nonlinear mooring restoring force and coupled fluid-structure interaction exciting force. The design of these systems, with inherent high degree of nonlinear dynamics, presents a challenge to the engineer. An experimental mooring system exhibiting nonlinear behavior due to geometric nonlinearity of mooring line angles

S. Narayanan; S. C. S. Yim

373

A Geometrically-exact rod model incorporating shear and torsion-warping deformation  

Microsoft Academic Search

A fully nonlinear. three-dimensional rod model is developed that incorporates transverse shear and torsion-warping deformation. The geometric setting is that of a constrained body model with contigurdtlon space modeled on W\\

J. C. SIMO

1991-01-01

374

Geometrical aspects of quantum spaces  

SciTech Connect

Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.

Ho, P.M. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group

1996-05-11

375

The Physics of Beams  

NSDL National Science Digital Library

This learning resources comprise a healthy introduction to the physics of beams. The site, from the American Physical Society and Michigan State University's Beam Theory and Dynamical Systems Group, contains a brochure providing a basic introduction to the study of beams and their applications. Sections include Accelerators of the World, Spectrometers, Scientific and Medical Applications, Non-linear Dynamics, and more.

376

Nonlinear light concentrators.  

PubMed

We propose a reconfigurable cylindrical concentrator designed using a transformation-optics approach when the core of the device contains a material with Kerr nonlinearity. We demonstrate that in the case of focusing Kerr nonlinearity of the material in the device, it functions as an axicon-like lens with a variable focus line that can be tuned by changing the incident electromagnetic field. We also numerically study the cases where the core of the device is made of a material with defocusing Kerr nonlinearity or consists of a negative index material and predict beam splitting or localized field enhancement at the boundary of the core, respectively. PMID:23258064

Pandey, Apra; Litchinitser, Natalia M

2012-12-15

377

A Geometric Scavenger Hunt  

NSDL National Science Digital Library

Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students discoveries was the fact that geometry was no longer just an isolated concept in their math books; rather, it provided a tool that allowed them to examine their world in a completely different way.

Marshall, Jeff; Smart, Julie

2007-10-01

378

Advances in Geometric Morphometrics  

Microsoft Academic Search

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape\\u000a from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can\\u000a be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric\\u000a space that can be approximated locally by a Euclidean

Philipp Mitteroecker; Philipp Gunz

2009-01-01

379

IKONOS GEOMETRIC ACCURACY VALIDATION  

Microsoft Academic Search

ABSTRACT: Since its launch in September of 1999, the IKONOS satellite has been consistently providing high quality 1-meter panchromatic and 4-meter multispectral images. Accurate interior and exterior orientation enable IKONOS to achieve high geometric accuracy with or without ground control. Exterior orientation is determined by on-board GPS receivers, star trackers, gyros, and interlock angles. Post-processing of GPS data with software

J. Grodecki; G. Dial

2002-01-01

380

Geometric measures of entanglement  

SciTech Connect

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.

Uyanik, K.; Turgut, S. [Department of Physics, Middle East Technical University, TR-06531, Ankara (Turkey)

2010-03-15

381

Algebro-Geometric Solutions of a Discrete System Related to the Trigonometric Moment Problem  

Microsoft Academic Search

We derive theta function representations of algebro-geometric solutions of a discrete system governed by a transfer matrix associated with (an extension of) the trigonometric moment problem studied by Szego and Baxter. We also derive a new hierarchy of coupled nonlinear difference equations satisfied by these algebro-geometric solutions.

Jeffrey S. Geronimo; Fritz Gesztesy; Helge Holden

2004-01-01

382

Non-Linear Analysis of Cylindrical Shells.  

National Technical Information Service (NTIS)

A theory to predict the influence of geometric nonlinearities on the natural frequencies of an empty anisotropic cylindrical shell was presented. It was a hybrid of finite element and classical thin shell theories. Sanders-Koiter's nonlinear and strain-di...

A. A. Lakis A. Toledano

1986-01-01

383

Energy harvesting from underwater base excitation of a piezoelectric composite beam  

NASA Astrophysics Data System (ADS)

In this paper, we investigate energy harvesting from underwater base excitation of a piezoelectric composite beam. Four different geometric configurations are experimentally studied in which the beam is either fully submerged or is partially immersed, with an eighth, a quarter, or a half of its length vibrating underwater. The frequency and the amplitude of base excitation are systematically varied along with the shunting resistance to investigate the principles of piezoelectric energy harvesting from underwater vibrations. Results demonstrate that increasing the wet length produces a consistent reduction of the resonance frequency and the quality factor of underwater vibrations. On the other hand, the harvested power is found to generally decrease as the submersion length is increased. Experimental results are interpreted through a distributed piezohydroelastic model that accounts for added mass and nonlinear hydrodynamic damping effects. A reduced order modal model is further established to parametrically explore the system response across a variety of geometrical and physical parameters.

Cha, Youngsu; Kim, Hubert; Porfiri, Maurizio

2013-11-01

384

GEOMETRIC OPERATIONS IN DIGITAL IMAGES  

Microsoft Academic Search

The geometrical transformations change the spatial relationship between objects in an image. One of the principle applications of geometric transformations concerns the possibility of correcting the digital images of the distortions introduced by the camera. Often the images produced by inexpensive cameras present geometric distortions of a very large nature. These images must be corrected in order to be used

Carlo Monti; Francesco Guerra; Caterina Balletti; Davide Miniutti

385

Study on highly nonlinear microstructured fibers  

NASA Astrophysics Data System (ADS)

A highly nonlinear dispersion flattened microstructured fiber is proposed. The new structure adopts two claddings with different pitches, air-holes diameters and air-holes arrayed fashions. The characteristics of such microstructured fiber such as nonlinearity and dispersion properties are investigated. The influence of the cladding structure parameters on the nonlinear coefficient and geometric dispersion is analyzed by full-vector finite element method with perfectly matched layer. Highly nonlinear coefficient and the dispersion properties of fibers are tailored by adjusting the cladding structure parameters. A novel microstructured fiber with highly nonlinear coefficient and dispersion flattened which is suited for supercontinuum generation is designed.

Liu, Zhaolun; Hou, Lantian; Wang, Wei; Gao, Fei

2008-01-01

386

Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments  

NASA Astrophysics Data System (ADS)

This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.

Karagiozis, K. N.; Païdoussis, M. P.; Amabili, M.; Misra, A. K.

2008-01-01

387

TRANSVERSE BEAM TRANSFER FUNCTIONS OF COLLIDING BEAMS IN RHIC  

SciTech Connect

We use transverse beam transfer functions to measure tune distributions of colliding beams in RHIC. The tune has a distribution due to the beam-beam interaction, nonlinear magnetic fields -- particularly in the interaction region magnets, and non-zero chromaticity in conjunction with momentum spread. The measured tune distributions are compared with calculations.

