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1

A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions  

NASA Astrophysics Data System (ADS)

The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the previously developed models of geometrically nonlinear vibrations of Euler-Bernoulli continuous beams, and multidof system models made of N masses placed at the end of elastic bars connected by linear spiral springs, presenting the beam flexural rigidity. The validation of the new model via the analysis of the convergence conditions of the nonlinear frequencies obtained by the N-dof system, when N increases, and those obtained in previous works using a continuous description of the beam. In addition to the above points, the models developed in the present work, may constitute, in our opinion, a good illustration, from the didactic point of view, of the origin of the geometrical nonlinearity induced by large transverse vibration amplitudes of constrained continuous beams, which may appear as a Pythagorean Theorem effect. The first step of the work presented here was the formulation of the problem of nonlinear vibrations of the discrete system shown in Fig. 1 in terms of the semi-analytical method, denoted as SAA, developed in the early 90's by Benamar and coauthors [3], and discussed for example in [6,7]. This method has been applied successfully to various types of geometrically nonlinear problems of structural dynamics [1-3,6-8,10-12] and the objective here was to use it in order to develop a flexible discrete nonlinear model which may be useful for presenting in further works geometrically nonlinear vibrations of real beams with discontinuities in the mass, the section, or the stiffness distributions. The purpose in the present work was restricted to developing and validating the model, via comparison of the obtained dependence of the resonance frequencies of such a system on the amplitude of vibration, with the results obtained previously by continuous beams nonlinear models. In the SAA method, the dynamic system under consideration is described by the mass matrix [M], the rigidity matrix [K], and the nonlinear rigidity matrix [B], which depends on the amplitude of vibration, and involves a fourth-order nonlinearity tensor bijkl. Details are given below, co

Rahmouni, A.; Beidouri, Z.; Benamar, R.

2013-09-01

2

Non-smooth and time-varying systems of geometrically nonlinear beams  

NASA Astrophysics Data System (ADS)

Bending vibrations of geometrically nonlinear beams, which are connected with some clearance in their contact areas, are analyzed during dynamic extending and retracting motion of the different segments. For the physical model of a fork lifter, as an example of application, the governing system equations are derived by applying Hamilton's principle. Using a discretization procedure, based on admissible shape functions, a system of coupled, nonlinear, time-varying, ordinary differential equations is generated. Linearization and model reduction leads to a sequence of simple models. On the basis of these models, an adaptive state regulator and an adaptive full-state observer ( Luenberger Observer) are designed for vibration suppression using the optimal linear quadratic regulator ( LQR). The adaptive controller and observer are applied to the original, significantly more complicated, geometrically nonlinear and time-varying system with clearance so that the robustness of the controlled system can be studied during dynamic extending and retracting motions.

Barthels, Pierre; Wauer, Jörg

2008-08-01

3

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

4

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

5

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

6

Nonlinear Geometrical Acoustics.  

National Technical Information Service (NTIS)

The development of the theory of nonlinear wave propagation in both bounded and semi-infinite dissipative media is followed from its origins in the theories of linear geometrical acoustics, simple waves, and acceleration fronts. In Part I, Sections 2 to 5...

B. R. Seymour, M. P. Mortell

1975-01-01

7

Dynamic analysis of an inclined Timoshenko beam traveled by successive moving masses\\/forces with inclusion of geometric nonlinearities  

Microsoft Academic Search

In the first part of this paper, the nonlinear coupled governing partial differential equations of vibrations by including\\u000a the bending rotation of cross section, longitudinal and transverse displacements of an inclined pinned–pinned Timoshenko beam\\u000a made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling\\u000a mass\\/force with constant velocity are derived. To

Ahmad Mamandi; Mohammad H. Kargarnovin

2011-01-01

8

Bending, Vibration and Buckling Response of Conventional and Modified Euler-Bernoulli and Timoshenko Beam Theories Accounting for the von Karman Geometric Nonlinearity  

E-print Network

theory and analysis that considers the nonlinear effects on the buckling response of beams. This thesis contains three new developments: (1) the conventional beam theories are generalized by accounting for nonlinear terms arising from ?zz and ?xz...

Mahaffey, Patrick Brian

2013-08-07

9

An investigation of the beam-column and the finite-element formulations for analyzing geometrically nonlinear thermal response of plane frames  

NASA Astrophysics Data System (ADS)

The objective of this study is to investigate the accuracy and computational efficiency of two commonly used formulations for performing the geometrically nonlinear thermal analysis of plane framed structures. The formulations considered are the followings: the Beam-Column formulation and the updated Lagrangian version of the finite element formulation that has been adopted in the commercially well-known software SAP2000. These two formulations are used to generate extensive numerical data for three plane frame configurations, which are then compared to evaluate the performance of the two formulations. The Beam-Column method is based on an Eulerian formulation that incorporates the effects of large joint displacements. In addition, local member force-deformation relationships are based on the Beam-Column approach that includes the axial strain, flexural bowing, and thermal strain. The other formulation, the SAP2000, is based on the updated Lagrangian finite element formulation. The results for nonlinear thermal responses were generated for three plane structures by these formulations. Then, the data were compared for accuracy of deflection responses and for computational efficiency of the Newton-Raphson iteration cycles required for the thermal analysis. The results of this study indicate that the Beam-Column method is quite efficient and powerful for the thermal analysis of plane frames since the method is based on the exact solution of the differential equations. In comparison to the SAP2000 software, the Beam-Column method requires fewer iteration cycles and fewer elements per natural member, even when the structures are subjected to significant curvature effects and to restrained support conditions. The accuracy of the SAP2000 generally depends on the number of steps and/or the number of elements per natural member (especially four or more elements per member may be needed when structure member encounters a significant curvature effect). Succinctly, the Beam-Column formulation requires considerably fewer elements per member, fewer iteration cycles, and less time for thermal analysis than the SAP2000 when the structures are subjected to significant bending effects.

Silwal, Baikuntha

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

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

12

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

13

Characterizing the Effects of Geometrical Nonlinearities on Aeroelastic Behavior of High-Aspect-Ratio Wings  

E-print Network

flight. Curved beams behave very differently from straight wings. The static, dynamic and aeroelasticCharacterizing the Effects of Geometrical Nonlinearities on Aeroelastic Behavior of High the results of nonlinear aeroelastic analysis of a representative large-aspect-ratio wing. The effects

Patil, Mayuresh

14

Classical light beams and geometric phases.  

PubMed

We present a study of geometric phases in classical wave and polarization optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarization optics, and the behavior of polarization in the eikonal or ray limit of Maxwell's equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarization state are both subject to change is dealt with, attention being paid to the validity of Maxwell's equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated. PMID:24977351

Mukunda, N; Chaturvedi, S; Simon, R

2014-06-01

15

Robustness of continuous-variable entanglement via geometrical nonlinearity  

NASA Astrophysics Data System (ADS)

We propose a scheme to generate robust stationary continuous-variable entanglement in optomechanical systems, based on geometrical nonlinearity that occurs for large mechanical displacements. Such nonlinearity is often used to correct the dynamics of the systems in the strong-coupling regime. It appears that geometrical nonlinearity enhances the entanglement and shifts its maximum towards high detuning values. Using the experimental parameters, we find that such a scheme generates a very robust entanglement against thermal decoherence even at room temperature. Our results show that geometrical nonlinearity affects entanglement as the optomechanical quantum interface.

Djorwé, Philippe; Engo, S. G. Nana; Woafo, Paul

2014-08-01

16

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

17

Gain scheduling for geometrically nonlinear flexible space structures  

E-print Network

A gain-scheduling approach for the control of geometrically nonlinear structures is developed. The objective is to improve performance over current linear design techniques that are applied to the same control problem. The ...

Yung, Jeremy Hoyt, 1971-

2002-01-01

18

Analysis of nonlinear dynamic response for delaminated fiber-metal laminated beam under unsteady temperature field  

NASA Astrophysics Data System (ADS)

The nonlinear dynamic response problems of fiber-metal laminated beams with delamination are studied in this paper. Basing on the Timoshenko beam theory, and considering geometric nonlinearity, transverse shear deformation, temperature effect and contact effect, the nonlinear governing equations of motion for fiber-metal laminated beams under unsteady temperature field are established, which are solved by the differential quadrature method, Nermark-? method and iterative method. In numerical examples, the effects of delamination length, delamination depth, temperature field, geometric nonlinearity and transverse shear deformation on the nonlinear dynamic response of the glass reinforced aluminum laminated beam with delamination are discussed in details.

Fu, Yiming; Chen, Yang; Zhong, Jun

2014-10-01

19

Possibilities and limitations of rod-beam theories. [nonlinear distortion tensor and nonlinear stress tensors  

NASA Technical Reports Server (NTRS)

Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.

Peterson, D.

1979-01-01

20

Geometrically nonlinear analysis of laminated elastic structures  

NASA Technical Reports Server (NTRS)

This final technical report contains three parts: Part 1 deals with the 2-D shell theory and its element formulation and applications. Part 2 deals with the 3-D degenerated element. These two parts constitute the two major tasks that were completed under the grant. Another related topic that was initiated during the present investigation is the development of a nonlinear material model. This topic is briefly discussed in Part 3. To make each part self-contained, conclusions and references are included in each part. In the interest of brevity, the discussions presented are relatively brief. The details and additional topics are described in the references cited.

Reddy, J. N.; Chandrashekhara, K.; Chao, W. C.

1993-01-01

21

Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector  

NASA Technical Reports Server (NTRS)

Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.

Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)

2001-01-01

22

Two-dimensional nonlinear beam shaping.  

PubMed

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion. PMID:22660146

Shapira, Asia; Shiloh, Roy; Juwiler, Irit; Arie, Ady

2012-06-01

23

Shuttle entry guidance revisited using nonlinear geometric methods  

NASA Astrophysics Data System (ADS)

The entry guidance law for the space shuttle orbiter is revisited using nonlinear geometric methods. The shuttle guidance concept is to track a reference drag trajectory that has been designed to lead a specified range and velocity. It is shown that the approach taken in the original derivation of the shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, an alternative, potentially superior, guidance law was formulated. Comparing the two guidance laws based performance domains in state space, taking into account the nonlinear dynamics, the alternative guidance law achieves the desired performance over larger domains in state space; the stability domain of the laws are similar. With larger operating domain for the shuttle or some other entry vehicle, the alternative guidance law should be considered.

Mease, Kenneth D.; Kremer, Jean-Paul

1994-11-01

24

Asynchronous variational Lie group integration for geometrically exact beam dynamics  

E-print Network

Asynchronous variational Lie group integration for geometrically exact beam dynamics F. Demoures1] is derived in the Lie group setting (SO (3) for the representation of rotational degrees of freedom, variational integrators, Lie group integrator, multi-time-step, dis- crete mechanics, geometric integration 1

Leyendecker, Sigrid

25

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

Microsoft Academic Search

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.

Adnan Ibrahimbegovic; Francois Frey

1994-01-01

26

Geometrically nonlinear analysis of layered composite plates and shells  

NASA Technical Reports Server (NTRS)

A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion.

Chao, W. C.; Reddy, J. N.

1983-01-01

27

A survey of the core-congruential formulation for geometrically nonlinear TL finite elements  

NASA Technical Reports Server (NTRS)

This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn

1994-01-01

28

Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections  

NASA Technical Reports Server (NTRS)

A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

29

Nonlinear flap-lag axial equations of a rotating beam  

NASA Technical Reports Server (NTRS)

It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.

Kaza, K. R. V.; Kvaternik, R. G.

1977-01-01

30

NON-LINEAR VIBRATIONS OF ROTATING CANTILEVER BEAMS: FINITE ELEMENTS VALIDATIONS OF VARIOUS REDUCED ORDER MODELS  

Microsoft Academic Search

The large amplitude non-linear vibratory behavior of a rotating cantilever beam is addressed in this study. The motivation of this work is to built a simplified model for analyzes of turbomachinery and turbopropeller blades vibrations in the geometrically non-linear regime. Since blades are designed more and more flexible, in particular when composite materials are used, quantifying the amount of non-

A. Senechal; O. Thomas; J.-F. Deü

31

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

32

Diffractive Nonlinear Geometrical Optics for Variational Wave Equations and the Einstein Equations  

E-print Network

We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly nonlinear geometrical optics for the Einstein equations with nonlinear geometrical optics theories for variational wave equations.

Giuseppe Ali; John K. Hunter

2005-11-02

33

Nonlinear analysis of a simply-supported composite beam under random excitations  

SciTech Connect

Nonlinear analysis of composite laminated beams subjected-to random excitation is studied here. The forcing function is a stationary Gaussian type random excitation. The governing partial differential equations of motion are obtained by considering the Von Karman type geometrical nonlinearity. These partial differential equations are transformed into nonlinear Ordinary differential equations of Duffing type by applying the Galerkin`s method. The resulting nonlinear ODE are first solved by using the equivalent linearization method and the numerical integration (Runge Kutta) method. The equations are reduced to that of isotropic beam and results are also compared with the previously published ones.

Eslami, H.; Gudmundson, S. [Embry-Riddle Aeronautical Univ., Daytona Beach, FL (United States)

1994-12-31

34

Hybrid analytical technique for the nonlinear analysis of curved beams  

NASA Technical Reports Server (NTRS)

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 fundamental unknowns, and their sensitivity derivatives with respect to material and geometric parameters of the beam, are first obtained by using the perturbation method. These functions are selected as coordinate functions (or modes) and the classical direct variational technique is then used to compute their amplitudes. The potential of the proposed hybrid technique for nonlinear analysis of structures is discussed. The effectiveness of the hybrid technique is demonstrated by means of numerical examples. The symbolic computation system Mathematica is used in the present study. The tasks performed on Mathematica include: (1) generation of algebraic expressions for the perturbation functions of the different response quantities and their sensitivity derivatives: and (2) determination of the radius of convergence of the perturbation series.

Noor, A. K.; Andersen, C. M.

1992-01-01

35

A numerical approach to directly compute nonlinear normal modes of geometrically nonlinear finite element models  

NASA Astrophysics Data System (ADS)

The nonlinear normal modes of a dynamical system provide a modal framework in which the dynamics of a structure can be readily understood. Current numerical approaches use continuation to find a nonlinear normal mode branch that initiates at a low energy, linearized mode. The predictor-corrector based approach follows the periodic solutions as the response amplitude increases, forming the nonlinear normal mode. This method uses the Jacobian of the shooting function in a Newton-Raphson algorithm to find the initial conditions and integration period that result in a periodic response of the conservative equations of motion. Large scale finite element models require that the Jacobian be computed using finite differences since the closed form equations are not explicitly available. The Jacobian must be computed with respect to all of the states, making the algorithm prohibitively expensive for models with many degrees-of-freedom. In this paper, the initial conditions of each periodic solution are determined based on a subset of the linear modes of a geometrically nonlinear finite element model. The first approach, termed enforced modal displacement, sets the initial conditions as a linear combination of linear mode shapes. The second approach, here called the applied modal force method, applies a static load to the structure in a combination of applied forces that would excite a single linear mode, computes the static response to that load, and uses that to set the initial conditions. Both of these algorithms greatly reduce the number of variables that are iterated on during continuation. As a result, the cost of computing each solution along the nonlinear normal mode is only on the order of ten times the cost required to integrate the finite element model over one period of the response. The algorithm is initiated with only one linear mode and additional modes are added in a systematic way as they become important to the periodic solutions along the nonlinear mode branch. The approach is demonstrated on two geometrically nonlinear finite element models, showing a dramatic reduction in the computational cost required to obtain the nonlinear normal mode.

Kuether, Robert J.; Allen, Matthew S.

2014-05-01

36

Numerically Generated Tangent Stiffness Matrices for Geometrically Non-Linear Structures  

NASA Astrophysics Data System (ADS)

The aim of this thesis is to develop a general numerical solution method for geometrically non-linear structures. Most common work involves tedious derivations of analytic tangent stiffness matrices. The major objective of the current work is to develop a numerically generated tangent stiffness matrix that allows for a general and easily implementable solution method. The thesis begins with the definition of the tangent stiffness matrix and a discussion of the Newton-Raphson incremental-iterative method typically used to solve geometrically non-linear problems. This is followed by a detailed description of how the tangent stiffness matrix is numerically generated using complex variable differentiation to approximate sensitivities. The thesis proceeds with details of the solution method applied to three different structural elements: 3D truss, membrane, and 3D beam. These discussions include numeric examples for each type of structure, the results of which are compared with the literature and ANSYS solutions. The results from the present work show that solutions obtained using the general numerically generated tangent stiffness matrix are accurate. While computational effort is increased, the method is especially attractive in the context of research involving small finite element models.

Lebofsky, Sonia

37

Dynamics of Airy beams in nonlinear media  

NASA Astrophysics Data System (ADS)

The dynamics of truncated Airy beams in optical media with Kerr nonlinearity is studied in the framework of the nonlinear Schrödinger (NLS) model. It is demonstrated that an intense Airy beam with zero total momentum can generate static solitons, as well as moving solitons. The parameters of these solitons are calculated using the Zakharov-Shabat scattering problem associated with the NLS equation. It is found that solitons take the main part of the initial power, while only a small fraction of the power is transformed into a self-accelerating linear packet. The threshold parameters of the Airy beam for the soliton formation are obtained. It is shown that the threshold for the formation of the first static soliton is also a threshold of the solitonless regime.

Allayarov, I. M.; Tsoy, E. N.

2014-08-01

38

Temperature modes for nonlinear Gaussian beams.  

PubMed

In assessing the influence of nonlinear acoustic propagation on thermal bioeffects, approximate methods for quickly estimating the temperature rise as operational parameters are varied can be very useful. This paper provides a formula for the transient temperature rise associated with nonlinear propagation of Gaussian beams. The pressure amplitudes for the Gaussian modes can be obtained rapidly using a method previously published for simulating nonlinear propagation of Gaussian beams. The temperature-mode series shows that the nth temperature mode generated by nonlinear propagation, when normalized by the fundamental, is weaker than the nth heat-rate mode (also normalized by the fundamental in the heat-rate series) by a factor of log(n)/n, where n is the mode number. Predictions of temperature rise and thermal dose were found to be in close agreement with full, finite-difference calculations of the pressure fields, temperature rise, and thermal dose. Applications to non-Gaussian beams were made by fitting the main lobe of the significant modes to Gaussian functions. PMID:19603899

Myers, Matthew R; Soneson, Joshua E

2009-07-01

39

A geometric calibration method for cone beam CT systems.  

PubMed

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 degrees). 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. PMID:16872077

Yang, Kai; Kwan, Alexander L C; Miller, DeWitt F; Boone, John M

2006-06-01

40

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

41

Ion beam formation in a low-pressure geometrically expanding argon plasma  

SciTech Connect

Supersonic ion beam formation has been observed in a geometrically expanding low-pressure inductively coupled argon plasma. It is found that the ion beam is only observed below 3 mTorr and only when the discharge is operated in inductive mode. The geometrical expansion of the plasma induces density and potential gradients leading to the ion beam formation. The ion beam energy increases with decreasing source tube radius. The results show that ion beam formation can be achieved by geometrical expansion alone and that the ion beam energy depends on the ratio of the cross-sectional area of the source and expansion region.

Corr, C. S.; Zanger, J.; Boswell, R. W.; Charles, C. [Space Plasma, Power, and Propulsion group, Research School of Physical Sciences and Engineering, Australian National University, Canberra, Australia Capital Territory 0200 (Australia)

2007-12-10

42

Geometrically non-linear vibration of spinning structures by finite element method  

Microsoft Academic Search

The geometrically non-linear steady state vibration of spinning structures is studied. Full flap-lag-torsional gyroscopic coupling effects are considered. The non-linearity arises mainly from the non-linear axial strain-displacement relation. The equations of motion are derived from Lagrangian equations. Spatial discretization is achieved by the finite element method and steady state nodal displacements are expanded into Fourier series. The harmonic balance method

A. Y. T. Leung; T. C. Fung

1990-01-01

43

Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media.  