FISCHER,W.; BLASKIEWICZ, M.; CALAGA, R.; CAMERON, P.; HERR, W.; PIELONI, T.

2007-06-25

388

Beam-beam interaction in P-P colliding accelerators  

SciTech Connect

One model for beam growth due to the beam-beam interaction in P-P colliding accelerators is that it is due to the presence of non-linear forces generated by the fields produced by the beam plus some radomizing effect like noise, or a tune modulation. According to this model, to limit beam-beam effects, one should try to limit the size of the non-linear forces and the sources of noise or tune modulation. This model can also be used to compare the severity of beam-beam effects in two situations by comparing the size of the non-linear forces. In this paper, this approach will be used to study three problems: to compare the effects of beam-beam non-linear resonances in the ISR with those in ISABELLE; to estimate the strength of a spectrometer magnet that may be placed at one of the beam crossing points, without appreciably increasing the beam-beam effects; and to compare the beam-beam interaction for colliding beam accelerators with different crossing-angles and different ..beta../sub x/ and ..beta../sub y/ at the crossing points.

Parzen, G.

1982-08-01

389

On various non-linear rod theories for the dynamic analysis of multi-body systems. I - Formulations. II - Applications  

NASA Astrophysics Data System (ADS)

The paper reviews and compares existing formulations for flexible beams under large overall motion with reference to both the inertial frame approach and to the floating frame approach. For the inertial frame approach, nonlinear partial differential equations based on two finite strain rod models are reviewed. For the floating frame approach, linear and nonlinear partial differential equations based on the finite strain rod model, the Euler-Bernoulli beam model with the von Karman geometric constraint, the consistent second-order theory, the Green-Lagrange theory, and the Kane-Ryan-Banerjee approach are derived and compared. The finite element implementation of these formulations are described, with the typical example of a chain of flexible links, constrained to remain in a horizontal plane without gravity loads.

Boutaghou, Z.-E.; Erdman, A. G.

1993-06-01

390

Geometric phase in Bohmian mechanics  

NASA Astrophysics Data System (ADS)

Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2?. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.

Chou, Chia-Chun; Wyatt, Robert E.

2010-10-01

391

Geometric theory of images  

NASA Astrophysics Data System (ADS)

This dissertation takes the first steps in the use of differential geometry in the study of images in pixel space. Unlike previous applications of geometry which focused on the surfaces of objects, this dissertation examines image manifolds. Previous work on image manifolds did not examine their intrinsic geometry. This work unifies many observations found in past work. Beyond that, many new results are obtained. In the first parts of this dissertation, the dimensions of some selected image manifolds are experimentally determined, yielding a ratio of pixel space dimension to image manifold dimension on the order of 100:1. This leads immediately to some new bounds on image source entropy. A novel approach to defining images as signals yields an analogous sampling theorem. The main repercussion of this approach is the discovery that sampling within reason is a geometric invariant. This work resurrects a classic signal interpolation method which has not been previously applied to images. With the geometric invariance of sampling in hand, more advanced aspects of image manifold geometry are explored. The first of these aspects is curvature, which is shown to be extremely high. The discovery of high curvature explains the well established but poorly understood fact that linear subspace coding methods applied to images are far from optimal. Some geometric theory concerning the use of geodesics to represent images is presented. More advanced aspects of image manifold structures are explored experimentally. Preliminary results in this area indicate that there may be a structural relation between images of crudely similar objects in similar poses. Supplementary to the theory, a novel approach to image warping is devised called multimorphing. Unlike traditional morphing, multimorphing allows one to combine several images.

Lu, Haw-Minn

1998-11-01

392

A fiber-section model based Timoshenko beam element using shear-bending interdependent shape function  

NASA Astrophysics Data System (ADS)

A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved using a shear-bending interdependent formulation (SBIF). The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking. The sectional fiber model is constituted with a multi-axial plasticity material model, which is used to simulate the coupled shear-axial nonlinear behavior of each fiber. By imposing deformation compatibility conditions among the fibers, the sectional and elemental resisting forces are calculated. Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections, an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element. In addition, the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach. The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented. Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation. Finally, the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.

Li, Ning; Li, Zhongxian; Xie, Lili

2013-09-01

393

Riemannian Geometrical Optics  

NASA Astrophysics Data System (ADS)

The geometrical diffraction theory, in the sense of Keller, is here reconsidered as an obstacle problem in the Riemannian geometry. The first result is the proof of the existence and the analysis of the main properties of the ``diffracted rays'', which follow from the non-uniqueness of the Cauchy problem for geodesics in a Riemannian manifold with boundary. Then, the axial caustic is here regarded as a conjugate locus, in the sense of the Riemannian geometry, and the results of the Morse theory can be applied. The methods of the algebraic topology allow us to introduce the homotopy classes of diffracted rays. These geometrical results are related to the asymptotic approximations of a solution of a boundary value problem for the reduced wave equation. In particular, we connect the results of the Morse theory to the Maslov construction, which is used to obtain the uniformization of the asymptotic approximations. Then, the border of the diffracting body is the envelope of the diffracted rays and, instead of the standard saddle point method, use is made of the procedure of Chester, Friedman and Ursell to derive the damping factors associated with the rays which propagate along the boundary. Finally, the amplitude of the diffracted rays when the diffracting body is an opaque sphere is explicitly calculated.

de Micheli, E.; Bragadin, G. Monti; Viano, G. A.

394

Applications of geometric quantization  

SciTech Connect

Two applications of geometric quantization are described here. In the first, the classical system whose phase space is a two-sphere is quantized with an anti-holomorphic Kahler polarization. The result is an isolated quantum spin degree of freedom, with integral or half-integral total spin. A convenient formalism for handling geometric quantization with a Kahler polarization is exhibited. The second application is a discussion of several approaches to the quantization of classical systems with first class constraints. It is shown that there is a quantization procedure, called here the constrained polarization method, which is equivalent to quantizing (with a real polarization) the true classical degrees of freedom. This new method is often more convenient than directly quantizing the reduced phase space. In an example, it is shown that the time-honored procedure of imposing constraints as quantum operator equations can result in a mathematically non-viable quantum theory, if the chosen polarization is not compatible with the constraints. For this particular example, which is somewhat reminiscent of the canonical description of general relativity, there is a polarization compatible with constraints.

Stillerman, M.A.

1986-01-01

395

Ionospheric waveguide system with nonlocal nonlinearity  

Microsoft Academic Search

Ionosphere plasma modification caused by a very intensive narrow beams propagation is considered. Most of theoretical and experimental investigations concerning the nonlinear problem of the powerful wave beams propagation are restricted by the local nonlinearity. However, it is correct only in the case of negligible thermal conductivity or other diffusion process. In the other cases it is necessary to include

V. Eremenko; N. Manaenkova

2002-01-01

396

Geometrical Wake of a Smooth Flat Collimator  

SciTech Connect

A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems - a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator.