PubMed

We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, the higher the intensities of interacting beams, the easier to form solitons; when the intensities are small enough, no solitons are generated. Upon adjusting the interval between the launched beams, their interaction exhibits different properties. If the interval is large relative to the width of the first lobes, the generated soliton pairs just propagate individually and do not interact much. However, if the interval is comparable to the widths of the maximum lobes, the pairs strongly interact and display varied behavior. PMID:24664064

Zhang, Yiqi; Beli?, Milivoj R; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Li, Yuanyuan; Zhang, Yanpeng

2014-03-24

44

Geometric manipulation of light : from nonlinear optics to invisibility cloaks  

E-print Network

In this work, we study two different manipulations of electromagnetic waves governed by macroscopic Maxwell's equations. One is frequency conversion of such waves using small intrinsic material nonlinearities. We study ...

Hashemi, Hila

2012-01-01

45

Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects  

NASA Technical Reports Server (NTRS)

The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.

Subrahmanyam, K. B.; Kaza, K. R. V.

1985-01-01

46

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

47

NONLINEAR DYNAMICS OF A CANTILEVER BEAM ACTUATED BY PIEZOELECTRIC LAYERS  

E-print Network

NONLINEAR DYNAMICS OF A CANTILEVER BEAM ACTUATED BY PIEZOELECTRIC LAYERS IN SYMMETRIC Dynamics of a Cantilever Beam Actuated by Piezoelectric Layers in Symmetric and Asymmetric Configuration K Abstract The nonlinear equations of motion for a cantilever beam, covered by piezoelectric PZT layers

Rimon, Elon

48

Multisymplectic Lie group variational integrator for a geometrically exact beam in R3  

E-print Network

Multisymplectic Lie group variational integrator for a geometrically exact beam in R3 François, and test a Lie group multisymplectic integrator for geometrically exact beams based on the covariant.V. All rights reserved. 1. Introduction In this paper we develop, study, and test a Lie group

Kobilarov, Marin

49

Development of geometrically-nonlinear finite element analysis for marine risers  

E-print Network

nonlinearities. The steady-state hydrodynamic drag loads quantified by Choo (6) are included to approximate the nonlinear tangential and normal drag forces act- ing upon a marine riser. The nonlinear solutions are calculated with a Modified Newton... , S;i . 6, s, i 'du+ 'r, , 6, ri;i 'du = 6'+ pI ? 'r;i 6, eef 'dv. (2. 5) Jiv By assuming that the nonlinear geometric strains, q, 3, have little contribution to the material strains and stresses, the Green-Lagrange strain tensor in the first term...

Haas, Mark Edward

2012-06-07

50

Nonlinear dynamics and chaos: Geometrical methods for engineers and scientists  

NASA Astrophysics Data System (ADS)

The fundamental principles of nonlinear dynamics are introduced, and a number of applications to specific physical and engineering problems are examined. Topics presented include nonlinear phenomena in damped and undamped, forced and unforced oscillators; point attractors and limit cycles in autonomous systems; periodic attractors in driven oscillators; chaotic attractors in forced oscillators; stability and bifurcations of equilibria and cycles; and iterated maps as dynamical systems. Consideration is given to the geometry of recurrence, the Lorenz system, Roessler's band, bifurcation geometry, the subharmonic resonances of an offshore structure, chaotic motions of an impacting system, the particle accelerator and Hamiltonian dynamics, and experimental observations of order and chaos.

Thompson, J. M. T.; Stewart, H. B.

51

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

52

An integrated approach to the synthesis of geometrically non-linear structures  

NASA Technical Reports Server (NTRS)

An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.

Smaoui, H.; Schmit, L. A.

1988-01-01

53

Geometric nonlinear analysis of microbeam under electrostatic loading  

E-print Network

This study investigates the behavior of a microbeam subjected to electrostatic loading. Two devices, namely, a tungsten microtweezer and a clamped-clamped beam which is part of a micro-electromechanical system (MEMS), are used as the vehicles...

Murgude, Nikhil C.

2012-06-07

54

Equivalent Linearization Analysis of Geometrically Nonlinear Random Vibrations Using Commercial Finite Element Codes  

NASA Technical Reports Server (NTRS)

Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.

Rizzi, Stephen A.; Muravyov, Alexander A.

2002-01-01

55

Geometrical phases and quantum numbers of solitons in nonlinear sigma-models  

Microsoft Academic Search

Solitons of a nonlinear field interacting with fermions often acquire a\\u000afermionic number or an electric charge if fermions carry a charge. We show how\\u000athe same mechanism (chiral anomaly) gives solitons statistical and rotational\\u000aproperties of fermions. These properties are encoded in a geometrical phase,\\u000ai.e., an imaginary part of a Euclidian action for a nonlinear sigma-model. In\\u000athe

A. G. Abanov; P. B. Wiegmann

2001-01-01

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

Geometrically nonlinear behaviour or spot welded joints in tensile and compressive shear loading  

Microsoft Academic Search

The geometrically nonlinear behaviour of spot welded joints including buckling and gap closure and its influence on local stress parameters at the weld spot edge (structural stresses, notch stress or fatigue notch factor, stress intensity factors) are determined by a large displacement analysis of the tensile shear specimen subjected to tensile and compressive loading. The local parameters mentioned are considered

D. Radaj; S. Zhang

1995-01-01

58

Stress resultant geometrically nonlinear shell theory with drilling rotations - Part 2. Computational aspects  

Microsoft Academic Search

In this work we discuss some details of the numerical implementation of the geometrically nonlinear shell theory presented in Part 1. Two possibilities to represent finite rotations, with an orthogonal matrix and with a rotation vector, are examined in detail, along with their mutual relationship in both spatial and material description. The issues pertinent to the consistent linearization procedure corresponding

Adnan Ibrahimbegovic; Francois Frey

1994-01-01

59

Stress resultant geometrically nonlinear shell theory with drilling rotations - Part 1. A consistent formulation  

Microsoft Academic Search

In this work we present a consistent theoretical framework for a novel stress resultant geometrically nonlinear shell theory. The main feature of the present shell theory development, which stands in contrast with the classical developments in the shell theory, is the presence of a rotation component around the shell normal (so called drilling rotation) in the description of shell finite

Adnan Ibrahimbegovic

1994-01-01

60

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

61

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

62

Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials  

NASA Astrophysics Data System (ADS)

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports.

Li, Nianbei; Ren, Jie

2014-08-01

63

Non-reciprocal geometric wave diode by engineering asymmetric shapes of nonlinear materials.  

PubMed

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports. PMID:25169668

Li, Nianbei; Ren, Jie

2014-01-01

64

Development of computer program NAS3D using Vector processing for geometric nonlinear analysis of structures  

NASA Technical Reports Server (NTRS)

An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.

Mangalgiri, P. D.; Prabhakaran, R.

1986-01-01

65

Application of the Cheng-Finnie method to the calculation of stress intensity factors in thin-walled pipes with long axial cracks with allowance for geometric nonlinearity  

Microsoft Academic Search

To calculate stress intensity factors in elastic pipes with long flaws, the known Cheng-Finnie method is used. A universal\\u000a description of the mode of behavior of beam is proposed, for which equations of the method of initial parameters with allowance\\u000a for geometric nonlinearity (effect of axial force on lateral deformation) have been derived and are employed. This allowed\\u000a us to

I. V. Orynyak; E. S. Yakovleva; V. V. Rozgonyuk

2007-01-01

66

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam  

NASA Technical Reports Server (NTRS)

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

67

Gaussian beam evolution in longitudinally and transversely inhomogeneous nonlinear fibres with absorption  

NASA Astrophysics Data System (ADS)

The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear Kerr type and saturable fibres. CGO reduces the problem of Gaussian beam evolution in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to other methods of nonlinear optics such as variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of Gaussian beam propagation in saturable fibres with either focusing and defocusing refractive profiles. Besides, the influence of initial curvature of the wave front, phenomenon of weak absorption and effect of either transverse and longitudinal inhomogeneity on GB propagation in nonlinear fibres is discussed in this paper.

Berczynski, P.

2013-09-01

68

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

69

Does the nonlinear Schrodinger equation correctly describe beam propagation?  

Microsoft Academic Search

This paper shows that in the analysis of nonlinear self-focusing (beam propagation) and self-guiding, the parabolic equation (nonlinear Schroedinger equation) of the standard approximation technique requires another term that takes into consideration the changes in the propagation constant along the direction of propagation, for a complete analytical description of the phenomena. The difference between application of the new technique and

Nail Akhmediev; Adrian Ankiewicz; Jose Maria Soto-Crespo

1993-01-01

70

Nonlinear Responses of Buckled Beams to Subharmonic-Resonance Excitations  

Microsoft Academic Search

We investigated theoretically and experimentally the nonlinear responseof a clamped-clamped buckled beam to a subharmonic resonance of orderone-half of its first vibration mode. We used a multi-mode Galerkindiscretization to reduce the governing nonlinear partial-differentialequation in space and time into a set of nonlinearly coupledordinary-differential equations in time only. We solved the discretizedequations using the method of multiple scales to obtain

Samir A. Emam; Ali H. Nayfeh

2004-01-01

71

Geometrically non-linear vibration of spinning structures by finite element method  

NASA Astrophysics Data System (ADS)

The geometrically non-linear steady state vibration of spinning structures is studied. Full flap-lag-torsional gyroscopic coupling effects are considered. The non-linearity arises mainly from the non-linear axial strain-displacement relation. The equations of motion are derived from Lagrangian equations. Spatial discretization is achieved by the finite element method and steady state nodal displacements are expanded into Fourier series. The harmonic balance method gives a set of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The non-linear algebraic equations are solved by a Newtonian algorithm iteratively. The importance of the conditions of completeness and balanceability in choosing the number of harmonic terms to be used is discussed. General frame structures with arbitrary orientation in a rotating frame can be investigated by the present method. Rotating blades and shafts are treated as special cases. Examples of a rotating ring with different orientations are given. The non-linear amplitude-frequency relation can be constructed parametrically.

Leung, A. Y. T.; Fung, T. C.

1990-05-01

72

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations  

NASA Technical Reports Server (NTRS)

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

Tessler, Alexander; Sleight, David W.

2006-01-01

73

Static analysis of offshore risers with a geometrically-exact 3D beam model subjected to unilateral contact  

NASA Astrophysics Data System (ADS)

In offshore applications there are elements that can be modeled as long beams, such as umbilical cables, flexible and rigid pipes and hoses, immersed in the sea water, suspended from the floating unit to the seabed. The suspended part of these elements is named "riser" and is subjected to the ocean environment loads, such as waves and sea current. This work presents a structural geometrically-exact 3D beam model, discretized using the finite element method for riser modeling. An updated Lagrangian framework for the rotation parameterization has been used for the description of the exact kinematics. The goal is to perform a complete static analysis, considering the oceanic loads and the unilateral contact with the seabed, extending the current standard analysis for situations in which very large rotations occurs, in particular, large torsion. Details of the nonlinear 3D model and loads from oceanic environment are discussed, including the contact unilateral constraint.

Neto, Alfredo Gay; Martins, Clóvis A.; Pimenta, Paulo M.

2014-01-01

74

Analysis of Pull-In Instability of Geometrically Nonlinear Microbeam Using Radial Basis Artificial Neural Network Based on Couple Stress Theory  

PubMed Central

The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS. PMID:24860602

Heidari, Mohammad; Heidari, Ali; Homaei, Hadi

2014-01-01

75

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

76

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures  

NASA Technical Reports Server (NTRS)

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.

1991-01-01

77

Topology optimization of geometrically nonlinear structures including thermo-mechanical coupling  

NASA Astrophysics Data System (ADS)

The goal of this research is to develop an efficient and robust methodology for the topology optimization of geometrically nonlinear structures actuated by thermal expansion. The corotational finite element method is used to model the geometric nonlinearity because its element independent nature and linear elastic element core provide a flexibility to introduce thermal loads and formulate analytical sensitivities for any element type. To create thermal expansion, this work uses both prescribed temperature changes and localized heat generation via Joule heating, where electrical and thermal conduction are additionally considered. In this coupled multi-physics problem, emphasis is put on material models and coupling to maintain accuracy and efficiency. One-way coupling is shown to be equivalent to a small strain assumption, and the proper modeling of convection properties in topology optimization is addressed. To model the thermal and electrical conduction in planar layered materials, an averaged (smeared) model based on the smoothed properties of the individual layers is introduced. Large displacement structures are prone to exhibit buckling and limit point behavior. To include instabilities in topology optimization, specialized techniques are introduced to overcome inherent numerical difficulties. A nodal density transformation is introduced to isolate structurally relevant eigenmodes, and a homotopy between linear and nonlinear finite elements is provided to limit the effects of mesh distortion. The proposed methodology is successfully applied to micro-mechanism applications capable of a three-dimensional range of motion, including novel designs reflective of the manufacturing technology used in the micro-electro-mechanical (MEMS) community.

Pajot, Joseph M.

78

Iterative nonlinear beam propagation method and its application in nonlinear devices  

E-print Network

In this thesis, an iterative nonlinear beam propagation method is introduced and applied to optical devices. This method is based on Hamiltonian ray tracing and the Wigner distribution function. First, wave propagation ...

Gao, Hanhong

2011-01-01

79

A Geometrically Exact Active Beam Theory for Multibody Dynamics Simulation  

E-print Network

. Various examples for both static and dynamic behavior of composite beams with embedded or attached fiber composites in a multibody dynamics code MBDyn to develop an integrated tool for aeroelastic mechanisms with piezoelectric sensors and actuators. Straub and Charles11 developed an aeroelastic analysis

Yu, Wenbin

80

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

81

A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity  

NASA Astrophysics Data System (ADS)

In this paper a new boundary element method formulation for elastoplastic analysis of plates with geometrical nonlinearities is presented. The von Mises criterion with linear isotropic hardening is considered to evaluate the plastic zone. Large deflections are assumed but within the context of small strain. To derive the boundary integral equations the von Kármán’s hypothesis is taken into account. An initial stress field is applied to correct the true stresses according to the adopted criterion. Isoparametric linear elements are used to approximate the boundary unknown values while triangular internal cells with linear shape function are adopted to evaluate the domain value influences. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator derived along the paper. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

Waidemam, Leandro; Venturini, Wilson Sergio

2010-03-01

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. PMID:23226584

Calderhead, Ben; Girolami, Mark

2011-01-01

83

Multisymplectic Lie group variational integrator for a geometrically exact beam in R3  

NASA Astrophysics Data System (ADS)

In this paper we develop, study, and test a Lie group multisymplectic integrator for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum map conservations associated to the temporal and spatial discrete evolutions.

Demoures, François; Gay-Balmaz, François; Kobilarov, Marin; Ratiu, Tudor S.

2014-10-01

84

Accurate technique for complete geometric calibration of cone-beam computed tomography systems.  

PubMed

Cone-beam computed tomography systems have been developed to provide in situ imaging for the purpose of guiding radiation therapy. Clinical systems have been constructed using this approach, a clinical linear accelerator (Elekta Synergy RP) and an iso-centric C-arm. Geometric calibration involves the estimation of a set of parameters that describes the geometry of such systems, and is essential for accurate image reconstruction. We have developed a general analytic algorithm and corresponding calibration phantom for estimating these geometric parameters in cone-beam computed tomography (CT) systems. The performance of the calibration algorithm is evaluated and its application is discussed. The algorithm makes use of a calibration phantom to estimate the geometric parameters of the system. The phantom consists of 24 steel ball bearings (BBs) in a known geometry. Twelve BBs are spaced evenly at 30 deg in two plane-parallel circles separated by a given distance along the tube axis. The detector (e.g., a flat panel detector) is assumed to have no spatial distortion. The method estimates geometric parameters including the position of the x-ray source, position, and rotation of the detector, and gantry angle, and can describe complex source-detector trajectories. The accuracy and sensitivity of the calibration algorithm was analyzed. The calibration algorithm estimates geometric parameters in a high level of accuracy such that the quality of CT reconstruction is not degraded by the error of estimation. Sensitivity analysis shows uncertainty of 0.01 degrees (around beam direction) to 0.3 degrees (normal to the beam direction) in rotation, and 0.2 mm (orthogonal to the beam direction) to 4.9 mm (beam direction) in position for the medical linear accelerator geometry. Experimental measurements using a laboratory bench Cone-beam CT system of known geometry demonstrate the sensitivity of the method in detecting small changes in the imaging geometry with an uncertainty of 0.1 mm in transverse and vertical (perpendicular to the beam direction) and 1.0 mm in the longitudinal (beam axis) directions. The calibration algorithm was compared to a previously reported method, which uses one ball bearing at the isocenter of the system, to investigate the impact of more precise calibration on the image quality of cone-beam CT reconstruction. A thin steel wire located inside the calibration phantom was imaged on the conebeam CT lab bench with and without perturbations in source and detector position during the scan. The described calibration method improved the quality of the image and the geometric accuracy of the object reconstructed, improving the full width at half maximum of the wire by 27.5% and increasing contrast of the wire by 52.8%. The proposed method is not limited to the geometric calibration of cone-beam CT systems but can be used for many other systems, which consist of one or more point sources and area detectors such as calibration of megavoltage (MV) treatment system (focal spot movement during the beam delivery, MV source trajectory versus gantry angle, the axis of collimator rotation, and couch motion), cross calibration between Kilovolt imaging and MV treatment system, and cross calibration between multiple imaging systems. Using the complete information of the system geometry, it was demonstrated that high image quality in CT reconstructions is possible even in systems with large geometric nonidealities. PMID:15895580

Cho, Youngbin; Moseley, Douglas J; Siewerdsen, Jeffrey H; Jaffray, David A

2005-04-01

85

Beam tapering effect in microsphere chains: from geometrical to physical optics  

NASA Astrophysics Data System (ADS)

By using polystyrene microspheres with index n=1.59 as a model system we study light focusing and transport properties of chains formed by spheres with diameters varying from 2 to 30 ?m. We used techniques of imaging based on light scattering perpendicular to the axis of the chain to visualize and study periodically focused beams in such structures. The results demonstrate good agreement with geometrical optics modeling for sufficiently large spheres, D>>10?, where D is the sphere diameter and ? is the wavelength of light. For mesoscale structures with 4><10 we observed two effects which cannot be explained by geometrical optics. One is a "beam tapering" effect which is stronger in normalized units than it is theoretically possible in the limit of geometrical optics in short chains. Another effect is reduced power attenuation in sufficiently long chains which is found to be smaller than it is possible in the limit of geometrical optics. Both effects are ascribed to the increased role of physical optics properties. We can also suggest some role of the microjoints developing between polystyrene microspheres in self-assembled structures. The results are important for developing applications requiring focusing of multimodal beams such as mid-infrared laser surgery.

Allen, Kenneth W.; Darafsheh, Arash; Astratov, Vasily N.