Stupakov, G.V.; /SLAC

2011-09-09

397

Acoustic nonlinearity in fluorinert FC43  

Microsoft Academic Search

Fluorinert FC-43 nonlinearity was investigated using two approaches: (i) a finite amplitude method with harmonic production; and (ii) a nonlinear frequency mixing in the fluid with consequent beam profile measurement of the difference frequency. The finite amplitude method provides information on the coefficient of nonlinearity, , through the amplitudes of the fundamental and the second harmonic, at a certain transmitter-receiver

Cristian Pantea; Dipen N Sinha; Curtis F Osterhoudt; Paul C Mombourquette

2009-01-01

398

Nonlinear cyclotron harmonic absorption  

SciTech Connect

Nonlinear oscillations of particle's energy occur when a particle stays in a resonance zone. In this work, we found that collisionless heating of particles occurs when they pass the microwave beam at first, second, and third harmonic resonances. It is found that the net energy gain of particles from the microwaves is inversely proportional to the wave frequency. It is also found that the net energy gain is dependent on the microwave beam width. The energy gain of particles from a single pass through a resonance zone has been formulated analytically. A numerical calculation has been performed and the results are in good agreement with the analytic calculation. Both analytic and numerical calculations show a strong frequency dependence and a beam width dependence of nonlinear cyclotron resonance heating.

Seol, Jae Chun [National Fusion Research Institute, Yuseong, Daejeon 555-333 (Korea, Republic of); Hegna, C. C.; Callen, J. D. [Department of Engineering Physics, University of Wisconsin, Madison, Wisconsin 53706-1609 (United States)

2009-05-15

399

Solitary waves in particle beams.  

National Technical Information Service (NTIS)

Since space charge waves on a particle beam exhibit both dispersive and nonlinear character, solitary waves or solitons are possible. Dispersive, nonlinear wave propagation in high current beams is found to be similar to ion-acoustic waves in plasmas with...

J. J. Bisognano

1996-01-01

400

Limits: Geometric and Harmonic Series  

NSDL National Science Digital Library

A geometric series is a sum of numbers such that the ratio between consecutive terms is constant. For instance, 1/2 + 1/4 + 1/8 + … is a geometric series. The harmonic series is the sum of all numbers 1/n for nn = 1, 2, 3, …. In this activity, you can see a representation of three geometric series and the harmonic series.

Mathematics, Illuminations N.

2010-05-26

401

Geometric measure of quantum discord  

SciTech Connect

Dakic, Vedral, and Brukner [arXiv:1004.0190 (2010)] introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. This measure is significant in capturing quantum correlations from a geometric perspective. In this brief report, we evaluate the geometric measure of quantum discord for an arbitrary state and obtain an explicit and tight lower bound. Furthermore, we reveal an intrinsic feature of geometric measure of quantum discord by showing that it actually coincides with a simpler quantity based on von Neumann measurements.

Luo Shunlong; Fu Shuangshuang [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing (China)

2010-09-15

402

Beam halo in high-intensity beams  

SciTech Connect

In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which in projection to the 2-D phase spaces results in a 2-component beam consisting of an inner core and a diffuse outer halo. The beam-halo is of concern for a next generation of cw, high-power proton linacs that could be applied to intense neutron generators for nuclear materials processing. The author describes what has been learned about beam halo and the evolution of space-charge dominated beams using numerical simulations of initial laminar beams in uniform linear focusing channels. Initial results are presented from a study of beam entropy for an intense space-charge dominated beam.

Wangler, T.P.

1993-01-01

403

Beam halo in high-intensity beams  

SciTech Connect

In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which in projection to the 2-D phase spaces results in a 2-component beam consisting of an inner core and a diffuse outer halo. The beam-halo is of concern for a next generation of cw, high-power proton linacs that could be applied to intense neutron generators for nuclear materials processing. The author describes what has been learned about beam halo and the evolution of space-charge dominated beams using numerical simulations of initial laminar beams in uniform linear focusing channels. Initial results are presented from a study of beam entropy for an intense space-charge dominated beam.

Wangler, T.P.

1993-06-01

404

A numerical and experimental study on the nonlinear behavior of laminated composite structural components  

Microsoft Academic Search

Nonlinear behavior of laminated composite plates and shells is studied. In the analysis, material nonlinearity due to the matrix degradation at the initial failure is considered along with the geometrical nonlinearity in the deformation process. An effective way of accounting the damage of the material due to initial failure is incorporated into a finite element analysis of the nonlinear behavior

Won-Man Cho; Sung-Kie Youn; Young-shin Lee

1995-01-01

405

The study on nonlinear dynamic behaviors of the structures with bolted-flange joint  

Microsoft Academic Search

With multiple nonlinear behaviors involved, bolted-flange joints are complex in nature, especially when exposed to dynamic loads. In this paper, a simplified nonlinear dynamic model is proposed for a cylinder assembled by the bolted-flange joint. The geometric, material and contact nonlinearity is modeled by nonlinear spring elements with different tensile and compressive stiffness. The moduli of the springs are obtained

Yu Luan; Zhen-qun Guan; Geng-dong Cheng

2010-01-01

406

Analytical expressions of transfer functions for a hard edge dipole magnet using a basic geometrical approach  

NASA Astrophysics Data System (ADS)

In charged particle accelerators, higher order optics studies become important from various points of view, such as dynamic aperture, emittance dilution, beam loss, etc. For some new applications, nonlinear study has become important in single pass optics also. For studying the higher order optics, each magnetic element is represented by a higher order transfer function (map, i.e., a function that relates output coordinates of a trajectory with initial coordinates and momentum deviation). Here in this paper we have provided an alternate method to obtain the analytical formulation of the transfer function for a dipole magnet. This formulation is obtained on the basis of basic geometrical analysis and is exact up to all orders under hard edge approximation. Being an analytical expression, the estimation of higher order effects of dipole magnet can be studied quickly. For checking the correctness of this formulation, we separated terms up to third order, which can be used to obtain the standard transfer matrices up to same order. An example of emittance growth and bunch length modification for a C-chicane-type electron beam bunch compressor is provided using the analytical expression.

Sharma, Amalendu; Singh, P.; Abdurrahim; Ghodke, A. D.; Singh, Gurnam

2013-01-01

407

AUTOLOFT: The AUTOLOFT geometric processor  

Microsoft Academic Search

I'm going to talk about one phase of the design automation problem, that of the geometric computer processor, using as an example North American's AUTOLOFT system. Any design automation system requires a modicum of geometric ability, both in the analytic definition and manipulation areas. In the APT (Automatic Programmed Tool) system, both areas are well-developed, with many automatic features provided

R. Maier

1964-01-01

408

Regular Labelings and Geometric Structures  

Microsoft Academic Search

Three types of geometric structure|grid triangulations, rectangular subdivisions, and orthogonal polyhedra| can each be described combinatorially by a regular la- beling: an assignment of colors and orientations to the edges of an associated maximal or near-maximal planar graph. We briey survey the connections and analogies between these three kinds of labelings, and their uses in designing ecient geometric algorithms. algorithm

David Eppstein

2010-01-01

409

Compass routing on geometric networks  

Microsoft Academic Search

this paper we study local routing algorithms on geometric networks. Formally speaking, suppose that we want to travel from a vertex s to a vertex t of a geometric network. A routing algorithm is called a local routing algorithm if it satisfies the following conditions:

Evangelos Kranakis; Harvinder Singh; Jorge Urrutia

1999-01-01

410

Conifolds and geometric transitions  

NASA Astrophysics Data System (ADS)

Conifold geometries have recieved much attention in string theory and string-inspired cosmology recently, in particular the Klebanov-Strassler background that is known as the “warped throat.” This paper provides a pedagogical explanation for the singularity resolution in this geometry and emphasizes its connection to geometric transitions. The first part focuses on the gauge theory dual to the Klebanov-Strassler background, including the T-dual intersecting branes description. Then, a connection to the Gopakumar-Vafa conjecture for open-closed string duality is presented and a series of papers verifying this model on the supergravity level is summarized. An appendix provides extensive background material about conifold geometries. Special attention is given to their complex structures and the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando Zayas-Tseytlin) conifolds are reevaluated. In agreement with earlier results, it is shown that only the singular solution allows a supersymmetric flux. However, the importance of using the correct complex structure to reach this conclusion is emphasized.

Gwyn, Rhiannon; Knauf, Anke

2008-10-01

411

Conifolds and geometric transitions  

SciTech Connect

Conifold geometries have recieved much attention in string theory and string-inspired cosmology recently, in particular the Klebanov-Strassler background that is known as the ''warped throat.'' This paper provides a pedagogical explanation for the singularity resolution in this geometry and emphasizes its connection to geometric transitions. The first part focuses on the gauge theory dual to the Klebanov-Strassler background, including the T-dual intersecting branes description. Then, a connection to the Gopakumar-Vafa conjecture for open-closed string duality is presented and a series of papers verifying this model on the supergravity level is summarized. An appendix provides extensive background material about conifold geometries. Special attention is given to their complex structures and the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando Zayas-Tseytlin) conifolds are reevaluated. In agreement with earlier results, it is shown that only the singular solution allows a supersymmetric flux. However, the importance of using the correct complex structure to reach this conclusion is emphasized.

Gwyn, Rhiannon; Knauf, Anke [Department of Physics, McGill University, 3600 Rue Universite, Montreal, Quebec, H3A 2T8 (Canada)

2008-10-15

412

Digital Planar Surface Segmentation Using Local Geometric Patterns  

Microsoft Academic Search

This paper presents a hybrid two-step method for segmenting a 3D grid-point cloud into planar surfaces by using discrete-geometry\\u000a results. Digital planes contain a finite number of local geometric patterns (LGPs). Such a LGP possesses a set of normal vectors.\\u000a By using LGP properties, we first reject non-linear points from a point cloud (edge-based step), and then classify non-rejected\\u000a points

Yukiko Kenmochi; Lilian Buzer; Akihiro Sugimoto; Ikuko Shimizu

2008-01-01

413

Nonlinear finite element analyses of FRP-reinforced concrete slabs using a new layered composite plate element  

NASA Astrophysics Data System (ADS)

A simple and shear-flexible rectangular composite layered plate element and nonlinear finite element analysis procedures are developed in this paper for nonlinear analysis of fiber reinforced plastic (FRP)-reinforced concrete slabs. The composite layered plate element is constructed based on Mindlin-Reissner plate theory and Timoshenko’s composite beam functions, and transverse shear effects and membrane-bending coupling effects are accounted for. Both geometric nonlinearity and material nonlinearity of the materials, which incorporates tension, compression, tension stiffening and cracking of the concrete, are included in the new model. The developed element and the nonlinear finite element analysis procedures are validated by comparing the computed numerical results of numerical examples with those obtained from experimental investigations and from the commercial finite element analysis package ABAQUS. The element is then employed to investigate the nonlinear structural behavior and the cracking progress of a clamped two-way FRP-reinforced concrete slab. The influences of reinforcement with different materials, ratio and layout in tension or compressive regions on structural behavior of the clamped slabs are investigated by parametric studies.

Zhu, Y.; Zhang, Y. X.

2010-08-01

414

Study of beam dynamics for an intense, high-brightness H- beam to design an efficient low-energy beam transport using ESQ lenses  

NASA Astrophysics Data System (ADS)

With an aim of transporting an initially diverging high-perveance (generalized beam perveance 2Ib/I0?3?3 = 0.003), high-brightness (normalized brightness ~1011 A/(m rad)2) H- beam and finally focusing it without any significant emittance dilution, a detailed simulation scheme has been set up incorporating the various nonlinear forces due to the beam and the external focusing elements, e.g., due to space charges, geometrical and chromatic aberrations. The analysis is done following a particular hierarchy to identify the mechanism of emittance growth; this procedure is used to optimize the lens parameters. A combination of six electrostatic quadrupole lenses is configured to deliver a satisfactory solution. The estimated emittance growth is a factor of about 1.6, and this is mainly due to chromatic aberrations. A relatively small group of particles is found to be responsible for the emittance growth. The analysis highlights a number of important issues, e.g., sensitivity to the beam distribution, beam current, lens misalignments, etc. An ESQ LEBT system with some novel features in terms of compactness and mechanical rigidity is developed, and its essential characteristics are described.

Guharay, S. K.; Allen, C. K.; Reiser, M.

1994-02-01

415

GEOMETRICAL ISOMERS OF RETINENE  

PubMed Central

Five crystalline retinenes have been isolated, which have every appearance of being cis-trans isomers of one another. They are all-trans retinene; three apparently mono-cis isomers: neoretinenes a and b and isoretinene a; and isoretinene b, an apparently di-cis isomer. The absorption spectra of these substances display the relations expected of cis-trans isomers. The main absorption band is displaced 5.5 to 7 mµ toward shorter wave lengths for each presumptive cis linkage. Some of the presumptive cis isomers also display a cis peak at 255 to 260 mµ. All five substances yield an identical blue product on mixing with antimony chloride. All of them are converted by light to what appears to be an identical mixture of stereoisomers. Heat isomerizes them very slowly; only neoretinene b exhibits large changes on heating at 70°C. for 3 hours. The various isomers have been extensively interconverted by gentle procedures, and all of them have been converted to all-trans retinene. The present theory of cis-trans isomerism in carotenoids predicts the existence of four stable isomers of retinene. Instead we seem to have five—specifically three mono-cis forms where two are expected. There is no doubt that all these substances are closely related isomers of one another. The only point in question is whether they differ in part by something other than cis-trans configuration. One possibility, as yet little supported by evidence, is that isomerization between ?- and ?-ionone rings may be involved. If, however, as seems more likely, all these substances are geometrical isomers of one another, some modification is needed in the present theory of configurational relationships in this class of compounds.