2012-02-01

86

A shear-shear torsional beam model for nonlinear aeroelastic analysis of tower buildings  

NASA Astrophysics Data System (ADS)

In this paper, an equivalent one-dimensional beam model immersed in a three-dimensional space is proposed to study the aeroelastic behavior of tower buildings: linear and nonlinear dynamics are analyzed through a simple but realistic physical modeling of the structure and of the load. The beam is internally constrained, so that it is capable to experience shear strains and torsion only. The elasto-geometric and inertial characteristics of the beam are identified from a discrete model of three-dimensional frame, via a homogenization process. The model accounts for the torsional effect induced by the rotation of the floors around the tower axis; the macroscopic shear strain is produced by bending of the columns, accompanied by negligible rotation of the floors. Nonlinear aerodynamic forces are evaluated through the quasi-steady theory. The first aim is to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions. Furthermore, the role of aerodynamic nonlinearities on the galloping post-critical behavior is analyzed through a perturbation solution which permits to obtain a reduced one-dimensional dynamical system, capable of capturing the essential dynamics of the problem.

Piccardo, G.; Tubino, F.; Luongo, A.

2014-09-01

87

Beam-driven linear and nonlinear THz source technology  

NASA Astrophysics Data System (ADS)

Advances in dielectric resonators and materials have arisen in the context of research into new particle acceleration techniques. In the wakefield accelerator, electromagnetic fields excited by an electron beam in a low loss dielectric structure are used to accelerate a second, trailing beam to high energy. Energy can be efficiently extracted from the beam in this manner and thus the accelerating structure can also be used as an RF source, with frequencies extending into the THz. New ferroelectrics are also finding significant uses in this technology; some of the applications discussed are nonlinear frequency multiplication and frequency agile (tunable) cavities.

Schoessow, Paul; Kanareykin, Alexei; Jing, C.; Baturin, Stanislav

2012-05-01

88

p-Version curved shell element for geometrically nonlinear analysis of laminated composite plates and shells  

SciTech Connect

This paper presents a p-version geometrically nonlinear formulation for laminated composites based on the total Lagrangian approach for a nine node three dimensional curved shell element. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the element and in the transverse direction. The element approximation functions are derived from the Lagrange family of interpolation functions and ensure C{degree} continuity. The lamina properties are incorporated by numerically integrating the element stiffness matrix for each lamina. Complete three dimensional stresses and strains are considered. Incremental equations of equilibrium are derived and solved using the standard Newton-Raphson method. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation.

Sorem, R.M.; Surana, K.S. [Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering

1997-07-01

89

Novel solutions to low-frequency problems with geometrically designed beam-waveguide systems  

NASA Technical Reports Server (NTRS)

The poor low-frequency performance of geometrically designed beam-waveguide (BWG) antennas is shown to be caused by the diffraction phase centers being far from the geometrical optics mirror focus, resulting in substantial spillover and defocusing loss. Two novel solutions are proposed: (1) reposition the mirrors to focus low frequencies and redesign the high frequencies to utilize the new mirror positions, and (2) redesign the input feed system to provide an optimum solution for the low frequency. A novel use of the conjugate phase-matching technique is utilized to design the optimum low-frequency feed system, and the new feed system has been implemented in the JPL research and development BWG as part of a dual S-/X-band (2.3 GHz/8.45 GHz) feed system. The new S-band feed system is shown to perform significantly better than the original geometrically designed system.

Imbriale, W. A.; Esquivel, M. S.; Manshadi, F.

1995-01-01

90

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

91

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

92

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

PubMed

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane. PMID:25361057

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

2014-11-21

93

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. PMID:21639933

2011-01-01

94

A higher-order theory for geometrically nonlinear analysis of composite laminates  

NASA Technical Reports Server (NTRS)

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Reddy, J. N.; Liu, C. F.

1987-01-01

95

Dynamic response of laminated open deep shells using a geometrically nonlinear theory  

SciTech Connect

In this paper a geometrically nonlinear theory for the analysis of open deep laminated shell panels is presented. The parabolic variation of the transverse shear stresses through the thickness of the shell and the effects of rotary inertia are included in the formulation. The linear and nonlinear stiffness matrices are derived using orthogonal curvilinear coordinate system for a general doubly curved deep laminated shell. The shell`s middle surface displacement and rotation components are modeled using Bezier surface patches and the resulting equation of motion is solved to obtain the transient response, using Beta-m time integration and Newton-Raphson iterations. A very good convergence of the responses is observed by using only the fifth order Bezier surface patches. The dynamic responses of cross-ply laminated circular and noncircular cylindrical panels pinned at the straight edges under a central point load are studied. The effect of the eccentricity on the dynamic response of noncircular cylindrical panels having same plane form as the circular cylindrical panel is also examined.

Kumar, V.; Singh, A.V. [Univ. of Western Ontario, London, Ontario (Canada). Dept. of Mechanical Engineering

1995-11-01

96

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

97

Use of off-axis injection as an alternative to geometrically merging beams in an energy-recovering linac  

SciTech Connect

A method of using off-axis particle beam injection in energy-recovering linear accelerators that increases operational efficiency while eliminating the need to merge the high energy re-circulating beam with an injected low energy beam. In this arrangement, the high energy re-circulating beam and the low energy beam are manipulated such that they are within a predetermined distance from one another and then the two immerged beams are injected into the linac and propagated through the system. The configuration permits injection without geometric beam merging as well as decelerated beam extraction without the use of typical beamline elements.

Douglas, David R. (York County, VA)

2012-01-10

98

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

99

Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades  

NASA Technical Reports Server (NTRS)

The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.

Subrahmanyam, K. B.; Kaza, K. R. V.

1986-01-01

100

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

101

Direct determination of cone-beam geometric parameters using the helical phantom  

NASA Astrophysics Data System (ADS)

Estimation of a set of parameters that describe the geometry of the cone-beam computed tomography system plays an important role in the geometrical calibration. In the calibration process, the helical phantom consisting of spherical markers arranged on a helical trajectory has been widely applied. To directly determine the complete nine geometric calibration parameters using the helical phantom, we propose a novel calibration method using explicit mathematical formulae. In the method, the geometric characteristics of the helix are utilized by converting the helix to delicately designed parallelograms. Then, the projections of the intersection points of the diagonals of parallelograms are obtained and used to identify the projections of the phantom coordinate axes, which are integrated into the calibration algorithm to calculate the geometric parameters. Our method makes full use of the markers, and has the property that flexible selection of the phantom coordinate system, which can deal with degenerate cases. To validate this method, simulation studies with various system geometries, different number of markers and different noise types are performed. A comparison of our proposed method with projection matrix method is also presented. The results show that our method can provide comparable accuracy of parameter estimation with the projection matrix method. The estimation of piercing points is even better using our method, which shows a factor of 8 × error reduction. The small animal studies also verify the accuracy and robustness of the proposed method.

Xu, M.; Zhang, C.; Liu, X.; Li, D.

2014-10-01

102

Extreme nonlinear optical processes with beams carrying orbital angular momentum  

NASA Astrophysics Data System (ADS)

Light beams carrying an isolated point singularity with a screw-type phase distribution are called an optical vortex (OV). The fact that in free space the Poynting vector of the beam gives the momentum flow leads to an orbital angular momentum (OAM) of the photons in such a singular beam, independent on the spin angular momentun1. There are many applications of optical OAM shown in literature that would benefit from the availability of optical vortex beams in all spectral regions. For example it was shown that transitions forbidden by selection rules in dipole approximation appear allowed when using photons with the additional degree of freedom of optical OAM2. However, the common techniques of producing new light frequencies by nonlinear optical processes seem problematic in conserving the optical vortex when the nonlinearity becomes large. We show that with the extremely nonlinear process of High Harmonic Generation (HHG) it is possible to transfer OVs from the near-infrared to the extreme ultraviolet (XUV)3 at wavelengths down to ~30 nm. The observed XUV light was examined spatially and spectrally. The spatial profile showed the expected singular behavior, a dark region in the center. A comparison of the far-field fringe pattern caused by a thin wire with corresponding simulations suggests that the XUV vortex beam carries a unit topological charge. A screw-like phase evolution around the profile was also verified by employing a Hartmann type measurement. The generated spectrum revealed that in all Harmonic orders an OV was present. The profile, however, looked the same in all orders, indicating identical topological charge, which runs counterintuitive to the assumption that the phase of exp(-il?) is multiplied by the harmonic order in a frequency up-conversion experiment.

Kern, C.; Zürch, M.; Hansinger, P.; Dreischuh, A.; Spielmann, Ch.

2014-03-01

103

Nonlinear geometric optics for contact discontinuities in three dimensional compressible isentropic steady flows  

NASA Astrophysics Data System (ADS)

In this paper, the stability of supersonic contact discontinuities in the three-dimensional compressible isentropic steady Euler flows is investigated by using the nonlinear geometric optics. We construct the asymptotic expansions of highly oscillatory contact discontinuities when a planar contact discontinuity is perturbed by a small amplitude high frequency oscillatory incident wave, and deduce there exists a large amplification of amplitudes in the reflected and refracted oscillatory waves when the high frequency oscillatory wave strikes the contact discontinuity front at three critical angles. Moreover, we obtain that the leading profiles of highly oscillatory waves are described by an initial boundary value problem of Burgers-transport equations, and the leading profile of contact discontinuity front satisfies an initial value problem of a Hamilton-Jacobi equation, respectively. The amplification phenomenon shows that this supersonic contact discontinuity is only weakly stable in the sense of Wang and Yu ["Stability of contact discontinuities in three-dimensional compressible steady flows," J. Differ. Equ. 255, 1278-1356 (2013)].

Wang, Ya-Guang; Yu, Fang

2014-09-01

104

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

SciTech Connect

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; Poli, Emanuele [Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748 Garching (Germany); Mariani, Alberto [Istituto di Fisica del Plasma 'P. Caldirola,' Consiglio Nazionale delle Ricerche, EURATOM-ENEA-CNR Association, via R. Cozzi 53, I-20125 Milano (Italy); Universita degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, 20133 Milano (Italy); Farina, Daniela [Istituto di Fisica del Plasma 'P. Caldirola,' Consiglio Nazionale delle Ricerche, EURATOM-ENEA-CNR Association, via R. Cozzi 53, I-20125 Milano (Italy)

2013-04-15

105

Nonlinear theory of the orotron with inclined electron beam  

SciTech Connect

In the conventional orotron (at least, in its classical configuration), a thickness of an electron beam propagating over the grating plate should be much smaller than a wavelength; also the clearance between the grating and the beam and possible misalignment should be smaller than this thickness. These requirements severely limit the choice of operating parameters and performance characteristics of this device. When a beam is slightly inclined to the grating surface, these limitations can be greatly mitigated: the operation can be more robust, beam thickness can be increased, so a higher microwave power can be generated. Such a configuration of the orotron with an inclined electron beam is studied in the present paper. The paper contains simplified equations describing nonlinear operation of such a device and results of numerical analysis of these equations with the electron velocity spread taken into account. The paper also contains a discussion of these results and their applicability to practical configurations, which can be designed for operation in the THz and sub-THz regions.

Nusinovich, G. S.; Sinitsyn, O. V. [Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742-3511 (United States)

2006-12-15

106

Shakedown analysis of beams using nonlinear kinematic hardening materials coupled with continuum damage mechanics  

Microsoft Academic Search

The nonlinear kinematic hardening theory of plasticity based on the Armstrong–Fredrick model and isotropic damage was used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. Damage and inelastic deformation were incorporated and they were used for the beam shakedown and ratcheting analysis. The beam material was assumed to follow the nonlinear strain

A. Nayebi; R. El Abdi

2008-01-01

107

A new pre-loaded beam geometric stiffness matrix with full rigid body capabilities  

NASA Technical Reports Server (NTRS)

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis.

Bosela, P. A.; Fertis, D. G.; Shaker, F. J.

1992-01-01

108

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

109

Filamentation and supercontinuum generation by singular beams in self-focusing nonlinear media  

E-print Network

Filamentation and supercontinuum generation by singular beams in self-focusing nonlinear media and supercontinuum generation. Our results show that the singular beams survive the process of mod- ulation] and supercontinuum (SC) generation [8]. Nonlinear optics benefits greatly from the development of ultra

Dreischuh, Alexander

110

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

111

Geometric calibration of a mobile C-arm for intraoperative cone-beam CT.  

PubMed

A geometric calibration method that determines a complete description of source-detector geometry was adapted to a mobile C-arm for cone-beam computed tomography (CBCT). The non-iterative calibration algorithm calculates a unique solution for the positions of the source (X(s), Y(s), Z(s)), detector (X(d), Y(d), Z(d)), piercing point (U(o), V(o)), and detector rotation angles (phi, theta, eta) based on projections of a phantom consisting of two plane-parallel circles of ball bearings encased in a cylindrical acrylic tube. The prototype C-arm system was based on a Siemens PowerMobil modified to provide flat-panel CBCT for image-guided interventions. The magnitude of geometric nonidealities in the source-detector orbit was measured, and the short-term (approximately 4 h) and long-term (approximately 6 months) reproducibility of the calibration was evaluated. The C-arm exhibits large geometric nonidealities due to mechanical flex, with maximum departures from the average semicircular orbit of deltaU(o) = 15.8 mm and deltaV(o) = 9.8 mm (for the piercing point), deltaX and deltaY = 6-8 mm and deltaZ = 1 mm (for the source and detector), and deltaphi approximately 2.9 degrees, deltatheta approximately 1.9 degrees, and delta eta approximately 0.8 degrees (for the detector tilt/rotation). Despite such significant departures from a semicircular orbit, these system parameters were found to be reproducible, and therefore correctable by geometric calibration. Short-term reproducibility was < 0.16 mm (subpixel) for the piercing point coordinates, < 0.25 mm for the source-detector X and Y, < 0.035 mm for the source-detector Z, and < 0.02 degrees for the detector angles. Long-term reproducibility was similarly high, demonstrated by image quality and spatial resolution measurements over a period of 6 months. For example, the full-width at half-maximum (FWHM) in axial images of a thin steel wire increased slightly as a function of the time (delta) between calibration and image acquisition: FWHM=0.62, 0.63, 0.66, 0.71, and 0.72 mm at delta = 0 s, 1 h, 1 day, 1 month, and 6 months, respectively. For ongoing clinical trials in CBCT-guided surgery at our institution, geometric calibration is conducted monthly to provide sufficient three-dimensional (3D) image quality while managing time and workflow considerations of the calibration and quality assurance process. The sensitivity of 3D image quality to each of the system parameters was investigated, as was the tolerance to systematic and random errors in the geometric parameters, showing the most sensitive parameters to be the piercing point coordinates (U(o), V(o)) and in-plane positions of the source (X(s), Y(s)) and detector (X(d), Y(d)). Errors in the out-of-plane position of the source (Z(s)) and detector (Z(d)) and the detector angles (phi, theta, eta) were shown to have subtler effects on 3D image quality. PMID:18561688

Daly, M J; Siewerdsen, J H; Cho, Y B; Jaffray, D A; Irish, J C

2008-05-01

112

Fast Calculations in Nonlinear Collective Models of Beam/Plasma Physics  

E-print Network

We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for solutions which allow to consider polynomial and rational type of nonlinearities. The solutions are represented via the multiscale decomposition in nonlinear high-localized eigenmodes (waveletons).

Antonina N. Fedorova; Michael G. Zeitlin

2002-12-31

113

A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation  

NASA Technical Reports Server (NTRS)

A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.

Crivelli, Luis A.; Felippa, Carlos A.

1992-01-01

114

Z-scan characterization of optical nonlinearities of an imperfect sample profits from radially polarized beams  

NASA Astrophysics Data System (ADS)

We present the Z-scan technique using azimuthal-variant vector beams for characterizing the nonlinear refractive index of an isotropic nonlinear medium. Compared with the conventional Z-scan measurements, the reliability of the vector beam Z-scan is improved because the focused azimuthal-variant vector beam exhibits a uniform-intensity focal ring instead of a focal spot. Experimentally, our investigation demonstrates that the Z-scan using radially polarized beams is a preferable technique for characterizing the optical nonlinearity of an imperfect sample.

Gu, Bing; Liu, Dahui; Wu, Jia-Lu; He, Jun; Cui, Yiping

2014-10-01

115

Numerical Investigation of Reinforced Concrete Frames Considering Nonlinear Geometric, Material and Time Dependent Effects with Incremental Construction Loadings  

NASA Astrophysics Data System (ADS)

Reliable prediction of forces, stresses, and deflections in reinforced concrete structures has long been the goal of structural engineers. In fact analytical determination of the displacements, internal forces, stresses and deformations of reinforced concrete structures throughout their load histories has been complicated by a number of factors. Non homogeneity of the material, continuously changing topology of the structural system due to cracking of concrete under increasing loads, nonlinear stress-strain relationship of concrete and reinforcing steel, variation of concrete deformations due to creep, shrinkage, and applied load history are classified as complicating factors. Due to mentioned difficulties, engineers in the past have been relying heavily on empirical formulas derived from numerous experiments for the design of concrete structures. In this study, it has been tried to determine the real behavior and vulnerability of reinforced concrete frames in the basis of developed numerical nonlinear analytical procedure, considering nonlinear response of the structure. In fact, in order to obtain more accurate results, material and geometric nonlinearities plus time dependent effects of creep and shrinkage in addition to incremental construction loadings are included in the analyses. More over the structural response of the structure is traced through its elastic, inelastic and ultimate load ranges. The analyses are adopted with a finite element displacement formulation coupled with a time step integration solution. Also an incremental and iterative scheme based upon a constant imposed displacement is used so that local instabilities or strain softening can also be analyzed accurately.

Esmaili, Omid; Epackachi, Siamak; Mirghaderi, Rasoul; Behbahani, Ali A. Taheri

2008-07-01

116

Geometric Smoothing of 3D Surfaces and Nonlinear Diffusion of 3D Images  

E-print Network

Geometric Smoothing of 3D Surfaces and Non­linear Diffusion of 3D Images Technical Report LEMS­144 for them. Keywords: Shape representation, deformation, scale, 3D smoothing, curvature dependent flow and formal theorems about its smoothing properties, the development of a similar process in 3D has been

117

Geometric Smoothing of 3D Surfaces and Non-linear Diffusion of 3D Images  

Microsoft Academic Search

In this paper we present a geometric smoothing technique for three-dimensional surfacesand images. The technique relies on curvature-dependent deformations of surfaces and theintuition that highly curved regions should move into their convexity by an amount proportionalto their curvature. While this intuition in 2D has lead to a well-defined process andformal theorems about its smoothing properties, the development of a similar

Predrag Neskovic; Benjamin B. Kimia

1995-01-01

118

A quasi-discrete Hankel transform for nonlinear beam propagation  

NASA Astrophysics Data System (ADS)

We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion (DQDHT) in this paper. By making use of the property that the zero-order Bessel function derivative J'0(0) = 0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parseval theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.

You, Kai-Ming; Wen, Shuang-Chun; Chen, Lie-Zun; Wang, You-Wen; Hu, Yong-Hua

2009-09-01

119

Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium  

SciTech Connect

Propagation of an asymmetric Gaussian beam in a cubic-quintic absorbing medium is analyzed and compared with that of a symmetric beam in both lossless and lossy media. A 'collective variable approach' technique, based on trial functions, is used for solution of the general nonlinear Schroedinger equation. Using this variational approach, we investigate the self-focusing and breathing of an intense asymmetric Gaussian beam, taking into account both linear and nonlinear absorption. For a lossless medium, we define regions of oscillatory and diffractive beam propagation, for both symmetric and asymmetric beams. In particular, for an asymmetric beam, we find that there is no sharp boundary between the oscillatory self-focusing and oscillatory diffractive regimes of propagation. In the oscillatory region, we detect an interesting phenomenon -'beats' of the amplitude and perpendicular widths of the beam. For a lossy medium, significant differences between the amplitudes, widths, and phases of the symmetric and asymmetric beams have been predicted.