Hubbard, Ruth; Gregerman, Robert I.; Wald, George

1953-01-01

416

Nonlinear airship aeroelasticity  

NASA Astrophysics Data System (ADS)

The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.

Bessert, N.; Frederich, O.

2005-12-01

417

Acoustic nonlinearity in fluorinert FC-43  

SciTech Connect

Fluorinert FC-43 nonlinearity was investigated using two approaches: (i) a finite amplitude method with harmonic production; and (ii) a nonlinear frequency mixing in the fluid with consequent beam profile measurement of the difference frequency. The finite amplitude method provides information on the coefficient of nonlinearity, {beta}, through the amplitudes of the fundamental and the second harmonic, at a certain transmitter-receiver distance. A calibrated hydrophone was used as a receiver, in order to obtain direct pressure measurements of the acoustic waves in the fluid. The role of transmitter-receiver distance in {beta} determination is investigated. In the second approach, a single transducer is used to provide two high-frequency beams. The collinear high-frequency beams mix nonlinearly in the fluid resulting in a difference frequency beam and higher order harmonics of the primaries. The difference frequency beam profite is investigated at lengths beyond the mixing distance. The experimental data are compured with the KZK theory.

Pantea, Cristian [Los Alamos National Laboratory; Sinha, Dipen N [Los Alamos National Laboratory; Osterhoudt, Curtis F [Los Alamos National Laboratory; Mombourquette, Paul C [Los Alamos National Laboratory

2009-01-01

418

Mechanisms of formation of metal cluster nonlinear optical light guide structures in LiNbO[sub 3] by ion beam implantation  

SciTech Connect

Metal nanoclusters of Ag, Au and Cu have been produced by ion implantation into x- and z-cut lithium niobate. MeV Ag implantation followed by heat treatment simultaneously produced a waveguide and Ag clusters with a high nonlinear index. Co-implantation of O with Ag at 500[degree] enhanced the ability of the clusters to withstand heat treatment. [copyright] [ital 1999 American Institute of Physics.

Williams, E.K.; Ila, D. (Center for Irradiation of Materials, PO Box 1447 Alabama AM University, Normal, Alabama 35762 (United States)); Sarkisov, S. (Department of Natural and Physical Sciences, Alabama AM University, Normal, Alabama 35762 (United States)); Hensley, D.K. (Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States))

1999-06-01

419

Mechanisms of formation of metal cluster nonlinear optical light guide structures in LiNbO{sub 3} by ion beam implantation  

SciTech Connect

Metal nanoclusters of Ag, Au and Cu have been produced by ion implantation into x- and z-cut lithium niobate. MeV Ag implantation followed by heat treatment simultaneously produced a waveguide and Ag clusters with a high nonlinear index. Co-implantation of O with Ag at 500{degree} enhanced the ability of the clusters to withstand heat treatment. {copyright} {ital 1999 American Institute of Physics.}

Williams, E.K.; Ila, D. [Center for Irradiation of Materials, PO Box 1447 Alabama AM University, Normal, Alabama 35762 (United States); Sarkisov, S. [Department of Natural and Physical Sciences, Alabama AM University, Normal, Alabama 35762 (United States); Hensley, D.K. [Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)

1999-06-01

420

On the Resolution of Nonlinear Elastic and Elastoplastic Problems by the Method of Finite Elements Sulla Risoluzione Dei Problemi di Elasticita Non Lineare E di Elasto-Plasticita Attraverso Il Metodo Degli Elementi Finiti.  

National Technical Information Service (NTIS)

The computational procedures on nonlinear solid mechanics which are differentiated primarly by the type of nonlinearity are discussed in terms of geometric and material nonlinearity. Iterative algorithms were analyzed. These include: functional iteration,...

A. Cella A. Depaulis C. Carmignani

1974-01-01

421

Optical traps with geometric aberrations  

SciTech Connect

We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems.

Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G

2006-05-20

422

Nonstationary nonlinear processes during the interaction between an electron beam and an electromagnetic field at the passband boundary of an electrodynamic system. I - The high-frequency boundary  

NASA Astrophysics Data System (ADS)

Computer-simulation results are presented on transient processes arising during the interaction between an electron beam and fields of an electrodynamic system at the high-frequency passband boundary. Depending on the parameters, the system can have the properties of a BWT, a TWT, or a resonance oscillator. Regions of the parameter space are specified in which regimes of stationary oscillation, self-modulation, hard excitation, and hysteresis are achieved. A qualitative explanation of the observed phenomena is given consisting in a mean velocity decrease of the electron beam connected with the transfer of its kinetic energy to the electromagnetic field.

Bulgakova, L. V.; Kuznetsov, S. P.

423

Manifestation of the geometric phase in neutron spin-echo experiments  

SciTech Connect

We show how the geometric (Berry's) phase becomes manifest on adiabatic rotation of the polarization vector in the magnetic field configuration in the arms in a neutron spin echo (NSE) experiment. When the neutron beam used is monochromatic, a geometric phase collected in one spin-echo arm can be exactly compensated in the other arm either by an opposite geometrical rotation or by adding/subtracting a dynamic (Larmor) phase. This is not possible in a white beam, because, contrary to the dynamic phase, the geometric phase is independent of wavelength. Therefore, the NSE pattern can be disturbed. We demonstrate that adiabatic resonant spin flippers inherently produce a geometric phase which can influence the performance of NSE setups based on such flippers. This effect can be avoided by a proper mutual symmetry of the gradient fields in these flippers.

Kraan, W. H.; Rekveldt, M. T. [Department R3, Faculty of Applied Sciences, Delft University of Technology, 2629 JB Delft (Netherlands); Grigoriev, S. V. [Department R3, Faculty of Applied Sciences, Delft University of Technology, 2629 JB Delft (Netherlands); Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300 (Russian Federation)

2010-07-15

424

Geometric phase around exceptional points  

SciTech Connect

A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly {pi} for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to {pi} for small cycles and changes as the cycle size and shape are varied. We find explicitly the leading asymptotic term of this dependence, and describe it in terms of interaction of different energy levels.