Ianetz, D.; Kaganovskii, Yu.; Rosenbluh, M. [Jack and Pearl Resnick Institute for Advanced Technology, Department of Physics, Bar-Ilan University, Ramat-Gan 52900 (Israel); Wilson-Gordon, A. D. [Department of Chemistry, Bar-Ilan University, Ramat Gan 52900 (Israel)

2010-05-15

120

Electrocardiogram analysis using a combination of statistical, geometric, and nonlinear heart rate variability features  

Microsoft Academic Search

ObjectiveThe paper addresses a common and recurring problem of electrocardiogram (ECG) classification based on heart rate variability (HRV) analysis. Current understanding of the limits of HRV analysis in diagnosing different cardiac conditions is not complete. Existing research suggests that a combination of carefully selected linear and nonlinear HRV features should significantly improve the accuracy for both binary and multiclass classification

Alan Jovic; Nikola Bogunovic

2011-01-01

121

Materially & Geometrically Nonlinear Woven Composite Micro-mechanical Model with Failure for Finite Element Simulations  

Microsoft Academic Search

A computational micro-mechanical material model of woven fabric composite material is developed to simulate failure. The material model is based on repeated unit cell approach. The fiber reorientation is accounted for in the effective stiffness calculation. Material non-linearity due to the shear stresses in the impregnated yarns and the matrix material is included in the model. Micro- mechanical failure criteria

Ala Tabiei; Ivelin Ivanov

122

Two-dimensional simulations of nonlinear beam-plasma interaction in isotropic and magnetized plasmas  

E-print Network

Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide two-dimensional wave spectrum is driven unstable, and we also study how nonlinear evolution of these structures is affected by the external magnetic field. In the case of isotropic plasma, nonlinear buildup of filamentation modes due to the combined effects of two-stream and oblique instabilities is found to exist and growth mechanisms of secondary instabilities destroying the BGK--type nonlinear wave are identified. In the weak magnetic field, the energy of beam-excited plasma waves at the nonlinear stage of beam-plasma interaction goes predominantly to the short-wavelength upper-hybrid waves propagating parallel to the magnetic field, whereas in the strong magnetic field the spectral energy is transferred to the electrostatic whistlers with oblique propagation.

Timofeev, I V

2012-01-01

123

Varying degrees of nonlinear mechanical behavior arising from geometric differences of urogynecological meshes.  

PubMed

Synthetic polypropylene meshes were designed to restore pelvic organ support for women suffering from pelvic organ prolapse; however, the FDA released two notifications regarding potential complications associated with mesh implantation. Our aim was to characterize the structural properties of Restorelle and UltraPro subjected to uniaxial tension along perpendicular directions, and then model the tensile behavior of these meshes utilizing a co-rotational finite element model, with an imbedded linear or fiber-recruitment local stress-strain relationship. Both meshes exhibited a highly nonlinear stress-strain behavior; Restorelle had no significant differences between the two perpendicular directions, while UltraPro had a 93% difference in the low (initial) stiffness (p=0.009) between loading directions. Our model predicted that early alignment of the mesh segments in the loading direction and subsequent stretching could explain the observed nonlinear tensile behavior. However, a nonlinear stress-strain response in the stretching regime, that may be inherent to the mesh segment, was required to better capture experimental results. Utilizing a nonlinear fiber recruitment model with two parameters A and B, we observed improved agreement between the simulations and the experimental results. An inverse analysis found A=120 MPa and B=1.75 for Restorelle (RMSE=0.36). This approach yielded A=30 MPa and B=3.5 for UltraPro along one direction (RMSE=0.652), while the perpendicular orientation resulted in A=130 MPa and B=4.75 (RMSE=4.36). From the uniaxial protocol, Restorelle was found to have little variance in structural properties along these two perpendicular directions; however, UltraPro was found to behave anisotropically. PMID:25011619

Feola, Andrew; Pal, Siladitya; Moalli, Pamela; Maiti, Spandan; Abramowitch, Steven

2014-08-22

124

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

125

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

NASA Technical Reports Server (NTRS)

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.

Baddourah, Majdi A.; Nguyen, Duc T.

1993-01-01

126

Fundamental radiological and geometric performance of two types of proton beam modulated discrete scanning systems  

SciTech Connect

Purpose: The purpose of this investigation was to compare and contrast the measured fundamental properties of two new types of modulated proton scanning systems. This provides a basis for clinical expectations based on the scanned beam quality and a benchmark for computational models. Because the relatively small beam and fast scanning gave challenges to the characterization, a secondary purpose was to develop and apply new approaches where necessary to do so.Methods: The following performances of the proton scanning systems were investigated: beamlet alignment, static in-air beamlet size and shape, scanned in-air penumbra, scanned fluence map accuracy, geometric alignment of scanning system to isocenter, maximum field size, lateral and longitudinal field uniformity of a 1 l cubic uniform field, output stability over time, gantry angle invariance, monitoring system linearity, and reproducibility. A range of detectors was used: film, ionization chambers, lateral multielement and longitudinal multilayer ionization chambers, and a scintillation screen combined with a digital video camera. Characterization of the scanned fluence maps was performed with a software analysis tool.Results: The resulting measurements and analysis indicated that the two types of delivery systems performed within specification for those aspects investigated. The significant differences were observed between the two types of scanning systems where one type exhibits a smaller spot size and associated penumbra than the other. The differential is minimum at maximum energy and increases inversely with decreasing energy. Additionally, the large spot system showed an increase in dose precision to a static target with layer rescanning whereas the small spot system did not.Conclusions: The measured results from the two types of modulated scanning types of system were consistent with their designs under the conditions tested. The most significant difference between the types of system was their proton spot size and associated resolution, factors of magnetic optics, and vacuum length. The need and benefit of mutielement detectors and high-resolution sensors was also shown. The use of a fluence map analytical software tool was particularly effective in characterizing the dynamic proton energy-layer scanning.

Farr, J. B.; Schoenenberg, D. [Westdeutsches Protonentherapiezentrum Essen, Universitaetsklinikum-Essen, Hufelandstrasse 55, 45147 Essen (Germany); Dessy, F.; De Wilde, O.; Bietzer, O. [Ion Beam Applications, Chemin du Cyclotron, 3, 1348 Louvain-la-Neuve (Belgium)

2013-07-15

127

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling  

NASA Astrophysics Data System (ADS)

The focus of this investigation is on a first assessment of the predictive capabilities of nonlinear geometric reduced order models for the prediction of the large displacement and stress fields of panels with localized geometric defects, the case of a notch serving to exemplify the analysis. It is first demonstrated that the reduced order model of the notched panel does indeed provide a close match of the displacement and stress fields obtained from full finite element analyses for moderately large static and dynamic responses (peak displacement of 2 and 4 thicknesses). As might be expected, the reduced order model of the virgin panel would also yield a close approximation of the displacement field but not of the stress one. These observations then lead to two “enrichment” techniques seeking to superpose the notch effects on the virgin panel stress field so that a reduced order model of the latter can be used. A very good prediction of the full finite element stresses, for both static and dynamic analyses, is achieved with both enrichments.

Perez, Ricardo; Wang, X. Q.; Mignolet, Marc P.

2014-12-01

128

Modeling and modulation of nonlinear ball-beam system controller based on matlab  

Microsoft Academic Search

The practical engineering systems mainly used nonlinear systems, but its controller is complex. The ball-beam system not only has the typical features of nonlinear systems, but also relatively simple. By analyzing and modeling the ball-beam system, its characteristics and components, a PID controller is designed in Simulink applying the Ziegler-Nichols 2nd method. Through observing the experimental results the design is

Wenzhuo Chen; Xiaomei Sui; Yonghui Xing

2012-01-01

129

Weight optimization for flexural reinforced concrete beams with static nonlinear response  

Microsoft Academic Search

The weight optimization of reinforced concrete (RC) beams with material nonlinear response is formulated as a general nonlinear optimization problem. Incremental finite element procedures are used to integrate the structural response analysis and design sensitivity analysis in a consistent manner. In the finite element discretization, the concrete is modelled by plane stress elements and steel reinforcement is modelled by discrete

T. T. Chung; T. C. Sun

1994-01-01

130

Propagation property of a Lorentz-Gauss vortex beam in a strongly nonlocal nonlinear media  

NASA Astrophysics Data System (ADS)

An analytical expression of a Lorentz-Gauss vortex beam with one topological charge propagating in a strongly nonlocal nonlinear media is derived. The analytical expressions of the beam width, the curvature radius, and the orbital angular momentum density for the Lorentz-Gauss vortex beam with one topological charge have been also presented. The normalized intensity distribution, the relative beam width, the curvature radius, and the orbital angular momentum density distribution of the Lorentz-Gauss vortex beam with one topological charge are demonstrated in the strongly nonlocal nonlinear media, respectively. The normalized intensity, the beam width, the curvature radius, and the orbital angular momentum density versus the axial propagation distance are all periodic and the period is T=?z0/?. The evolution of the propagation property of the Lorentz-Gauss vortex beam with one topological charge has been exhibited in the strongly nonlocal nonlinear media. When the parameter ? reaches the critical value, the beam width keeps invariant upon propagation, and the corresponding curvature radius is infinite. The propagation of Lorentz-Gauss vortex beams with larger topological charge propagating in the strongly nonlocal nonlinear media can be analyzed by the same procedure as here.

Zhou, Guoquan

2014-11-01

131

A simple geometric algorithm to predict optimal starting gantry angles using equiangular-spaced beams for intensity modulated radiation therapy of prostate cancer  

Microsoft Academic Search

A fast, geometric beam angle optimization (BAO) algorithm for clinical intensity-modulated radiation therapy (IMRT) was implemented on ten localized prostate cancer patients on the Radiation Therapy Oncology Group (RTOG) 0126 protocol. The BAO algorithm computed the beam intersection volume (BIV) within the rectum and bladder using five and seven equiangular-spaced beams as a function of starting gantry angle for comparison

Zoann Nugent; Adel S. El-Gubtan; James B. Butler; Boyd M. C. McCurdy; Peter S. Potrebko

2007-01-01

132

Complex geometric optics for symmetric hyperbolic systems II: nonlinear theory in one space dimension  

E-print Network

This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the \\emph{naive} coherence condition on the complex phases, which is required in the construction of the approximate solution. Formally the theory applies also in several space dimensions, but the \\emph{naive} coherence condition appears to be too restrictive; the identification of the optimal coherence condition is still an open problem.

Omar Maj

2008-02-12

133

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

134

Approximate solutions for nonlinear transverse vibrations of elastically restrained tapered beams  

Microsoft Academic Search

This paper introduces the approximate solutions of the mathematical model of an elastically restrained tapered beam. At the beginning of the study, the equation of motion is derived in a detailed way. The frequency–amplitude relation is deduced and solved numerically. The nonlinear natural frequencies for the transverse vibrations of an elastically restrained tapered beam are provided using Mathematica software. The

Seher Durmaz; Sezgin Altay Demirba?; Metin Orhan Kaya

2012-01-01

135

Influence of nonlinearity and double elasticity on flexure of rock beams — II. Characterization of Dionysos marble  

Microsoft Academic Search

A technical bending theory of beams accounting for nonlinearity due to damage and bimodularity of brittle rocks was proposed in Part I. In order to check the validity of the above theory, a series of three-point bending (3PB) tests has been carried out using Dionysos marble beams that have been sampled from the same extracted block. Although the modeling of

G. E. Exadaktylos; I. Vardoulakis; S. K. Kourkoulis

2001-01-01

136

Ray matrix for Gaussian beam propagation in a nonlinear medium: experimental results  

NASA Astrophysics Data System (ADS)

The validity of a ray-matrix formulation of Gaussian beam propagation in a liquid nonlinear medium exhibiting self-defocusing is examined experimentally. By comparing the measured spot size of a Gaussian laser beam passing through the medium with the calculated spot size, it was found that the theory is consistent with the experimental results as long as the waist position of the input beam is not close to the exit surface of the medium.

Nemoto, Shojiro

1995-09-01

137

The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread  

NASA Astrophysics Data System (ADS)

The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency.

Kong, Ling-Bao; Wang, Hong-Yu; Hou, Zhi-Ling; Jin, Hai-Bo; Du, Chao-Hai

2013-12-01

138

Transient analysis of nonlinear Euler-Bernoulli micro-beam with thermoelastic damping, via nonlinear normal modes  

NASA Astrophysics Data System (ADS)

In this paper an Euler-Bernoulli model has been used for vibration analysis of micro-beams with large transverse deflection. Thermoelastic damping is considered to be the dominant damping mechanism and introduced as imaginary stiffness into the equation of motion by evaluating temperature profile as a function of lateral displacement. The obtained equation of motion is analyzed in the case of pure single mode motion by two methods; nonlinear normal mode theory and the Galerkin procedure. In contrast with the Galerkin procedure, nonlinear normal mode analysis introduces a nonconventional nonlinear damping term in modal oscillator which results in strong damping in case of large amplitude vibrations. Evaluated modal oscillators are solved using harmonic balance method and tackling damping terms introduced as an imaginary stiffness is discussed. It has been shown also that nonlinear modal analysis of micro-beam with thermoelastic damping predicts parameters such as inverse quality factor, and frequency shift, to have an extrema point at certain amplitude during transient response due to the mentioned nonlinear damping term; and the effect of system's characteristics on this critical amplitude has also been discussed.

Haddadzadeh Hendou, Ramtin; Karami Mohammadi, Ardeshir

2014-11-01

139

Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads  

PubMed Central

This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209

Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.

2013-01-01

140

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

141

Nonlinear beam-based vibration energy harvesters and load cells  

E-print Network

This thesis studies a novel nonlinear spring mechanism that is comprised of a cantilever wrapping around a curved surface as it deflects. Static force versus displacement tests and dynamic "initial displacement" tests ...

Kluger, Jocelyn Maxine

2014-01-01

142

Nondiffracting and nonattenuating vortex light beams in media with nonlinear absorption of orbital angular momentum  

NASA Astrophysics Data System (ADS)

We show that a high-order Bessel beam propagating in a medium with nonlinear absorption is not completely absorbed, but survives in the form of a new propagation invariant vortex beam in which the beam energy and orbital angular momentum are permanently transferred to matter and at the same time refueled by spiral inward currents of energy and angular momentum. Unlike vortex solitons and dissipative vortex solitons, these vortex beams are not supported by specific dispersive nonlinearities (self-focusing or self-defocusing) and do not require gain. Propagation invariance in presence of multiple absorption of photons carrying (possibly high) orbital angular momentum makes these beams attractive for optical pumping of angular momentum over long distances.

Porras, Miguel A.; Ruiz-Jiménez, Carlos

2014-11-01

143

Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device  

NASA Astrophysics Data System (ADS)

This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free-free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.

Nili Ahmadabadi, Z.; Khadem, S. E.

2014-09-01

144

Angular distribution of molecular beams and homogeneous layer growth: optimization of geometrical parameters in molecular beam epitaxy  

Microsoft Academic Search

Preceding studies of angular distribution flows issued from molecular beam sources used in molecular beam epitaxy are analysed by comparison with analogous studies as performed on the Knudsen effusion cell method. A new architecture of the effusion sources and substrate relative disposition for epitaxial growth is proposed which discards any re-vaporized parasitic flow of molecules and which is aimed to

Jean-Luc Vassent; Alain Marty; Bruno Gilles; Christian Chatillon

2001-01-01

145

Nonlinear Potential Model of Space-Charge Electron Beams  

Microsoft Academic Search

This body of work is new and comprises theoretical analysis, numerical simulation and experimental investigations of the vircator, a tunable, compact, simply constructed, high power reflexing electron device that is used as a microwave source. A 1D theoretical model is formulated that is based on a time-varying, nonlinear potential to better understand the sensitivities of individual electron trajectories to macroscopic

Marc Stuart Litz

1995-01-01

146

Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor  

NASA Technical Reports Server (NTRS)

A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion extension, shear deformation, and warping of an initially curved and twisted beam.

Danielson, D. A.; Hodges, D. H.

1987-01-01

147

Nonlinear beam kinematics by decomposition of the rotation tensor  

NASA Technical Reports Server (NTRS)

A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion, extension, shear deformation, and warping of an initially curved and twisted beam.

Danielson, D. A.; Hodges, D. H.

1987-01-01

148

Measurement of nonlinear observables in the Large Hadron Collider using kicked beams  

NASA Astrophysics Data System (ADS)

The nonlinear dynamics of a circular accelerator such as the Large Hadron Collider (LHC) may significantly impact its performance. As the LHC progresses to more challenging regimes of operation it is to be expected that the nonlinear single particle dynamics in the transverse planes will play an increasing role in limiting the reach of the accelerator. As such it is vital that the nonlinear sources are well understood. The nonlinear fields of a circular accelerator may be probed through measurement of the amplitude detuning: the variation of tune with single particle emittance. This quantity may be assessed experimentally by exciting the beam to large amplitudes with kicks, and obtaining the tunes and actions from turn-by-turn data at Beam Position Monitors. The large amplitude excitations inherent to such a measurement also facilitate measurement of the dynamic aperture from an analysis of beam losses following the kicks. In 2012 these measurements were performed on the LHC Beam 2 at injection energy (450 GeV) with the nominal magnetic configuration. Nonlinear coupling was also observed. A second set of measurements were performed following the application of corrections for b4 and b5 errors. Analysis of the experimental results, and a comparison to simulation are presented herein.

Maclean, E. H.; Tomás, R.; Schmidt, F.; Persson, T. H. B.

2014-08-01

149

Geometric studies on variable radius spiral cone-beam scanning Yangbo Yea)  

E-print Network

technology, electron-beam CT scanners1 are quite different from the main stream mechani- cal CT scanners.2 Most distinctively, electron-beam CT scan- ners allow scan times down to 50 ms. In the EBCT design animal studies.3 Although there has been an explosive growth in the development of micro-CT scanners

Virginia Tech

150

Simulations of nonlinear harmonic generation by an internal wave beam incident on a pycnocline  

NASA Astrophysics Data System (ADS)

Internal wave beams generated by oceanic tidal flows propagate upward and interact with the increasing stratification found at the pycnocline. The nonlinear generation of harmonic modes by internal wave beams incident on a pycnocline has recently been demonstrated by laboratory experiments and numerical simulations. In these previous studies, the harmonic modes were trapped within the pycnocline because their frequencies exceeded that of the stratified fluid below. Here, two-dimensional numerical simulations are used to explore the effect of incidence angle on harmonic generation at a thin pycnocline. At incidence angles less than 30 degrees (typical of oceanic beams), the lowest harmonic mode freely radiates in the form of an internal wave beam rather than being trapped within the pycnocline. The results indicate that nonlinear refraction is the primary mechanism for harmonic generation at incidence angles exceeding 30 degrees, but that interaction of the incident and reflected beams is more important at smaller incidence angles. The simulations are compared to weakly nonlinear theory based on refraction at the pycnocline. The results yield good agreement for trapped harmonics, but weakly nonlinear theory substantially underpredicts the amplitude of the radiated harmonics.

Wunsch, S.; Ku, H.; Delwiche, I.; Awadallah, R.

2014-08-01

151

Effects of Transverse Physics on Nonlinear Evolution of Longitudinal Space-Charge Waves in Beams  

SciTech Connect

Longitudinal space-charge waves can introduce energy perturbations into charge particle beams and degrade the beam quality, which is critical to many modern applications of particle accelerators. Although many longitudinal phenomena arising from small perturbations can be explained by a one-dimensional cold fluid theory, nonlinear behavior of space-charge waves observed in experiments has not been well understood. In this paper, we summarize our recent investigation by means of more detailed measurements and self-consistent simulations. Combining the numerical capability of a PIC code, WARP, with the detailed initial conditions measured by our newly developed time resolved 6-D phase space mapping technique, we are able to construct a self consistent model for studying the complex physics of longitudinal dynamics of space-charge dominated beams. Results from simulation studies suggest that the unexplained nonlinear behavior of space-charge waves may be due to transverse mismatch or misalignment of beams.

K. Tian, I. Haber, R.A. Kishek, P.G. O'Shea, M. Reiser, D. Stratakis

2009-05-01

152

Three-dimensional beam propagation analysis of nonlinear optical fibers and optical logic gates  

Microsoft Academic Search

A three-dimensional (3-D) beam propagation method is described for the analysis of nonlinear optical fibers, where the finite element and finite difference methods are, respectively, utilized for discretizing the fiber cross section and the propagation direction. For efficient evaluation of wide-angle beam propagation Pade approximation is applied to the differential operator along the propagation direction. In order to improve the

Akira Niiyama; Masanori Koshiba

1998-01-01

153

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

PubMed

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. PMID:22060448

Zhang, Likun; Marston, Philip L

2011-09-01

154

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

155

Beam loading in the nonlinear regime of plasma-based acceleration  

NASA Astrophysics Data System (ADS)

An analytical theory for the interaction of a negatively charged bunch with a nonlinear plasma wave is developed to make it possible to design efficient laser- and/or beam-driven accelerators that generate truly monoenergetic electron beams. This theory allows us to choose the charge, the shape and the placing of the beam so that the efficiency is maximized and the beam quality optimized. For intense drivers the nonlinear wake is described by the trajectory of the blowout radius and beam loading arises when the radial space-charge force of the beam acts back on the trajectory. Starting from the nonlinear theory by W. Lu et al. [1], an equation for the wakefield in the presence of an electron bunch is derived. The shape of the ion channel in an unloaded wake is determined and the modification of the wake due to the presence of flat-top electron bunches is studied. It is shown that the energy spread of an externally injected flat-top (or Gaussian) electron bunch can be kept low by choosing the correct charge per unit length and the analytical results are confirmed with PIC simulations. The bunch profile that leads to zero energy spread is found to be trapezoidal. The conversion efficiency from the fields of the bubble to the accelerating electrons is determined, and it is shown that for optimal bunches it approaches 100%. The differences between nonlinear and linear [2] theory are described and the advantages of operating in the nonlinear regime are discussed. [1] W. Lu et al., Phys. Rev. Lett. 96, 165002 (2006); Phys. Plasmas 13, 056709 (2006). [2] T. Katsouleas et al., Particle Accelerators, 1987, 22, pp. 81-99.

Tzoufras, Michail

2008-11-01

156

Multi-harmonic measurements and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary  

E-print Network

Multi-harmonic measurements and numerical simulations of nonlinear vibrations of a beam with non This study presents a direct comparison of measured and predicted nonlinear vibrations of a clamped with measurements is performed in the vicinity of the primary resonance. First of all, a nonlinear analytical model

Boyer, Edmond

157

Numerical Modeling of Nonlinear Coupling between Lines/Beams with Multiple Floating Bodies  

E-print Network

spring model and the three(3) dimensional FE beam model. The coupling of the TLP motion with the reaction force at the tie-down clamp is considered by using exact nonlinear dynamic equations of the motion with the reaction forces modeled with the spring...

Yang, Chan K.

2010-07-14

158

Influence of non-linear forces on beam behaviour in flutter conditions  

NASA Astrophysics Data System (ADS)

Appropriate researches on non-linear panel flutter behaviour have been already performed by many authors. In most cases the intent of them focuses on the limit cycle determination, with particular interest towards its amplitude versus the flow dynamic pressure. This paper deals first with a study of all the solutions without damping of beam flutter versus the vibration frequency in non-linear post-critical conditions. A numerical model, which takes into account the influence of the non-linear contribution of the structural forces, due to the axial stretching of the beam, has been implemented. A complete analysis of all the possible non-linear solutions without damping leads to the possibility of characterizing the most appropriate conditions for the presence of the post-critical panel flutter limit cycles. Then the complete model, which also takes into account aerodynamic damping, has been utilized, according to the "Piston Theory", to verify the state evolution of the fluttering damped beam towards the limit cycle, which is very near to the undamped vibrating beam state with minimum amplitude. This convergence test is an interesting aspect of the numerical results.

Tizzi, S.

2003-10-01

159

Application of Chebyshev formalism to identify nonlinear magnetic field components in beam transport system  

NASA Astrophysics Data System (ADS)

An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.

Spata, Michael

160

Nonlinear plasma waves excitation by intense ion beams in background plasma  

E-print Network

Nonlinear plasma waves excitation by intense ion beams in background plasma Igor D. Kaganovich, Edward A. Startsev, and Ronald C. Davidson Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 Received 2 February 2004; accepted 6 April 2004 Plasma neutralization of an intense

Kaganovich, Igor

161

Concatenated beam splitters, optical feed-forward and the nonlinear sign gate  

E-print Network

We consider a nonlinear sign gate implemented using a sequence of two beam splitters, and consider the use of further sequences of beam splitters to implement feed-forward so as to correct an error resulting from the first beam splitter. We obtain similar results to Scheel et al. [Scheel et al., Phys. Rev. A 73, 034301 (2006)], in that we also find that our feed-forward procedure is only able to produce a very minor improvement in the success probability of the original gate.

Kurt Jacobs; Jonathan P. Dowling

2006-06-26

162

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

163

Modeling transient response of PN junction diode under radiation beams considering nonlinear effects  

NASA Astrophysics Data System (ADS)

Diodes are used as dosimeter to measure the delivered dose from the radiation beams of linear accelerators used in the radiation therapy field. Diode sensitivity S, defined as charge collected per unit absorbed dose, has been found to increase with an increase in instantaneous dose rate r of the radiation beam. In order to calculate the dependence of S on r, one has to solve for the excess minority-carrier concentration Deltap (= Deltan) from the carrier transportation equation. This equation is a nonlinear partial different equation (PDE), with two variables of space coordinate x and time t. The nonlinear term in the PDE is the net recombination-generation (R-G) rate U. The historical solutions were either the transient solution from the linear PDE or the steady state solution from the nonlinear differential equation. This dissertation solves the nonlinear PDE with simplified nonlinear term U. The analytical solution is the first to include both transient and nonlinearity at the same time. The analytical solution for Deltap (x, t) from the PDE is used to derive the current density J p of the minority carriers and the diode sensitivity S. A computer software program has also been developed to numerically solve the non-simplified PDE. The agreement of the calculations for Deltap (x) and Jp (t) is excellent between the numerical and the analytical solutions, proving the analytical solution is legitimate. A theoretical model is established with the analytical solution to explain the r dependence of diode sensitivity S under pulsed radiation beam. The sensitivity of several different types of diodes was measured with the 18 MV photon beam of a medical linear accelerator. The diode sensitivity from the experiment is compared with the calculations from both the analytical and the numerical solutions. The theoretical calculations yield the instantaneous dose rate dependence of the diode sensitivity. The agreement is generally good between the theory and the experiments. The results are discussed and possible error sources are analyzed.

Shi, Jie

164

Analytical and experimental studies on nonlinear characteristics of an L-shape beam structure  

NASA Astrophysics Data System (ADS)

This paper focuses on theoretical and experimental investigations of planar nonlinear vibrations and chaotic dynamics of an L-shape beam structure subjected to fundamental harmonic excitation, which is composed of two beams with right-angled L-shape. The ordinary differential governing equation of motion for the L-shape beam structure with two-degree-of-freedom is firstly derived by applying the substructure synthesis method and the Lagrangian equation. Then, the method of multiple scales is utilized to obtain a four-dimensional averaged equation of the L-shape beam structure. Numerical simulations, based on the mathematical model, are presented to analyze the nonlinear responses and chaotic dynamics of the L-shape beam structure. The bifurcation diagram, phase portrait, amplitude spectrum and Poincare map are plotted to illustrate the periodic and chaotic motions of the L-shape beam structure. The existence of the Shilnikov type multi-pulse chaotic motion is also observed from the numerical results. Furthermore, experimental investigations of the L-shape beam structure are performed, and there is a qualitative agreement between the numerical and experimental results. It is also shown that out-of-plane motion may appear intuitively.

Cao, Dong-Xing; Zhang, Wei; Yao, Ming-Hui

2010-12-01

165

Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam  

NASA Technical Reports Server (NTRS)

The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.

Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.

1991-01-01

166

Understanding the nonlinear beam dynamics of the Advanced Light Source  

SciTech Connect

Frequency map analysis is used to study the single particle transverse beam dynamics in ALS. The maps, which provide details about the diffusion of orbits and limits on long term stability, are generated by a postprocessor attached to a tracking code. This paper describes the method and shows how the map is changed when the 12- fold symmetry of the linear lattice is perturbed by including measured magnetic field imperfections. Also the long term stability of orbits that reside in regions of large diffusion is studied.

Robin, D. [Lawrence Berkeley National Lab., CA (United States); Laskar, J. [Centre National de la Recherche Scientifique (CNRS), 75 - Paris (France)

1996-09-18

167

Applications of electron lenses: scraping of high-power beams, beam-beam compensation, and nonlinear optics  

E-print Network

Electron lenses are pulsed, magnetically confined electron beams whose current-density profile is shaped to obtain the desired effect on the circulating beam. Electron lenses were used in the Fermilab Tevatron collider for bunch-by-bunch compensation of long-range beam-beam tune shifts, for removal of uncaptured particles in the abort gap, for preliminary experiments on head-on beam-beam compensation, and for the demonstration of halo scraping with hollow electron beams. Electron lenses for beam-beam compensation are being commissioned in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Hollow electron beam collimation and halo control were studied as an option to complement the collimation system for the upgrades of the Large Hadron Collider (LHC) at CERN; a conceptual design was recently completed. Because of their electric charge and the absence of materials close to the proton beam, electron lenses may also provide an alternative to wires for long-range beam-beam compens...

Stancari, Giulio

2014-01-01

168

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. PMID:24022688

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

2013-01-01

169

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

SciTech Connect

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 Schroedinger 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 [International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum (Germany); Department of Physics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 (China); Shukla, P. K. [International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum (Germany); Department of Mechanical and Aerospace Engineering and Center for Energy Research, University of California San Diego, La Jolla, California 92093 (United States); School of Chemistry and Physics, KwaZulu-Natal University, Durban 4000 (South Africa); Eliasson, B. [International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum (Germany)

2013-01-15

170

Numerical investigation of beam-driven PWFA in quasi-nonlinear regime  

NASA Astrophysics Data System (ADS)

In beam-driven Plasma Based Wakefield Acceleration (PWFA), the quasi-nonlinear model has been designed to combine high efficient ‘blowout' regimes, where cold and overdense driving electron beams form a totally rarefied plasma channel, with low charge beam distribution assuring the excited wakefield preserves relevant linear properties. This scheme can have applications in experimental facilities, like SPARC 150 MeV linac at LNF-INFN laboratories, where low-emittance, low-charge narrow electron beams can be produced to be injected on a preformed plasma channel. Here we present a preliminary numerical investigation of this configuration, using the fully 3D ALaDyn PIC code, as a preparatory work to design optimal conditions for the COMB experimental set-up. Specific numerical tools, having computational and diagnostic advantages in PWFA conditions and checks of the numerical outcomes with analytical results, are also presented and discussed.

Londrillo, P.; Gatti, C.; Ferrario, M.

2014-03-01

171

The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities  

E-print Network

Very-high energy gamma-rays from extragalactic sources pair-produce off of the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the "oblique" instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here, we show with numerical calculations that the effective damping rate is $8\\times 10^{-4}$ of the growth rate of the linear instability, which is sufficient for the "oblique" instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wavenumber and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to ap...

Chang, Philip; Lamberts, Astrid

2014-01-01

172

Multiple Beam Two-Plasmon Decay: Linear Threshold to Nonlinear Saturation in Three Dimensions  

NASA Astrophysics Data System (ADS)

The linear stability of multiple coherent laser beams with respect to two-plasmon-decay instability in an inhomogeneous plasma in three dimensions has been determined. Cooperation between beams leads to absolute instability of long-wavelength decays, while shorter-wavelength shared waves are shown to saturate convectively. The multibeam, in its absolutely unstable form, has the lowest threshold for most cases considered. Nonlinear calculations using a three-dimensional extended Zakharov model show that Langmuir turbulence created by the absolute instability modifies the convective saturation of the shorter-wavelength modes, which are seen to dominate at late times.

Zhang, J.; Myatt, J. F.; Short, R. W.; Maximov, A. V.; Vu, H. X.; DuBois, D. F.; Russell, D. A.

2014-09-01

173

Analytical theory for the propagation of laser beams in nonlinear media  

SciTech Connect

The propagation of a laser beam of intensity I in a nonlinear medium with a refractive index n(I) of arbitrary form is studied. In particular, the influence of the functional form n=n(I) on self-focusing and self-trapping is investigated. Starting from the propagation equations and using symmetry considerations and the Bogoliubov renormalization group approach, we derive a general equation relating the self-focusing distance, the intensity, and n(I). For different polynomial dependences of n(I) on I, we construct analytical solutions for the spatial intensity profile I(r) for an initially collimated Gaussian beam inside the medium. We also explicitly analyze the case of nonlinear self-focusing accompanied by multiphoton ionization. For particular (already studied) cases, we considerably improve the accuracy of the results with respect to previous semianalytical studies and obtain very good agreement with recent numerical simulations.

Tatarinova, Larisa L.; Garcia, Martin E. [Theoretische Physik, Universitaet Kassel, FB 18, Heinrich-Plett-Strasse 40, 34132 Kassel (Germany)

2007-10-15

174

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

175

Nonlinear self-focus of pulsed-wave beams in Kerr media  

SciTech Connect

A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.

Judkins, J.B.

1992-12-31

176

Nonlinear control via approximate input-output linearization - The ball and beam example  

NASA Technical Reports Server (NTRS)

A study is made of approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree. For such systems, a method is provided for constructing approximate systems that are input-output linearizable. The analysis presented in this note is motivated through its application to a common undergraduate control laboratory experiment, the ball and beam system, where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization.

Hauser, John; Sastry, Shankar; Kokotovic, Petar

1992-01-01

177

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

178

Tracker-on-C for cone-beam CT-guided surgery: evaluation of geometric accuracy and clinical applications  

NASA Astrophysics Data System (ADS)

Conventional surgical tracking configurations carry a variety of limitations in line-of-sight, geometric accuracy, and mismatch with the surgeon's perspective (for video augmentation). With increasing utilization of mobile C-arms, particularly those allowing cone-beam CT (CBCT), there is opportunity to better integrate surgical trackers at bedside to address such limitations. This paper describes a tracker configuration in which the tracker is mounted directly on the Carm. To maintain registration within a dynamic coordinate system, a reference marker visible across the full C-arm rotation is implemented, and the "Tracker-on-C" configuration is shown to provide improved target registration error (TRE) over a conventional in-room setup - (0.9+/-0.4) mm vs (1.9+/-0.7) mm, respectively. The system also can generate digitally reconstructed radiographs (DRRs) from the perspective of a tracked tool ("x-ray flashlight"), the tracker, or the C-arm ("virtual fluoroscopy"), with geometric accuracy in virtual fluoroscopy of (0.4+/-0.2) mm. Using a video-based tracker, planning data and DRRs can be superimposed on the video scene from a natural perspective over the surgical field, with geometric accuracy (0.8+/-0.3) pixels for planning data overlay and (0.6+/-0.4) pixels for DRR overlay across all C-arm angles. The field-of-view of fluoroscopy or CBCT can also be overlaid on real-time video ("Virtual Field Light") to assist C-arm positioning. The fixed transformation between the x-ray image and tracker facilitated quick, accurate intraoperative registration. The workflow and precision associated with a variety of realistic surgical tasks were significantly improved using the Tracker-on-C - for example, nearly a factor of 2 reduction in time required for C-arm positioning, reduction or elimination of dose in "hunting" for a specific fluoroscopic view, and confident placement of the x-ray FOV on the surgical target. The proposed configuration streamlines the integration of C-arm CBCT with realtime tracking and demonstrated utility in a spectrum of image-guided interventions (e.g., spine surgery) benefiting from improved accuracy, enhanced visualization, and reduced radiation exposure.

Reaungamornrat, S.; Otake, Y.; Uneri, A.; Schafer, S.; Mirota, D. J.; Nithiananthan, S.; Stayman, J. W.; Khanna, A. J.; Reh, D. D.; Gallia, G. L.; Taylor, R. H.; Siewerdsen, J. H.

2012-02-01

179

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

180

A numerical investigation of nonlinear aeroelastic effects on flexible high aspect ratio wings  

Microsoft Academic Search

A nonlinear aeroelastic analysis that couples a nonlinear structural model with an Euler\\/Navier-Stokes flow solver is developed for flexible high aspect ratio wings. To model the nonlinear structural characteristics of flexible high aspect ratio wings, a two-dimensional geometric nonlinear methodology, based on a 6 degree-of-freedom (DOF) beam finite element, is extended to three dimensions based on a 12 DOF beam

Joseph Avila Garcia

2002-01-01

181

Phased Nonlinear Finite-Element Analysis of Precracked RC T-Beams Repaired in Shear with CFRP Sheets  

E-print Network

Phased nonlinear finite-element (FE) analyses were carried out to predict the behavior of precracked reinforced concrete (RC) T-beams repaired in shear with externally bonded (EB) carbon fiber–reinforced polymer (CFRP) sheets and subjected to two...

Dirar, Samir; Lees, Janet M.; Morley, Chris

2012-10-17

182

Image formation by linear and nonlinear digital scanned light-sheet fluorescence microscopy with Gaussian and Bessel beam profiles  

PubMed Central

We present the implementation of a combined digital scanned light-sheet microscope (DSLM) able to work in the linear and nonlinear regimes under either Gaussian or Bessel beam excitation schemes. A complete characterization of the setup is performed and a comparison of the performance of each DSLM imaging modality is presented using in vivo Caenorhabditis elegans samples. We found that the use of Bessel beam nonlinear excitation results in better image contrast over a wider field of view. PMID:22808423

Olarte, Omar E.; Licea-Rodriguez, Jacob; Palero, Jonathan A.; Gualda, Emilio J.; Artigas, David; Mayer, Jurgen; Swoger, Jim; Sharpe, James; Rocha-Mendoza, Israel; Rangel-Rojo, Raul; Loza-Alvarez, Pablo

2012-01-01

183

Nonlinear excitation of kinetic Alfvén waves and whistler waves by electron beam-driven Langmuir waves in the solar corona  

Microsoft Academic Search

We study a new nonlinear excitation mechanism of kinetic Alfvén waves (KAWs) and whistler waves (Ws) by electron beam-driven Langmuir waves (Ls). The generation conditions for the parametric decay instability L rightleftarrows W + KAW are determined and the growth rate is calculated. We show that the resonant pairs of KAWs and whistler waves are nonlinearly coupled to the pump

Yu. Voitenko; M. Goossens; O. Sirenko; A. C.-L. Chian

2003-01-01

184

Problems in nonlinear acoustics: Scattering of sound by sound, parametric arrays, focused sound beams, and noncollinear tone-noise interactions  

Microsoft Academic Search

Five projects are discussed involving nonlinear acoustics: (1) scattering of sound by sound, a theoretical study of two noncollinear Gaussian beams which interact to produce sum and difference frequency sound; (2) parametric receiving arrays, a theoretical and numerical study of parametric reception in a reverberant environment; (3) noncollinear interaction of a tone with noise, an experimental investigation of the nonlinear

Mark F. Hamilton

1988-01-01

185

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

186

Geometric Effects on Electron Cloud  

SciTech Connect

The development of an electron cloud in the vacuum chambers of high intensity positron and proton storage rings may limit the machine performances by inducing beam instabilities, beam emittance increase, beam loss, vacuum pressure increases and increased heat load on the vacuum chamber wall. The electron multipacting is a kind of geometric resonance phenomenon and thus is sensitive to the geometric parameters such as the aperture of the beam pipe, beam shape and beam bunch fill pattern, etc. This paper discusses the geometric effects on the electron cloud build-up in a beam chamber and examples are given for different beams and accelerators.