Mailybaev, Alexei A.; Kirillov, Oleg N.; Seyranian, Alexander P. [Institute of Mechanics, Moscow State Lomonosov University, Michurinskii pr. 1, 119192 Moscow, (Russian Federation)

2005-07-15

425

Guitars, Violins, and Geometric Sequences  

ERIC Educational Resources Information Center

|This article describes middle school mathematics activities that relate measurement, ratios, and geometric sequences to finger positions or the placement of frets on stringed musical instruments. (Contains 2 figures and 2 tables.)|

Barger, Rita; Haehl, Martha

2007-01-01

426

The promise of geometric morphometrics  

Microsoft Academic Search

Nontraditional or geometric morphomet- ric methods have found wide application in the biological sciences, especially in anthropology, a field with a strong history of measurement of biological form. Controversy has arisen over which method is the \\

Joan T. Richtsmeier; Valerie Burke Deleon; Subhash R. Lele

2002-01-01

427

Stochastic pump effect and geometric phases in dissipative and stochastic systems  

SciTech Connect

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

Sinitsyn, Nikolai [Los Alamos National Laboratory

2008-01-01

428

Optimal Design of Pitched Tapered Laminated Wood Beams.  

National Technical Information Service (NTIS)

The optimal design of a pitched tapered laminated woood beam is considered. An engineering formulation is given in which the volume of the beam is minimized. The problem is then reformulated and solved as a generalized geometric (signomial) program. Sampl...

J. D. Barrett M. Avriel

1976-01-01

429

Beam Formation and Characterization for Neutron Radiography  

Microsoft Academic Search

Neutron flux and geometrical parameters (L\\/D and D) have been used as principal parameters to characterize a neutron beam. The parameters are also important from the standpoint of obtaining a neutron beam which provides a high quality image. Aneffective energy of the neutron beam, which is easily modulated by insertion of filters, is also important, and the quantification of these

H. Kobayashi; R. H. Plaut

2001-01-01

430

Computational aeroelastic analysis of aircraft wings including geometry nonlinearity  

Microsoft Academic Search

The objective of the present study is to show the ability of solving fluid structural interaction problems more realistically by including the geometric nonlinearity of the structure so that the aeroelastic analysis can be extended into the onset of flutter, or in the post flutter regime. A nonlinear Finite Element Analysis software is developed based on second Piola-Kirchhoff stress and

Binyu Tian

2003-01-01

431

Asymptotic numerical method for problems coupling several nonlinearities  

Microsoft Academic Search

The objective of this paper is to assess the efficiency of the asymptotic numerical method to solve problems coupling various nonlinearities. The 3D hemispherical stretching of a circular sheet, that involves geometrical, material and red unilateral contact nonlinearities is chosen as an example. An elastoplastic model based on the plasticity deformation theory is adopted. The structural discretization is performed by

H. Abichou; H. Zahrouni; M. Potier-Ferry

2002-01-01

432

A nonlinear thermal stress analysis of surface mount solder joints  

Microsoft Academic Search

A set of nonlinear finite-element (FE) cyclic thermal stress analyses of leaded ceramic chip carriers (LCCC) was performed. The FE models included the geometric and elastic compliance effects associated with the LCCC cavity, Kovar lid, copper solder pads and thermal joints, the orthotropic printed wiring board (PWB), and a constraining thermal core. The effect of nonlinear and rate-dependent constitutive characteristics

Burhan Ozmat

1990-01-01

433

A nonlinear composite shell element with continuous interlaminar shear stresses  

Microsoft Academic Search

A numerical model for layered composite structures based on a geometrical nonlinear shell theory is presented. The kinematic is based on a multi-director theory, thus the in-plane displacements of each layer are described by independent director vectors. Using the isoparametric apporach a finite element formulation for quadrilaterals is developed. Continuity of the interlaminar shear stresses is obtained within the nonlinear

F. Gruttmann; W. Wagner; L. Meyer; P. Wriggers

1993-01-01

434

Phase-Space Nonlinear Control Toolbox: The Maglev Experience  

Microsoft Academic Search

We describe the Phase-Space Nonlinear Control Toolbox, a suite of computational tools for synthesizingand evaluating control laws for a broad class of nonlinear dynamical systems. The Toolboxcomprises computational algorithms for identifying optimal control reference trajectories in the phasespace of dynamical systems and experimental methods for evaluating performance of the control laws.These algorithms combine knowledge of the geometric theory of modern

Zhao Feng; Shiou C. Loh; Jeff A. May

1997-01-01

435

Prediction to nonlinear behavior of steel frames subjected to fire  

Microsoft Academic Search

A new approach is presented for analysis of nonlinear behavior of steel frames subjected to fire. The material and geometrical nonlinearity as well as the non-uniform profile of temperature across section of frame members are taken into account. Thermal forces induced by temperature variation are also considered. The elasto-plastic stiffness equation of elements is established by using the generalized Clough

Guo-Qiang Li; Shou-Chao Jiang

1999-01-01

436

Comparison of beam-position-transfer functions using circular beam-position monitors  

SciTech Connect

A cylindrical beam-position monitor (BPM) used in many accelerator facilities has four electrodes on which beam-image currents induce bunched-beam signals. These probe-electrode signals are geometrically configured to provide beam-position information about two orthogonal axes. An electronic processor performs a mathematical transfer function (TF) on these BPM-electrode signals to produce output signals whose time-varying amplitude is proportional to the beam`s vertical and horizontal position. This paper will compare various beam-position TFs using both pencil beams and will further discuss how diffuse beams interact with some of these TFs.

Gilpatrick, J.D.

1997-10-01

437

Dispersive shock waves with nonlocal nonlinearity  

Microsoft Academic Search

We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.