Wang, L

2007-07-06

187

Trapping induced nonlinear behavior of backward stimulated Raman scattering in multi-speckled laser beams  

SciTech Connect

In inertial confinement fusion experiments, stimulated Raman scattering (SRS) occurs when electron density fluctuations are amplified resonantly by the incident laser beams and scattered light. These beams comprise several thousands of individual laser speckles. We have found in single-speckle studies that electron trapping lowers the threshold intensity for SRS onset to a value below that from linear theory and enhances scattering. The trapping-induced plasma-wave frequency shift leads to wave-front bowing and filamentation processes that saturate SRS and limit scattering within a speckle. With large-scale simulations, we have now examined how laser speckles interact with one another through three-dimensional (3D) particle-in-cell (PIC) simulations of two interacting speckles and 2D PIC simulations of ensembles of laser speckles (hundreds of speckles). Our work shows that kinetic trapping physics also governs the onset and saturation of SRS in ensembles of speckles. Speckles interact in a manner that is nonlinear and nonlocal: An intense speckle can destabilize its neighbors through transport of hot electrons and SRS waves, resulting in enhanced emission of particles and waves that, in turn, act upon the original speckle. In this manner, speckles below threshold when in isolation can be above the threshold in multi-speckled beams under conditions for laser-driven fusion experiments at the National Ignition Facility (NIF) and ensembles of speckles are thus found to collectively lower the SRS onset threshold. Simulations of the hohlraum interior where laser beams overlap show that multi-speckled laser beams at low average intensity (a few times 10{sup 14} W/cm{sup 2}) have correspondingly lower thresholds for enhanced SRS and that the sub-ps bursts of SRS saturate through trapping induced nonlinearities. Because of electron trapping effects, SRS reflectivity grows slowly with average laser intensity. While SRS reflectivity saturates under NIF conditions, SRS hot electron energy increases with increasing laser intensity and may contribute to capsule preheat.

Yin, L.; Albright, B. J.; Rose, H. A.; Bowers, K. J.; Bergen, B.; Montgomery, D. S.; Kline, J. L. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Kirkwood, R. K.; Hinkel, D. E.; Langdon, A. B.; Michel, P. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)

2012-05-15

188

Collisionless Damping of Circularly Polarized Nonlinear Alfvén Waves in Solar Wind Plasmas with and without Beam Protons  

NASA Astrophysics Data System (ADS)

The damping process of field-aligned, low-frequency right-handed polarized nonlinear Alfvén waves (NAWs) in solar wind plasmas with and without proton beams is studied by using a two-dimensional ion hybrid code. The numerical results show that the obliquely propagating kinetic Alfvén waves (KAWs) excited by beam protons affect the damping of the low-frequency NAW in low beta plasmas, while the nonlinear wave-wave interaction between parallel propagating waves and nonlinear Landau damping due to the envelope modulation are the dominant damping process in high beta plasmas. The nonlinear interaction between the NAWs and KAWs does not cause effective energy transfer to the perpendicular direction. Numerical results suggest that while the collisionless damping due to the compressibility of the envelope-modulated NAW plays an important role in the damping of the field-aligned NAW, the effect of the beam instabilities may not be negligible in low beta solar wind plasmas.

Nariyuki, Y.; Hada, T.; Tsubouchi, K.

2014-10-01

189

The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread  

SciTech Connect

The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.

Kong, Ling-Bao, E-mail: konglingbao@gmail.com [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China) [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Wang, Hong-Yu [School of Physics, Anshan Normal University, Anshan 114005 (China)] [School of Physics, Anshan Normal University, Anshan 114005 (China); Hou, Zhi-Ling, E-mail: houzl@mail.buct.edu.cn [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China) [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Jin, Hai-Bo [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China)] [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); Du, Chao-Hai [Institute of Electronics, Chinese Academy of Sciences, Beijing 100190 (China)] [Institute of Electronics, Chinese Academy of Sciences, Beijing 100190 (China)

2013-12-15

190

Nonlinear theory of electron neutralization waves in ions beams with dissipation  

NASA Technical Reports Server (NTRS)

An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.

Wilhelm, H. E.

1974-01-01

191

Multiharmonic cubic-nonlinear theory of plasma-beam superheterodyne free-electron lasers of the dopplertron type  

SciTech Connect

A multiharmonic cubic-nonlinear theory of a plasma-beam superheterodyne free-electron laser of the dopplertron type is constructed. A retarded electromagnetic wave propagating in the magnetized plasma-beam system toward the electron beam is used for pumping. The multiharmonic interaction of waves which plays an important role is taken into account. Saturation levels and mechanisms are analyzed. The promising application of such systems for generating high-power electromagnetic radiation in the millimeter wavelength range is demonstrated.

Kulish, V. V.; Lysenko, A. V.; Koval, V. V. [Sumy State University (Ukraine)

2010-12-15

192

Nonlinear and long-term beam dynamics in low energy storage rings  

NASA Astrophysics Data System (ADS)

Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF+ ions at 93keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3-30 keV ions with a gas jet target are summarized.

Papash, A. I.; Smirnov, A. V.; Welsch, C. P.

2013-06-01

193

PHYSICAL REVIEW B 88, 014304 (2013) Effects of geometric and material nonlinearities on tunable band gaps and low-frequency  

E-print Network

-reduction devices,8 and vibration isolators.9 It has also been recognized that phononic crystals are characterized band gaps and low-frequency directionality of phononic crystals Pai Wang,1 Jongmin Shim,2 and Katia nonlinearities introduced by deformation on the linear dynamic response of two-dimensional phononic crystals. Our

194

Justification of a nonlinear Schrödinger model for laser beams in photopolymers  

NASA Astrophysics Data System (ADS)

A nonstationary model that relies on the spatial nonlinear Schrödinger (NLS) equation with the time-dependent refractive index describes laser beams in photopolymers. We consider a toy problem, when the rate of change of refractive index is proportional to the squared amplitude of the electric field and the spatial domain is a plane. After formal derivation of the NLS approximation from a two-dimensional quasilinear wave equation, we establish local well-posedness of the original and reduced models and perform rigorous justification analysis to control smallness of the approximation error for appropriately small times.

Pelinovsky, Dmitry; Ponomarev, Dmitry

2014-06-01

195

Nonlinear programming analysis of multi-mode wave propagating characteristics in ion-beam plasma system  

NASA Astrophysics Data System (ADS)

Propagating characteristics of multimode waves are analyzed in an ion-beam plasma system by means of nonlinear programming techniques. A fine structure of each wave mode such as a wavenumber, damping rate, a wave amplitude, a wave peak point, and a phase relation among the waves is obtained from the observed interferometer traces of multimode waves. The wave pattern assembled with the separated patterns into each wave mode is confirmed to be quite similar to the observed one. A qualitative agreement of wave dispersion relation is obtained between the values analyzed by the present method and calculated by the plasma kinetic theory.

Yagura, Shinya; Fujita, Hiroharu; Kankubo, Kouichi

1989-08-01

196

Nonlinear Elastic J-Integral Measurements in Mode I Using a Tapered Double Cantilever Beam Geometry  

NASA Technical Reports Server (NTRS)

An expression for the J-integral of a nonlinear elastic material is derived for an advancing crack in a tapered double cantilever beam fracture specimen. The elastic and plastic fracture energies related to the test geometry and how these energies correlates to the crack position are discussed. The dimensionless shape factors eta(sub el and eta(sub p) are shown to be equivalent and the deformation J-integral is analyzed in terms of the eta(sub el) function. The fracture results from a structural epoxy are interpreted using the discussed approach. The magnitude of the plastic dissipation is found to strongly depend upon the initial crack shape.

Macon, David J.

2006-01-01

197

2D Corotational Beam Formulation by Louie L. Yaw  

E-print Network

1 2D Corotational Beam Formulation by Louie L. Yaw Walla Walla University November 30, 2009 key words: geometrically nonlinear analysis, 2d corotational beam, variationally consistent, load control Introduction This article presents information necessary for a simple two-dimensional corotational beam

Yaw, Louis L.

198

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

199

Materially and geometrically non-linear woven composite micro-mechanical model with failure for finite element simulations  

Microsoft Academic Search

A computational micro-mechanical material model of woven fabric composite material is developed to simulate failure. The material model is based on repeated unit cell approach. The fiber reorientation is accounted for in the effective stiffness calculation. Material non-linearity due to the shear stresses in the impregnated yarns and the matrix material is included in the model. Micro-mechanical failure criteria determine

Ala Tabiei; Ivelin Ivanov

2004-01-01

200

A simple geometric algorithm to predict optimal starting gantry angles using equiangular-spaced beams for intensity modulated radiation therapy of prostate cancer  

SciTech Connect

A fast, geometric beam angle optimization (BAO) algorithm for clinical intensity-modulated radiation therapy (IMRT) was implemented on ten localized prostate cancer patients on the Radiation Therapy Oncology Group (RTOG) 0126 protocol. The BAO algorithm computed the beam intersection volume (BIV) within the rectum and bladder using five and seven equiangular-spaced beams as a function of starting gantry angle for comparison to the V 75 Gy and V 70 Gy. A mathematical theory was presented to explain the correlation of BIV with dose and dose-volume metrics. The class solution 'W' pattern in the rectal V 75 Gy and V 70 Gy as a function of starting gantry angle using five equiangular-spaced beams (with two separate minima centered near 20 deg. and 50 deg. ) was reproduced by the 5 BIV within the rectum. A strong correlation was found between the rectal 5 BIV and the rectal V 75 Gy and V 70 Gy as a function of starting gantry angle. The BAO algorithm predicted the location of the two dosimetric minima in rectal V 75 Gy and V 70 Gy (optimal starting gantry angles) to within 5 deg. . It was demonstrated that the BIV geometric variations for seven equiangular-spaced beams were too small to translate into a strong dosimetric effect in the rectal V 75 Gy and V 70 Gy. The relatively flat distribution with starting gantry angle of the bladder V 75 Gy and V 70 Gy was reproduced by the bladder five and seven BIV for each patient. A geometric BAO method based on BIV has the advantage over dosimetric BAO methods of simplicity and rapid computation time. This algorithm can be used as a standalone optimization method or act as a rapid calculation filter to reduce the search space for a dosimetric BAO method. Given the clinically infeasible computation times of many dosimetric beam orientation optimization algorithms, this robust geometric BIV algorithm has the potential to facilitate beam angle selection for prostate IMRT in clinical practice.

Potrebko, Peter S.; McCurdy, Boyd M. C.; Butler, James B.; El-Gubtan, Adel S.; Nugent, Zoann [Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 (Canada) and Division of Medical Physics, CancerCare Manitoba, 675 McDermot Avenue, Winnipeg, Manitoba R3E 0V9 (Canada); Division of Medical Physics, CancerCare Manitoba, 675 McDermot Avenue, Winnipeg, Manitoba R3E 0V9 (Canada); Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada) and Department of Radiology, University of Manitoba, Winnipeg, Manitoba R3A 1R9 (Canada); Department of Radiation Oncology, CancerCare Manitoba, 675 McDermot Avenue, Winnipeg, Manitoba R3E 0V9 (Canada) and Department of Radiology, University of Manitoba, Winnipeg, Manitoba R3A 1R9 (Canada); Department of Epidemiology, CancerCare Manitoba, 675 McDermot Avenue, Winnipeg, Manitoba R3E 0V9 (Canada)

2007-10-15

201

Vibration of vehicle-pavement coupled system based on a Timoshenko beam on a nonlinear foundation  

NASA Astrophysics Data System (ADS)

This paper focuses on the coupled nonlinear vibration of vehicle-pavement system. The pavement is modeled as a Timoshenko beam resting on a six-parameter foundation. The vehicle is simplified as a spring-mass-damper oscillator. For the first time, the dynamic response of vehicle-pavement coupled system is studied by modeling the pavement as a Timoshenko beam resting on a nonlinear foundation. Consequently, the shear effects and the rotational inertia of the pavement are included in the modeling process. The pavement model is assumed to be a linear-plus-cubic Pasternak-type foundation. Furthermore, the convergent Galerkin truncation is used to obtain approximate solutions to the coupled vibratory response of the vehicle-pavement coupled system. The dynamic responses of the vehicle-pavement system with the asphalt pavement on soft soil foundation are investigated via the numerical examples. The numerical results show that the calculation for the coupled vibratory response needs high-order modes. Moreover, the coupling effects between the pavement and the vehicle are numerically examined by using the convergent modal truncation. The physical parameters of the vehicle-pavement system such as the shear modulus are compared for determining their influences on the coupled vibratory response.

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

2014-12-01

202

Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.  

PubMed

A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements. PMID:24180754

Dibaji, Seyed Ahmad Reza; Banerjee, Rupak K; Soneson, Joshua E; Myers, Matthew R

2013-11-01

203

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

SciTech Connect

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. [Department of Physics, Faculty of Sciences, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil 56199-11367 (Iran, Islamic Republic of)] [Department of Physics, Faculty of Sciences, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil 56199-11367 (Iran, Islamic Republic of)

2013-06-15

204

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

NASA Astrophysics Data System (ADS)

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.; Pécseli, H. L.; Trulsen, J. K.; Ulriksen, M. I.; Eliasson, B.; Stenflo, L.

2011-05-01

205

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

206

Nonlinear electron-acoustic rogue waves in electron-beam plasma system with non-thermal hot electrons  

NASA Astrophysics Data System (ADS)

The properties of nonlinear electron-acoustic rogue waves have been investigated in an unmagnetized collisionless four-component plasma system consisting of a cold electron fluid, non-thermal hot electrons obeying a non-thermal distribution, an electron beam and stationary ions. It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of rogue wave profiles on the electron beam and energetic population parameter are discussed. The results of the present investigation may be applicable in auroral zone plasma.

Elwakil, S. A.; El-hanbaly, A. M.; Elgarayh, A.; El-Shewy, E. K.; Kassem, A. I.

2014-11-01

207

Measurement of the Beam Longitudinal Profile in a Storage Ring by Non-Linear Laser Mixing  

NASA Astrophysics Data System (ADS)

We report on the development of a new technique for the measurement of the longitudinal beam profile in storage rings. This technique, which has been successfully demonstrated at the Advanced Light Source, mixes the synchrotron radiation with the light from a mode-locked solid-state laser oscillator in a non-linear crystal. The up-converted radiation is then detected with a photomultiplier and processed to extract, store, and display the required information. The available choices of laser repetition frequency, pulse width, and phase modulation give a wide range of options for matching the bunch configuration of a particular storage ring. Besides the dynamic measurement of the longitudinal profile of each bunch, the instrument can monitor the evolution of the bunch tails, the presence of un trapped particles, and their diffusion into nominally empty RF buckets ("ghost bunches").

Beche, J.-F.; Byrd, J.; De Santis, S.; Denes, P.; Placidi, M.; Turner, W.; Zolotorev, M.

2004-11-01

208

Nonlinear estimation of geometric parameters in FEMs of volcano deformation: Integrating tomography models and geodetic data for Okmok volcano, Alaska  

NASA Astrophysics Data System (ADS)

The internal structure, loading processes, and effective boundary conditions of a volcano control the deformation observed at the Earth's surface. Using finite element models (FEMs), we simulate the response due to a pressurized magma chamber embedded in a domain having a distribution of elastic material properties. We present the Pinned Mesh Perturbation method (PMP) to automate the mesh generation process in response to perturbations of the position of a simulated magma chamber within an FEM domain. Using InSAR-observed deformation for the 1997 eruption of Okmok volcano, Alaska, as an example, we combine PMP with nested Monte Carlo methods to estimate a set of linear and nonlinear parameters that characterize the depressurization and location of the magma chamber beneath Okmok's caldera. The three-dimensional FEMs used in the PMP method simulate the distribution of material properties of tomography models and account for the irregular geometry of the topography and bathymetry. The estimated depth of an assumed spherical magma chamber is 3527-54+55 m below sea level and is sensitive to the distribution of material properties. This depth is consistent with lithostatic pressure constraints and very long period tremor observations. The fit of this FEM to the InSAR data is a significant improvement, at the 95% confidence level, compared to the fit of a corresponding FEM having homogeneous material properties. The methods presented here allow us to construct deformation models that integrate tomography models with geodetic observations, in an effort to achieve a deeper understanding of active volcanoes.

Masterlark, Timothy; Feigl, Kurt L.; Haney, Matthew; Stone, Jonathan; Thurber, Clifford; Ronchin, Erika

2012-02-01

209

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

210

Volume 129, number 5,6 PHYSICS LETTERS A 30 May 1988 THE NONLINEAR DYNAMICS OF DENSE ELECTRON BEAMS  

E-print Network

Volume 129, number 5,6 PHYSICS LETTERS A 30 May 1988 THE NONLINEAR DYNAMICS OF DENSE ELECTRON BEAMS IN THE AUTORESONANCE LASER ACCELERATOR A. LOEB Centerfor Plasma Physics, Racah Institute ofPhysics, Hebrew University a In this Letter we shall discuss the collective ac- linearly) polarized laser radiation propagating along

Friedland, Lazar

211

Nonlinear Earthquake Analysis of Reinforced Concrete Frames with Fiber and Bernoulli-Euler Beam-Column Element  

PubMed Central

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-? method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667

Karaton, Muhammet

2014-01-01

212

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

213

Nonlinear problems of aeroelasticity  

NASA Astrophysics Data System (ADS)

The presently treated nonlinear problems of aeroelasticity arise from both geometric and aerodynamic nonlinearities, and are characterized by the possibility of multiple solutions, chaos, and instabilities that often settle down to steady-state limit cycles. Structurally, nonlinearities can arise both geometrically and due to material nonlinearity that leads to nonlinear stiffness characteristics and hysteresis loops; from aerodynamics, nonlinearities are generated by high angles of attack and from bluff bodies, as well as from the transonic speed regime.

Dugundji, John

214

Multi-harmonic measurements and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary conditions  

NASA Astrophysics Data System (ADS)

This study presents a direct comparison of measured and predicted nonlinear vibrations of a clamped-clamped steel beam with non-ideal boundary conditions. A multi-harmonic comparison of simulations with measurements is performed in the vicinity of the primary resonance. First of all, a nonlinear analytical model of the beam is developed taking into account non-ideal boundary conditions. Three simulation methods are implemented to investigate the nonlinear behavior of the clamped-clamped beam. The method of multiple scales is used to compute an analytical expression of the frequency response which enables an easy updating of the model. Then, two numerical methods, the Harmonic Balance Method and a time-integration method with shooting algorithm, are employed and compared one with each other. The Harmonic Balance Method enables to simulate the vibrational stationary response of a nonlinear system projected on several harmonics. This study then proposes a method to compare numerical simulations with measurements of all these harmonics. A signal analysis tool is developed to extract the system harmonics' frequency responses from the temporal signal of a swept sine experiment. An evolutionary updating algorithm (Covariance Matrix Adaptation Evolution Strategy), coupled with highly selective filters is used to identify both fundamental frequency and harmonic amplitudes in the temporal signal, at every moment. This tool enables to extract the harmonic amplitudes of the output signal as well as the input signal. The input of the Harmonic Balance Method can then be either an ideal mono-harmonic signal or a multi-harmonic experimental signal. Finally, the present work focuses on the comparison of experimental and simulated results. From experimental output harmonics and numerical simulations, it is shown that it is possible to distinguish the nonlinearities of the clamped-clamped beam and the effect of the non-ideal input signal.