Christopher Barsi; Wenjie Wan; Can Sun; Jason W. Fleischer

2007-01-01

438

Nonlinear dynamics experiments  

SciTech Connect

The goal of nonlinear dynamics experiments is to improve the understanding of single particle effects that increase the particle amplitude and lead to loss. Particle motion in storage rings is nearly conservative and for transverse dynamics the Hamiltonian in action angle variables (I{sub x},I{sub y},{phi}{sub x},{phi}{sub y}) near an isolated resonance k{nu}{sub x} + l{nu}{sub y} {approx} p is H = I{sub x}{nu}{sub x0} + I{sub y}{nu}{sub y0} + g(I{sub x}, I{sub y}) + h(I{sub x}, I{sub y})cos(k{phi}{sub x} + l{phi}{sub y} - p{theta}), (1) where k, l, p are integers, {theta} = 2{pi}s/L is the azimuth, and s and L are the path length and circumference respectively. The amplitude dependent tunes are given by {nu}{sub x,y}(I{sub x},I{sub y}) = {nu}{sub x0,y0} + {partial_derivative}g(I{sub x},I{sub y})/{partial_derivative}I{sub x,y} (2) and h(I{sub x},I{sub y}) is the resonance driving term (RDT). If the motion is governed by multiple resonances, h(I{sub x},I{sub y}) has to be replace by a series of terms. The particle motion is completely determined by the terms g and h, which can be calculated from higher order multipoles (Sec. ??), or obtained from simulations. Deviations from pure Hamiltonian motion occur due to synchrotron radiation damping (Sec. ??) in lepton or very high energy hadron rings, parameter variations, and diffusion processes such as residual gas and intrabeam scattering. The time scale of the non-Hamiltonian process determines the applicability of the Hamiltonian analysis. Transverse nonlinearities are introduced through sextupoles or higher order multipoles and magnetic field errors in dipoles and quadrupoles. Sextupoles can already drive all resonances. The beam-beam interaction and space charge also introduce nonlinear fields. Intentionally introduced nonlinearities are used to extract beam on a resonance or through capture in stable islands. Localization and minimization of nonlinearities in a ring is a general strategy to decrease emittance growth and increase the beam lifetime. The minimization of nonlinear effects can be done locally or globally. Except for resonant extraction, amplitude increase and particle loss is the result of chaotic particle motion. Large chaotic regions allow particles to increase their amplitudes, and ensures their ultimate loss. However, chaotic particles can, on average, still survive the time period of interest, i.e. the storage time. Nonlinear dynamics experiments aim to determine either the detuning and driving terms g and h directly, or their effect on other quantities. Nonlinear phenomena observed in experiments include phase space deformations and resonant islands in Poincare surfaces of section, nonlinear phase advances, amplitude detuning g, decoherence (Sec. ??), resonance driving terms h, smear, halo formation, echoes (Sec. ??), the tune response matrix, dynamic aperture (Sec. ??), emittance growth, and particle loss. Nonlinear experiments can also be done in the longitudinal plane.

Fischer, W.

2011-01-01

439

Modeling Nonlinear Non-Stationary Self-Organized Asymptotic States in High Energy Density Plasmas Driven by Intense Crossing Laser Beams  

NASA Astrophysics Data System (ADS)

The multiscale dynamics of Vlasov-Maxwell and Vlasov-Poisson systems where non-stationary self-organized states can be formed is a grand challenge. From chaotic particle orbits there arise collective self-consistent fields which are highly coherent. We will explain the novel aspects of these states and contrast them with electron plasma waves which are small amplitude disturbances that are naturally resonant. We will also point out connections between these systems and the high Reynolds number limit of 2D incompressible (Euler) turbulence, galaxy formation models and applications in the nonlinear optics of laser-matter interactions. Techniques will be given of capturing the multiscale dynamics and the conformal invariance hypothesis in the fine scale structures beneath the large scale order found in such systems.

Afeyan, Bedros

2012-02-01

440

Spatial solitons in nonlinear liquid waveguides  

Microsoft Academic Search

Spatial solitons are studied in a planar waveguide filled with nonlinear liquids. Spectral and spatial measurements for different\\u000a geometries and input power of the laser beam show the influence of different nonlinear effects as stimulated scatterings on\\u000a the soliton propagation and in particular on the beam polarization. The stimulated scattering can be used advantageously to\\u000a couple the two polarization components.

R. Barillé; G. Rivoire

2001-01-01

441

Geometric scalar theory of gravity  

NASA Astrophysics Data System (ADS)

We present a geometric scalar theory of gravity. Our proposal will be described using the ``background field method" introduced by Gupta, Feynman, Deser and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor — which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models — does not apply to our geometric scalar theory. From the very beginning this is not a special relativistic scalar gravity. The adjective ``geometric" pinpoints its similarity with general relativity: this is a metric theory of gravity. Some consequences of this new scalar theory are explored.

Novello, M.; Bittencourt, E.; Moschella, U.; Goulart, E.; Salim, J. M.; Toniato, J. D.

2013-06-01

442

Nonlinear stability and control of gliding vehicles  

Microsoft Academic Search

In this thesis we use nonlinear systems analysis to study dynamics and design control solutions for vehicles subject to hydrodynamic or aerodynamic forcing. Application of energy-based methods for such vehicles is challenging due to the presence of energy-conserving lift and side forces. We study how the lift force determines the geometric structure of vehicle dynamics. A Hamiltonian formulation of the

Pradeep Bhatta

2006-01-01

443

Geometrical spin symmetry and spin  

SciTech Connect

Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.

Pestov, I. B., E-mail: pestov@theor.jinr.ru [Joint Institute for Nuclear Research (Russian Federation)

2011-07-15

444

Geometrically based optimization of extracranial radiosurgery treatment planning  

NASA Astrophysics Data System (ADS)

Steterotactic radiosurgery (SRS) is a non-invasive surgical technique of using multiple high intensity external beams of x-rays to obliterate lesions. It has been successfully utilized for many intracranial diseases. There has been an interest in extending the technology to extraceanial treatment sites. Much effort has been made to improve the precision of tumor localization to make extracranial radiosurgery available for many centers. Ultrasound-guided extracranial radiosurgery, for example, has been used successfully at the University of Iowa. However, little effort has been made on extracranial radiosurgery treatment planning. For static conformal extracranial radiosurgery, a key component of a treatment plan is the selection of the number of beams and their orientations since the geometry of the beam arrangement dominates overall dose distribution. Maximizing beam separation in three dimensions decreases beam overlap, thus maximizing dose conformality and gradient outside the tumor volume. As a general rule, many centers place the beams manually in such a way that beam separations in the available space are maximal. The beam orientations are then modified to avoid the critical structure based on the planner's inspection of the beam's eye view. However manually placement and modification of beam orientations are impractical when a treatment uses a large number of beams. In this investigation, a geometrically based optimization of extracranial radiosurgery treatment planning system is developed. It begins with generating a maximally separated beam bouquets using a Monte Carlo process. These maximally separated beam bouquets are then optimized for a patient by considering the critical structure avoidances. Using this optimization process as a template, we have determined the optimal number of beams used in extracranial radiosurgery based on dose conformality, gradient, and biological indices. To evaluate the benefit of using non-coplanar beams in the treatment plan, a systematic comparison between conventional coplanar beam treatment plans and non-coplanar beam treatment plans is also addressed. Two beam shaping techniques, conformal and IMRT are used in this comparison. Decision and conclusion are made base on dose conformality, gradient, and biological indices.

Liu, Ruiguo

445

Pressure control of a two-stage turbocharged diesel engine using a novel nonlinear IMC approach  

Microsoft Academic Search

This paper deals with nonlinear multivariable output feedback control of a two-stage turbocharged diesel engine. The feedback structure of internal model control (IMC) is used in combination with a nonlinear feedforward controller based on geometric nonlinear control design methods. Input saturations as well as measured disturbances are taken into account and a severe rank deficiency is handled. This novel control

Dieter Schwarzmann; Rainer Nitsche; Jan Lunze; Andreas Schanz

2006-01-01

446

The Nonlinear Behaviour of a MacPherson Strut Wheel Suspension  

Microsoft Academic Search

Three nonlinear models of a MacPherson strut wheel suspension have been studied. The nonlinearities considered are due to the nonlinear geometrical effects in the mechanism, the amplitude limitation due to the bumpstop, the progressive stiffness of the bumpstop and the different damping coefficients for the shock absorber in bump and rebound. The models have been derived according to physical parameter

A. STENSSON; C. ASPLUND; L. KARLSSON

1994-01-01

447

Differential Geometric Methods in Control.  