Claeys, M.; Sinou, J.-J.; Lambelin, J.-P.; Alcoverro, B.

2014-12-01

215

Nonlinear antenna technology  

Microsoft Academic Search

Nonlinear antennas combine advances in nonlinear dynamics, active antenna design, and analog microelectronics to generate beam steering and beam forming across an array of nonlinear oscillators. Nonlinear antennas exploit two phenomena typically shunned in traditional designs: nonlinear unit cells and interelement coupling. The design stems from nonlinear coupled differential equation analysis that by virtue of the dynamic control is far

BRIAN K. MEADOWS; TED H. HEATH; JOSEPH D. NEFF; EDGAR A. BROWN; DAVID W. FOGLIATTI; MICHAEL GABBAY; V. In; P. Hasler; S. P. Deweerth; W. L. Ditto

2002-01-01

216

Experimental observations of nonlinearly enhanced 2omega-UH electromagnetic radiation excited by steady-state colliding electron beams  

NASA Technical Reports Server (NTRS)

Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.

Intrator, T.; Hershkowitz, N.; Chan, C.

1984-01-01

217

Energy conservation in the transient response of nonlinear beam vibration problems subjected to pulse loading - A numerical approach  

NASA Technical Reports Server (NTRS)

The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system. It is also shown that while the fundamental response is contained in a first mode envelope, the fluctuations caused by the higher order modes must be resolved.

Moyer, E. T., Jr.

1984-01-01

218

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

219

Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces I: Non-linear model and stability analysis  

Microsoft Academic Search

The stability of a cantilever elastic beam with rectangular cross-section under the action of a follower tangential force and a bending conservative couple at the free end is analyzed. The beam is herein modeled as a non-linear Cosserat rod model. Non-linear, partial integro-differential equations of motion are derived expanded up to cubic terms in the transversal displacement and torsional angle

Achille Paolone; Marcello Vasta; Angelo Luongo

2006-01-01

220

A molecular beam study of nonlinearity in the CO-induced surface restructuring of Ir{100}  

NASA Astrophysics Data System (ADS)

The kinetics of CO chemisorption on both the (1×5) and (1×1) surfaces of Ir{100}, including the CO-induced surface restructuring process, have been studied by measuring the sticking probability as a function of the surface temperature and beam flux. Due to competition between desorption from the (1×5) phase and growth of (1×1) islands, the sticking probability on the initial (1×5) surface is strongly flux-dependent at surface temperatures Ts in the range 480<=Ts<=510 K. It is shown that this is due to a strongly nonlinear dependence of the (1×1) growth rate on the local CO coverage on the (1×5) substrate, with an apparent reaction order of around 5. Desorption energies and pre-exponentials of desorption for CO from both the (1×1) and (1×5) surfaces have been determined by means of a modified lifetime measurement technique. Equilibrium coverages as well as isothermal desorption rates of CO were determined for both surface phases. The zero coverage desorption energy of CO from the (1×1) substrate is 196+/-5 kJ/mol and from the (1×5) surface it is around 150 kJ/mol. This difference in adsorption energies is the driving force for the CO-induced (1×5) to (1×1) phase transition. TEAS data show that the local CO coverage on the growing (1×1) islands during the phase transformation is 0.5 ML.

Ali, T.; Klötzer, B.; Walker, A. V.; King, D. A.

1998-12-01

221

Theory of Gaussian beam Z scan with simultaneous third- and fifth-order nonlinear refraction based on a Gaussian decomposition method  

Microsoft Academic Search

We present a detailed theoretical investigation on the Gaussian beam Z scan for arbitrary aperture and arbitrary nonlinear refraction phase shifts, based on the Gaussian decomposition method, including cases when the medium exhibits the single (2n+1)th-order nonlinear refraction effect and the simultaneous third- and fifth-order nonlinear refraction effects. We find the optimum sum upper limit, which is of great importance

Bing Gu; Jing Chen; Ya-Xian Fan; Jianping Ding; Hui-Tian Wang

2005-01-01

222

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

223

Geometric Solids  

NSDL National Science Digital Library

This tool lets learners explore various geometric solids and their properties. Learners can manipulate and color each shape to explore the faces, edges, and vertices, and they can use this tool to investigate the relationship among the number of faces, vertices, and edges. This tool supports the 5-lesson unit "Geometric Solids and Their Properties" (cataloged separately).

2011-01-01

224

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

225

Geometric Mechanics  

Microsoft Academic Search

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

Richard Talman

1999-01-01

226

Dynamic Response of Strain Rate Dependent Glass\\/Epoxy Composite Beams Using Finite Difference Method  

Microsoft Academic Search

This paper deals with a numerical analysis of the transient response of composite beams with strain rate dependent mechanical properties by use of a finite difference method. The equations of motion based on Timoshenko beam theory are derived. The geometric nonlinearity effects are taken into account with von Kármán large deflection theory. The finite difference method in conjunction with Newmark

M. M. Shokrieh; A. Karamnejad

2010-01-01

227

Unconventional finite element method for nonlinear analysis of beams and plates  

E-print Network

performance under various boundary conditions. In the linear convergence study, solutions are compared with analytical solutions available and solutions of existing models. For non-linear equation solving direct method and Newton-Raphson method are used...

Kim, Wooram

2009-05-15

228

Nonlinear charge and current neutralization of an ion beam pulse in a pre-formed plasma  

E-print Network

to high-energy lepton colliders, are discussed in Refs. 3­10. In particular, both heavy ion fusion of a high-current finite-length ion beam in a cold pre-formed plasma is investigated. The outcome performed for parameters relevant to heavy ion fusion assuming long, dense beams with length lb Vb / b

Kaganovich, Igor

229

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

230

Nonlinear generation of harmonics through the interaction of an internal wave beam with a model oceanic pycnocline  

NASA Astrophysics Data System (ADS)

The interaction of an internal wave beam (IWB) with an idealized oceanic pycnocline is examined using two-dimensional fully nonlinear direct numerical simulations based on a spectral multidomain penalty method in the vertical direction. The phenomenon of focus is the nonlinear generation of harmonics. A total of 24 simulations have been performed, varying the normalized pycnocline thickness and the ratio of peak pycnocline Brunt-Väisälä frequency to that of the stratified lower layer. Harmonics at the point of IWB entry into the pycnocline increase in amplitude and number with a measure of the maximum gradient of the Brunt-Väisälä frequency, suggesting refraction as an important factor in harmonic generation. Among the simulations performed, two distinct limits of pycnocline thickness are identified. For thin pynoclines, whose thickness is 10% of the incident IWB's horizontal wavelength, harmonics trapped within the pycnocline have maximum amplitude when their frequency and wavenumber match those of the natural pycnocline interfacial wave mode. Results in this case are compared with weakly nonlinear theory for harmonic generation by plane wave refraction. For thicker pycnoclines, whose thickness is equal the incident IWB's horizontal wavelength, IWB refraction results in harmonic generation at multiple locations in addition to pycnocline entry, giving rise to complex flow structure inside the pycnocline.

Diamessis, P. J.; Wunsch, S.; Delwiche, I.; Richter, M. P.

2014-06-01

231

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

232

Nonlinear Analysis of Beams Using Least-Squares Finite Element Models Based on the Euler-Bernoulli and Timoshenko Beam Theories  

E-print Network

equations ( ) ( ) ( ) ( ) 0 0 1 1 4 2 2 0 0 0 0 2 2 3 3 5 1 6 22 0 0 b a b a x e e e e xx x x e e e e e e e e xx xx x d u N f x u x dx Q Q dx dx d w dw d wN M q x w x dx Q Q Q Q dx dx dx... point on the neutral axis, and 0w is the transverse displacement of the point on the neutral axis. x z, w0 x,u 0z Undeformed (u ,w )0 0 (u,w) u 0 -dw 0 dxTBT ? Figure 3.4. Deformation of a beam in Timoshenko theory 3.3.3 Nonlinear strain...

Raut, Ameeta A.

2010-07-14

233

Two-wave interaction of helical light beams in a nonlinear medium  

NASA Astrophysics Data System (ADS)

The paper presents a theoretical study of the interaction of helical beams with arbitrary topological charges in the autowave propagation regime. The self-similar solution describing two-dimensional two-wave collapse is obtained. Finally, it is suggested that the feasibility of the experimental generation of such helical beams is connected with the isolation of angular harmonics in the ring resonator whose power must exceed a certain critical value depending on the topological charge (the helicity).

Kruglov, V. I.; Vlasov, R. A.; Volkov, V. M.

1989-06-01

234

Measurement of Nonlinear Responses and Optical Limiting Behavior of TIO2/PS Nano-Composite by Single Beam Technique with Different Incident Intensities  

NASA Astrophysics Data System (ADS)

Titanium dioxide (titania) is a cheap, nontoxic and highly efficient photocatalyst being extensively applied for the degradation of organic pollutants, air purification, water splitting, reduction of nitrogen to ammonia, and optical devices due to its optical behaviors. The third-order nonlinear optical properties of TiO2/PS nano-composite were studied by means of single beam transmission technique, using a continuous-wave (CW) He-Ne laser beam with a wavelength of 632.8 nm with three different incident intensities. The magnitude and sign of the third-order nonlinear refractive index (n2) and nonlinear absorption (?) of TiO2/PS nano-composite were determined by use of both the closed-aperture and opened-aperture z-scan techniques. Z-scan technique, developed by Sheik-Bahae et al., has been used widely in material characterization. A single-beam (also called z-scan method) for measuring the sign and magnitude of nonlinear refraction that has simplicity and very high sensitivity has been reported recently. Optical limiting property of TiO2/PS nano-composite is studied. The positive sign obtained for nonlinear refractive index indicated that there is a self-focusing effect in the sample. The nonlinear refractive index was in order of 10-8 (cm2/W) and the nonlinear absorption coefficient was obtained in order of 10-2 (cm/W) with negative sign. The values of nonlinear refractive index and nonlinear absorption coefficient are enhanced by decreasing the intensity.

Majles Ara, M. H.; Dehghani, Z.

235

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

236

Forced Vibration Analysis of a Beam Structure with Nonlinear Support Elements  

NASA Astrophysics Data System (ADS)

In computing a periodic steady-state vibration generated in a large-scale nonlinear structure by the incremental transfer stiffness coefficient method suggested in a previous paper, the stable and unstable solutions can be computed without distinction. Thus, the stability of the obtained solution must be examined. However, it is very difficult to analyze the stability of the solution of the nonlinear system with high degree of freedom. To overcome this difficulty, a method to reduce the dimension of the equation used for stability analysis without spoiling the accuracy is developed by applying the concept of modal analysis to the variational equation used for the stability analysis. Two types of modal matrices are considered in the reduction of dimension, and a method is proposed to extract the modes that dominate the stability of the solution. The validity of the incremental transfer stiffness coefficient method and the method of stability analysis using the reduction model is confirmed by numerical computational results.

Sasaki, Takumki; Kondou, Takahiro

237

Geometric Solids  

NSDL National Science Digital Library

This tool allows you to learn about various geometric solids and their properties. You can manipulate each solid, seeing it from every angle. You can also color each shape to explore the number of faces, edges, and vertices. With that information, you are challenged to investigate the following question: For any polyhedron, what is the relationship between the number of faces, vertices, and edges?

Illuminations, Nctm

2000-01-01

238

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

239

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

SciTech Connect

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. [Theoretical Plasma Physics Division, PINSTECH, Nilore, 44000 Islamabad (Pakistan) [Theoretical Plasma Physics Division, PINSTECH, Nilore, 44000 Islamabad (Pakistan); National Centre For Physics (NCP), Shahdra Valley Road, 44000 Islamabad (Pakistan); Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad (Pakistan); El-Tantawy, S. A.; Moslem, W. M. [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt)] [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt)

2013-08-15

240

Journal of Machine Learning Research 1 (3000) 1 Submitted 0/00; Published 0/00 A Geometric View of Non-Linear  

E-print Network

of Non-Linear On-Line Stochastic Gradient Descent Krzysztof A. Krakowski KRZYSZTOF.KRAKOWSKI" in order to generalise the derivation of the c 3000 Krzysztof A. Krakowski, Robert E. Mahony, Robert C. Williamson and Manfred K. Warmuth. #12;KRAKOWSKI, MAHONY, WILLIAMSON AND WARMUTH OCTOBER 31, 2007 EG

Botea, Adi

241

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  

SciTech Connect

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 the presence of the ring of nonlinear magnetic fields. The main part of the work deals with sextupole magnets. Formula for the beam size in the presence of octupole fields are also developed to the first order in the octupole strength, although octupole magnets are not widely used in present storage ring designs. This calculation is done mainly because the octupole field has the same symmetry as the beam-beam force for the head-on collision. This will give us the opportunity to compare the conduct of the bunch due to this two types of nonlinear kicks. The general terms of the applicability of the Green's function method is discussed in the first part of this work.

Kheifets, S.

1983-01-01

242

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.

2012-03-01

243

Nonlinear transfer map treatment of beams through systems with absorbing material  

Microsoft Academic Search

Summary form only given. Particle optical systems are usually comprised of electric and magnetic bending elements, focusing elements, and high-order multipoles for correction of aberrations. However, various modern systems for the transport and manipulation of large acceptance beams of rare and short-lived particles require the detailed treatment of more advanced optical elements. In particular, in recent years the reduction of

K. Makino; M. Berz; D. Errede; C. J. Johnstone

2003-01-01

244

Neurocontroller Alternatives for "Fuzzy" Ball-and-Beam Systems With Nonuniform, Nonlinear Friction  

E-print Network

.S.A. ABSTRACT The ball-and-beam problem is a benchmark for testing control algorithms. In the World Congress Congress On Neural Networks, 1994, and later, at the IFAC 13th Triennial World Congress in San Francisco provided another example fuzzy material, sticky tape, in his earlier plenary talk at World Congress

Prokhorov, Danil

245

Characterizing proton beam of 6.7 MeV LEDA RFQ by fitting wire-scanner profiles to 3D nonlinear simulations  

Microsoft Academic Search

Quadrupole scans were used to characterize the transverse beam of the LEDA RFQ. The original scan data, obtained when the HEBT was installed immediately downstream of the RFQ, were reanalyzed by fitting to the 3-D nonlinear simulation code IMPACT. All the data in the measured profiles at the wire scanner were used, not just the rms widths. The measured and

W. P. Lysenko; J. D. Gilpatrick; J. Qiang; L. J. Rybarcyk; R. D. Ryne; J. D. Schneider; H. V. Smith; L. M. Young; M. E. Schultze

2001-01-01

246

Geometric Models  

NSDL National Science Digital Library

Created by Kyle Siegrist of the University of Alabama-Huntsville, this is an online, interactive lesson on geometric models. The author provides examples, exercises, and applets which include Buffon's problems, Bertrand's paradox, and random triangles. Additionally, the author provides links to external resources for students wanting to engage further in this topic. This is simply one lesson in a series of seventeen. They are all easily accessible as the author has formated his site much like an online textbook.

Siegrist, Kyle

2009-02-23

247

Nonlinear Analysis of Conventional and Microstructure Dependent Functionally Graded Beams under Thermo-mechanical Loads  

E-print Network

x(xa; t)Q3 x(xb; t)Q6 (5.3b) 5.1.2. Microstructure dependent beam The weak form of Eqs. (3.9a) and (3.9b) for microstructure dependent beam can be given as 0 = Z xb xa I 0 u @2u @t2 I 1 u @3w @t2@x + @ u @x Nxx dx Q1 u(xa; t) Q... + @ w @x Qx + @ w @x Nxx @w @x wq dx Q2 w(xa; t) Q5 w(xb; t) (5.7b) 0 = Z xb xa I 1 x @2u @t2 + I2 x @2 x @t2 + xQx + @ x @x Mxx dx Q3 x(xa; t) Q6 x(xb; t) (5.7c) where Qi are the generalized forces...

Arbind, Archana

2012-10-19

248

Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system  

NASA Technical Reports Server (NTRS)

It is shown that the unstable electron-plasma waves of a beam-plasma system can generate electromagnetic radiation in a uniform plasma. The generation mechanism is a scattering of the unstable electron plasma waves off ion-acoustic waves, producing electromagnetic waves whose frequency is near the local plasma frequency. The wave vector and frequency matching conditions of the three-wave mode coupling are experimentally verified. The electromagnetic radiation is observed to be polarized with the electric field parallel to the beam direction, and its source region is shown to be localized to the unstable plasma wave region. The frequency spectrum shows negligible intensity near the second harmonic of the plasma frequency. These results suggest that the observed electromagnetic radiation of type III solar bursts may be generated near the local plasma frequency and observed downstream where the wave frequency is near the harmonic of the plasma frequency.

Whelan, D. A.; Stenzel, R. L.

1985-01-01

249

Geometric Algebra  

E-print Network

This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines a product that's strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane. This system was invented by William Clifford and is more commonly known as Clifford algebra. It's actually older than the vector algebra that we use today (due to Gibbs) and includes it as a subset. Over the years, various parts of Clifford algebra have been reinvented independently by many people who found they needed it, often not realizing that all those parts belonged in one system. This suggests that Clifford had the right idea, and that geometric algebra, not the reduced version we use today, deserves to be the standard "vector algebra." My goal in these notes is to describe geometric algebra from that standpoint and illustrate its usefulness. The notes are work in progress; I'll keep adding new topics as I learn them myself.

Eric Chisolm

2012-05-27

250

Parametric phase conjugation for the second harmonic of a nonlinear ultrasonic beam  

Microsoft Academic Search

The effect of phase conjugation for the second harmonic of a focused ultrasonic beam was investigated experimentally and by\\u000a numerical simulation. An ultrasonic pulse with the carrier frequency f=3 MHz was emitted into water and focused at a point between the source and the phase conjugating system. The phase conjugation\\u000a for the second harmonic of the incident wave (2f=6 MHz)

A. P. Brysev; F. V. Bunkin; M. F. Hamilton; R. V. Klopotov; L. M. Krutyanskii; K. Yan

2003-01-01

251

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment  

Microsoft Academic Search

Free vibration of statically thermal postbuckled functionally graded material (FGM) beams with surface-bonded piezoelectric\\u000a layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on\\u000a the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric\\u000a layers subject to thermo-electromechanical loadings are formulated. It is assumed that the

Shi-rong Li; Hou-de Su; Chang-jun Cheng

2009-01-01

252

Application of the crack compliance method to long axial cracks in pipes with allowance for geometrical nonlinearity and shape imperfections (dents)  

Microsoft Academic Search

Application of the crack compliance method to the analysis of thin-walled rings with a radial crack has two features: a crack is considered as a concentrated angular compliance and the deformation of all other sections of the rings is calculated as for a curvilinear beam. The latter can be most conveniently found by the method of initial parameters where the

I. V. Orynyak; Ye. S. Yakovleva

2008-01-01

253

Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals  

SciTech Connect

The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions.