National Technical Information Service (NTIS)

The report consists of 6 papers on Control theory which use differential geometery and Lie Group theoretic methods to investigate controllability, observability, and minimal realizations theory for certain classes of linear and nonlinear systems. (Author)

R. W. Brockett V. Jurdjevic A. Rahimi H. J. Sussmann

1971-01-01

448

New Nonlinear Multifrequency TWT Model  

Microsoft Academic Search

We outline a new nonlinear multifrequency Travel- ing Wave Tube (TWT) model based on Eulerian electron beam equations. We identify and illustrate with preliminary exam- ples types of problems the model may be applied to. In partic- ular, the model is well suited to accommodate many closely- spaced frequencies in simulation and analysis.

John G. Wohlbier; John H. Booske; Ian Dobson

449

Geometrical view of quantum entanglement  

Microsoft Academic Search

Although a precise description of microscopic physical problems requires a full quantum-mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which apparently has no classical counterpart. We demonstrate here how quantum entanglement may be within the de Broglie-Bohm interpretation of quantum mechanics visualized in geometrical terms, giving new insight into this mysterious

A. Ramsak

2011-01-01

450

Platonic Symmetry and Geometric Thinking  

ERIC Educational Resources Information Center

|Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…

Zsombor-Murray, Paul

2007-01-01

451

Surface Approximations in Geometric Modeling.  

National Technical Information Service (NTIS)

One of the major research efforts in the field of solid modeling focuses on extending the geometric coverage of modeling systems and on incorporating complex free-form surfaces. Some major obstacles to this goal include computing and rendering very comple...

J. H. Chuang

1990-01-01

452

Surface approximations in geometric modeling  

Microsoft Academic Search

One of the major research efforts in the field of solid modeling focuses on extending the geometric coverage of modeling systems and on incorporating complex free-form surfaces. Some major obstacles to this goal include computing and representing intersection curves of two general surfaces, and computing and rendering very complex surfaces, including offset, Voronoi, and blending surfaces. We present local and

Jung-Hong Chuang

1990-01-01

453

Geometric Modeling Using Octree Encoding.  

National Technical Information Service (NTIS)

Results are described of an effort to devise a new 3-D geometric modeling scheme and associated linear growth algorithms in which objects of arbitrary complexity can be encoded, manipulated, analyzed, and displayed interactively in real time or close to r...

D. Meagher

1981-01-01

454

Geometric Methods for Vortex Extraction  

Microsoft Academic Search

This paper presents two vortex detection methods which are based on the geometric properties of streamlines. Unlike traditional vortex detection meth- ods, which are based on point-samples of physical quantities, one of our methods is also effective in detecting weak vortices. In addition, it allows for quantitative feature extraction by calculating numerical attributes of vortices. Results are pre- sented of

I. Ari Sadarjoen; Frits H. Post

455

Integrating nutrition: a geometrical approach  

Microsoft Academic Search

We present and illustrate using data from insects an integrative approach to modelling animal nutrition. This framework enables the unification within simple geometrical models of several nutritionally relevant measures. These include: the optimal balance and amounts of nutrients required to be ingested and allocated to growth by an animal over a given time period (the intake and growth targets, respectively);

D. Raubenheimer; S. J. Simpson

1999-01-01

456

Parametric FEM for geometric biomembranes  

Microsoft Academic Search

We consider geometric biomembranes governed by an L2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with

Andrea Bonito; Ricardo H. Nochetto; M. Sebastian Pauletti

2010-01-01

457

Eighteen-beam gun design for high power, high repetition rate, broadband multiple-beam klystrons  

Microsoft Academic Search

This paper presents the design of a high repetition rate electron gun to be employed in future high-power broadband multiple-beam amplifiers operating in S-band. Special emphasis is placed on the geometric layout of the gun to ensure high repetition rate operation at moderate beam switching voltages, good beam optics, and optimal beam packing for long life, efficient beam-wave interaction and

Khanh T. Nguyen; Dean E. Pershing; David K. Abe; George Miram; Baruch Levush

2005-01-01

458

Geometrical model fitting for interferometric data: GEM-FIND  

NASA Astrophysics Data System (ADS)

We developed the tool GEM-FIND that allows to constrain the morphology and brightness distribution of ob- jects. The software fits geometrical models to spectrally dispersed interferometric visibility measurements in the N-band using the Levenberg-Marquardt minimization method. Each geometrical model describes the bright- ness distribution of the object in the Fourier space using a set of wavelength-independent and/or wavelength- dependent parameters. In this contribution we numerically analyze the stability of our nonlinear fitting approach by applying it to sets of synthetic visibilities with statistically applied errors, answering the following questions: How stable is the parameter determination with respect to (i) the number of uv-points, (ii) the distribution of points in the uv-plane, (iii) the noise level of the observations?

Klotz, Daniela; Sacuto, Stephane; Paladini, Claudia; Hron, Josef; Wachter, Georg

2012-07-01

459

Finite-amplitude, pulsed, ultrasonic beams  

Microsoft Academic Search

An analytical, approximate solution of the inviscid KZK equation for a nonlinear pulsed sound beam radiated by an acoustic source with a Gaussian velocity distribution, is obtained by means of the renormalization method. This method involves two steps. First, the transient, weakly nonlinear field is computed. However, because of cumulative nonlinear effects, that expansion is non-uniform and breaks down at

François Coulouvrat; Kjell-Eivind Frøysa

1995-01-01

460

Confined energy distribution for charged particle beams  

DOEpatents

A charged particle beam is formed to a relatively larger area beam which is well-contained and has a beam area which relatively uniformly deposits energy over a beam target. Linear optics receive an accelerator beam and output a first beam with a first waist defined by a relatively small size in a first dimension normal to a second dimension. Nonlinear optics, such as an octupole magnet, are located about the first waist and output a second beam having a phase-space distribution which folds the beam edges along the second dimension toward the beam core to develop a well-contained beam and a relatively uniform particle intensity across the beam core. The beam may then be expanded along the second dimension to form the uniform ribbon beam at a selected distance from the nonlinear optics. Alternately, the beam may be passed through a second set of nonlinear optics to fold the beam edges in the first dimension. The beam may then be uniformly expanded along the first and second dimensions to form a well-contained, two-dimensional beam for illuminating a two-dimensional target with a relatively uniform energy deposition. 8 figs., 2 tabs.

Jason, A.J.; Blind, B.

1989-09-29