Assanto, Gaetano [Department of Electronic Engineering, NooEL-Nonlinear Optics and OptoElectronics Lab, University of Rome 'Roma Tre', Via della Vasca Navale 84, 00146 Rome (Italy); Minzoni, Antonmaria A. [Department of Mathematics and Mechanics, Fenomenos Nonlineales y Mecanica (FENOMEC), Instituto de Investigacion en Matematicas Aplicadas y Sistemas, Universidad Nacional Autonoma de Mexico, 01000 Mexico D.F. (Mexico); Smyth, Noel F. [School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); Worthy, Annette L. [School of Mathematics and Applied Statistics, University of Wollongong, Northfields Avenue, Wollongong, New South Wales 2522 (Australia)

2010-11-15

254

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

255

Geometrically nonlinear numerical procedure for Saint-Venant's problem for a symmetrical elastic shell with a closed contour and circular axis  

Microsoft Academic Search

An original numerical procedure of treating Saint-Venant's problem for toroidal-like shells under pressure and bending moment is suggested. Its peculiarity consists in that the loading and displacement parameters are separated into two groups: the first one describes the ring-like transverse deformation of the shell cross section, while the second the beam-like axial deformation of the latter. One of them is

I. V. Orynyak; A. V. Bogdan; S. A. Radchenko

2009-01-01

256

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

257

Nonlinear waves: Propagation and interaction  

Microsoft Academic Search

Papers are presented on such topics as nonlinear temperature waves in heat-releasing materials, nonlinear oscillatory phenomena in biology, the interaction of intense electromagnetic waves with dense plasmas, nonlinear motions of atoms in a light field, and geometric-optic methods for the estimation of fields in foci and on caustics. Consideration is also given to nonlinear acoustics, synoptic ocean eddies, the diffusion

A. V. Gaponov-Grekhov

1981-01-01

258

Fast 4D cone-beam reconstruction using the McKinnon-Bates algorithm with truncation correction and nonlinear filtering  

NASA Astrophysics Data System (ADS)

A challenge in using on-board cone beam computed tomography (CBCT) to image lung tumor motion prior to radiation therapy treatment is acquiring and reconstructing high quality 4D images in a sufficiently short time for practical use. For the 1 minute rotation times typical of Linacs, severe view aliasing artifacts, including streaks, are created if a conventional phase-correlated FDK reconstruction is performed. The McKinnon-Bates (MKB) algorithm provides an efficient means of reducing streaks from static tissue but can suffer from low SNR and other artifacts due to data truncation and noise. We have added truncation correction and bilateral nonlinear filtering to the MKB algorithm to reduce streaking and improve image quality. The modified MKB algorithm was implemented on a graphical processing unit (GPU) to maximize efficiency. Results show that a nearly 4x improvement in SNR is obtained compared to the conventional FDK phase-correlated reconstruction and that high quality 4D images with 0.4 second temporal resolution and 1 mm3 isotropic spatial resolution can be reconstructed in less than 20 seconds after data acquisition completes.

Zheng, Ziyi; Sun, Mingshan; Pavkovich, John; Star-Lack, Josh

2011-03-01

259

Nonlinear change of on-axis pressure and intensity maxima positions and its relation with the linear focal shift effect  

Microsoft Academic Search

A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude

Yu. N. Makov; V. J. Sánchez-Morcillo; F. Camarena; V. Espinosa

2008-01-01

260

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

261

Three-Dimensional Postbuckling Analysis of Curved Beams  

NASA Technical Reports Server (NTRS)

Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.

Pai, P. Frank; Lee, Seung-Yoon

2002-01-01

262

a Comparison of Three Techniques Using Steady State Data to Identify Non-Linear Modal Behavior of AN Externally Excited Cantilever Beam  

NASA Astrophysics Data System (ADS)

Non-linear system identification is used to generate models of modes in physical structures. Analysis of the theoretical non-linear model of a cantilevered beam is used to predict the inputs to the physical system that will produce responses suitable for enhanced parameter estimation, thereby improving the model. Three identification techniques are described and applied to both numerical and experimental data: the first is based on the continuous-time differential equation model of the system, the second uses relationships generated by the method of harmonic balance, and the third is based on fitting steady state response data to the amplitude and phase modulation equations resulting from a multiple time scales analysis. The performance of each method improves as the non-linearities in the system become more pronounced. The benefits and limitations of the methods are discussed.

DOUGHTY, T. A.; DAVIES, P.; BAJAJ, A. K.

2002-01-01

263

Generation of broad-bandwidth femtosecond 270-nm light by third-order nonlinear coupling with focusing beams in a single crystal of BBO  

Microsoft Academic Search

By third-order nonlinear coupling and tightly focusing the beams in a single crystal of BBO, high intensity broad-bandwidth femtosecond pulses are used to generate 50muJ of light at 270nm (up to 1% THG efficiency). And it is proved that the major contribution to the THG observed is the third-order process, not the cascaded second-order process.

Keyu Li; Kun Li; Xiaoming Zeng; Yiqiu Gu; Wei Hang; Bin Zhang; Kainan Zhou; Bin Feng; Fuquan Li; Huaiting Jia; Yong Xiang; Wei Zhong; Bing Xu; Tian'en Li; Liquan Wang; Xu Diao; Xiaojun Huang; Qihua Zhu; Feng Jing; Xiaofeng Wei

2007-01-01

264

Nonlinear dynamics  

SciTech Connect

Following an introduction on analytical mechanics, canonical transformations, and perturbation theory, a description is given of nonlinear effects for near-integrable systems associated with resonances, amplitude variations with multiple crossings, adiabatic changes of the parameters, and time variation of the perturbation. Examples of applications coming from observations and calculations related to CERN accelerators concern coupling measurements, intra-beam scattering, beam-beam effects magnetic imperfections, two-beam overlap knockout, and synchro-betatron resonances. Finally, the notions of invariant distortion and aperture of bounded motion in the presence of multipoles are introduced.

Guignard, G.

1989-04-01

265

Single-beam Z-scan measurement of the third-order optical nonlinearities of triarylmethane dyes  

NASA Astrophysics Data System (ADS)

Solid-state dye-doped polymers are an attractive alternative to the conventional liquid-dye solutions. The search for new materials which have potential application in optoelectronic devices has lead us to probe the organic dyes. The solid state being a better medium when compared to a liquid medium has lead to the incorporation of dyes in the polymer matrix. The study of nonlinear characteristics of dyes in polymeric media is essential for developing such potential application devices. In this paper, the third-order nonlinear optical properties of three dyes from the Triarylmethane family were measured in 1-Butanol and in dye-doped polymer films by the Z-scan technique using a cw diode-pumped Nd:YAG laser at 532 nm. The Z-scan technique has also been used to present the observation of a nonlinear refractive index resulting from the photochromism of one of the dyes. These materials exhibit a large negative optical nonlinearity resulting due to the thermal effect. The relative contributions from the nonlinear absorption (NLA) and nonlinear refraction (NLR) are dependent on the chemical structure and linear absorption of the dyes. The dyes exhibited a nonlinear refractive coefficient n 2, a nonlinear absorption coefficient ?, and susceptibility x(3) on the order of 10-8 cm2/W, 10-4 cm/W, and 10-6 esu, respectively, in both liquid and solid media. The results show that these dyes have potential applications in nonlinear optics.

Vinitha, G.; Ramalingam, A.

2008-10-01

266

FREE VIBRATION OF HEATED EULER–BERNOULLI BEAMS WITH THERMAL POSTBUCKLING DEFORMATIONS  

Microsoft Academic Search

Based on the accurate geometrical nonlinear theory for Euler–Bernoulli beams, considering the coupling of the longitudinal and transverse motions, the harmonic responses of small vibration of uniformly heated beams with and without static thermal postbuckling deformations are presented by employing the numerical shooting technique. Characteristic curves of the lower order frequencies versus the temperature parameter are illustrated for pinned-pinned, fixed-fixed,

Shi-Rong Li; Zhao-Chun Teng; You-He Zhou

2004-01-01

267

Measurement of the nonlinear refractive index (n(2)) and stimulated Raman scattering in optical fibers as a function of germania content, using the photorefractive beam coupling technique  

NASA Astrophysics Data System (ADS)

One of the greatest challenges in optical communication is the understanding and control of optical fiber nonlinearities. While these nonlinearites limit the power handling capacity of optical fibers and can cause noise, signal distortion and cross talk in optically amplified transmission systems, they have been equally harnessed for the development of new generations of optical amplifiers and tunable laser sources. The two prominent parameters that characterize the nonlinear properties of an optical fiber are the nonlinear refractive index (n2) and the Raman gain coefficient (gR). These parameters are related to the third order nonlinear susceptibility [chi (3)]. In this work, the photorefractive beam coupling technique, also called induced grating autocorrelation (IGA), has been used to measure the nonlinear refractive index (n2) and the Raman gain coefficient (gR) of short lengths (z ˜ 20 m) of optical fibers. In the IGA experiment, a transform limited Gaussian pulse is propagated through a short length of an optical fiber, where it undergoes self-phase modulation (SPM) and other nonlinear distortions, and the output pulse is split into two. The two-excitation pulses are then coupled into a photorefractive crystal, where they interfere and form a photorefractive phase grating. The IGA response is determined by delaying one beam (the probe) and plotting the diffracted intensity of the probe versus the relative delay (tau). Analysis of the IGA response yields information about the nonlinear phase distortions and other calibration parameters of the fiber. Using the IGA technique the author has measured the nonlinear refractive index in several types of fibers, including pure silica, Er-Al-Ge doped fibers, DCF (dispersion compensating fiber) and the recently developed TrueWave Rs fiber, and investigated the dependence of n2 on the doping profiles of Er, Al, and Ge in optical fibers. The standard IGA model for n2 measurements was derived from the solution of the nonlinear wave equation for pulse propagation in the limit of pure self-phase modulation. This model assumed that GVD (group velocity dispersion) and other nonlinear processes such as SRS (stimulated Raman scattering) are negligible. This model has been successfully used to fit the experimental data and determine the n2 of the fiber from the time dependent phase shift. However, SRS has been observed to distort the IGA trace, thus leading to a breakdown of the standard IGA model. A new IGA model has been developed in this study from the solution of the coupled-amplitude nonlinear Schrodinger equation, using both analytical and numerical approaches. This new model successfully accounts for the SRS effects on the IGA trace, in the limit of zero GVD, and allows the direct determination of the Raman gain coefficient from the fit of the SRS-distorted IGA trace. The measured nonlinear refractive index and Raman gain coefficients are in good agreement with published results. It was also shown that in the limit of zero GVD and no Raman, the IGA technique reduces to the widely accepted spectral domain SPM technique pioneered by Stolen and Lin, but is readily applicable to shorter lengths of fiber and is sensitive to smaller phase shifts.

Oguama, Ferdinand Anayo

268

Analysis of nonlinear dynamics of a cantilever beam-rigid-body MEMS gyroscope using a continuation method  

E-print Network

The nonlinear dynamics of a microbeam-rigid body gyroscope are investigated by using a continuation method. To study the nonlinear dynamics of the system, the Lagrangian of the system is discretized and the reduced-order model is obtained. By using the continuation method, the frequency-response curves are computed and the stability of response is determined.

Lajimi, Seyed Amir Mousavi

2014-01-01

269

Comparing the Nonlinear Behaviors of Steel and Concrete Link Beams in Coupled Shear Walls System by Finite Element Analysis  

Microsoft Academic Search

Regarding the role of link beams in the seismic behavior of coupled shear walls, in this study, at first a pre-designed concrete link beam of a coupled shear walls system, tested previusly under cyclic loading, has been analyzed by Finite Element Modeling (FEM). Then it has been substituted by a steel link beam, and the analyses have been repeated to

Mahmood Hosseini; Hossein Sadeghi; Seidali Habiby

2011-01-01

270

Nonlinear ordinary difference equations  

NASA Technical Reports Server (NTRS)

Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.

Caughey, T. K.

1979-01-01

271

A numerical investigation of nonlinear aeroelastic effects on flexible high aspect ratio wings  

NASA Astrophysics Data System (ADS)

A nonlinear aeroelastic analysis that couples a nonlinear structural model with an Euler/Navier-Stokes flow solver is developed for flexible high aspect ratio wings. To model the nonlinear structural characteristics of flexible high aspect ratio wings, a two-dimensional geometric nonlinear methodology, based on a 6 degree-of-freedom (DOF) beam finite element, is extended to three dimensions based on a 12 DOF beam finite element. The three-dimensional analysis is developed in order to capture the nonlinear torsion-bending coupling, which is not accounted for by the two-dimensional nonlinear methodology. Validation of the three-dimensional nonlinear structural approach against experimental data shows that the approach accurately predicts the geometric nonlinear bending and torsion due to bending for configurations of general interest. Torsion is slightly overpredicted in extreme cases and higher order modeling is then required. The three-dimensional nonlinear beam model is then coupled with an Euler/Navier-Stokes computational fluid dynamics (CFD) analysis. Solving the equations numerically for the two nonlinear systems results in an increase in computational time and cost needed to perform the aeroelastic analysis. To improve the computational efficiency of the nonlinear aeroelastic analysis, the nonlinear structural approach uses a second-order accurate predictor-corrector methodology to solve for the displacements. Static aeroelastic results are presented for an unswept and swept high aspect ratio wing in the transonic flow regime, using the developed nonlinear aeroelastic methodology. Unswept wing results show a reversal in twist due to the nonlinear torsion-bending coupling effects. Specifically, the torsional moments due to drag become large enough to cause the wing twist rotations to washin the wing tips, while the linear results show a washout twist rotation. The nonlinear twist results are attributed to the large bending displacements coupled with the large drag experienced by this flexible high aspect ratio wing at the transonic flow conditions. Swept wing results show that nonlinear torsion-bending effects tend to reduce the amount of washout as compared to a linear structural aeroelastic analysis making the wing more prone to tip stall. Finally, this thesis lays the groundwork for further development of dynamic aeroelastic computational capabilities using nonlinear finite element methods coupled to nonlinear computational fluid dynamics methods.

Garcia, Joseph Avila

2002-01-01

272

Three-dimensional nonlinear efficiency enhancement analysis in free-electron laser amplifier with prebunched electron beam and ion-channel guiding  

SciTech Connect

Efficiency enhancement in free-electron laser is studied by three-dimensional and nonlinear simulation using tapered helical wiggler magnetic field or tapered ion-channel density. In order to reduce the saturation length, prebunched electron beam is used. A set of nonlinear and coupled differential equations are derived that provides the self-consistent description of the evolution of both an ensemble of electrons and the electromagnetic radiation. These equations are solved numerically to show that the combined effect of tapering and prebunching results in significant enhancement of power and considerable reduction of the saturation length. To have a deeper insight into the problem, an analytical treatment is also presented that uses the small signal theory to derive a modified pendulum equation.

Jafari Bahman, F.; Maraghechi, B. [Department of Physics, Amirkabir University of Technology, Post Code 15916-34311 Tehran (Iran, Islamic Republic of)

2013-02-15

273

Advances in dynamic relaxation techniques for nonlinear finite element analysis  

SciTech Connect

Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies.

Sauve, R.G.; Metzger, D.R. [Ontario Hydro Technologies, Toronto, Ontario (Canada)

1995-05-01

274

Nonlinear dynamics aspects of particle accelerators  

SciTech Connect

This book contains 18 selections. Some of the titles are: Integrable and Nonintegrable Hamiltonian Systems; Nonlinear Dynamics Aspects of Modern Storage Rings; Nonlinear Beam-Beam Resonances; Synchro-Betatron Resonances; Review of Beam-Beam Simulations; and Perturbation Method in Nonlinear Dynamics.

Araki, H.; Ehlers, J.; Hepp, K.; Kippenhahn, R.; Weidenmuller, A.; Zittartz, J.

1986-01-01

275

Geometrically nonlinear analysis of laminated elastic structures  

NASA Technical Reports Server (NTRS)

Laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many other were analyzed. The finite element method, a numerical technique for engineering analysis of structures, is used to model the geometry and approximate the solution. Various alternative formulations for analyzing laminated plates and shells are developed and their finite element models are tested for accuracy and economy in computation. These include the shear deformation laminate theory and degenerated 3-D elasticity theory for laminates.

Reddy, J. N.

1984-01-01

276

Geometric Photonic Spin Hall Effect with Metapolarization  

E-print Network

We develop a geometric photonic spin Hall effect (PSHE) which manifests as spin-dependent shift in momentum space. It originates from an effective space-variant Pancharatnam-Berry (PB) phase created by artificially engineering the polarization distribution of the incident light. Unlikely the previously reported PSHE involving the light-matter interaction, the resulting spin-dependent splitting in the geometric PSHE is purely geometrically depend upon the polarization distribution of light which can be tailored by assembling its circular polarization basis with suitably magnitude and phase. This metapolarization idea enables us to manipulate the geometric PSHE by suitably tailoring the polarization geometry of light. Our scheme provides great flexibility in the design of various polarization geometry and polarization-dependent application, and can be extrapolated to other physical system, such as electron beam or atom beam, with the similar spin-orbit coupling underlying.

Ling, Xiaohui; Yi, Xunong; Luo, Hailu; Wen, Shuangchun

2014-01-01

277

PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism  

Microsoft Academic Search

Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon

Jason S. Gardner

2011-01-01

278

Constrained ballistics and geometrical optics  

E-print Network

The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the initially unconstrained formulation. Although the resulting equations are not, in principle, obtained from a variational statement, it is shown that the trajectories coincide with those of geometrical optics in a medium with a suitably chosen refractive index, as prescribed by Fermat's principle of least time. This fact gives rise to an intriguing mechano-optical analogy. The trajectories are further studied and discussed.

Epstein, Marcelo

2014-01-01

279

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft  

NASA Astrophysics Data System (ADS)

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

Patil, Mayuresh Jayawant

280

Propagation of ion-acoustic solitons in an electron beam-superthermal plasma system with finite ion-temperature: Linear and fully nonlinear investigation  

SciTech Connect

The propagation of ion-acoustic (IA) solitons is studied in a plasma system, comprised of warm ions and superthermal (Kappa distributed) electrons in the presence of an electron-beam by using a hydrodynamic model. In the linear analysis, it is seen that increasing the superthermality lowers the phase speed of the IA waves. On the other hand, in a fully nonlinear investigation, the Mach number range and characteristics of IA solitons are analyzed, parametrically and numerically. It is found that the accessible region for the existence of IA solitons reduces with increasing the superthermality. However, IA solitons with both negative and positive polarities can coexist in the system. Additionally, solitary waves with both subsonic and supersonic speeds are predicted in the plasma, depending on the value of ion-temperature and the superthermality of electrons in the system. It is examined that there are upper critical values for beam parameters (i.e., density and velocity) after which, IA solitary waves could not propagate in the plasma. Furthermore, a typical interaction between IA waves and the electron-beam in the plasma is confirmed.

Saberian, E. [Department of Physics, Faculty of Sciences, Azarbaijan Shahid Madani University, 53714-161 Tabriz (Iran, Islamic Republic of); Department of Physics, Faculty of Basic Sciences, University of Neyshabur, Neyshabur (Iran, Islamic Republic of); Esfandyari-Kalejahi, A.; Rastkar-Ebrahimzadeh, A.; Afsari-Ghazi, M. [Department of Physics, Faculty of Sciences, Azarbaijan Shahid Madani University, 53714-161 Tabriz (Iran, Islamic Republic of)

2013-03-15

281

Parallel processors and nonlinear structural dynamics algorithms and software  

NASA Technical Reports Server (NTRS)

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Belytschko, Ted

1989-01-01

282

On geometric factors for neutral particle analyzersa)  

NASA Astrophysics Data System (ADS)

Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.

Stagner, L.; Heidbrink, W. W.

2014-11-01

283

Survey and development of finite elements for nonlinear structural analysis. Volume 1: Handbook for nonlinear finite elements  

NASA Technical Reports Server (NTRS)

A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.

1976-01-01

284

Anatomy-based inverse optimization in high-dose-rate brachytherapy combined with hypofractionated external beam radiotherapy for localized prostate cancer: Comparison of incidence of acute genitourinary toxicity between anatomy-based inverse optimization and geometric optimization  

SciTech Connect

Purpose: To evaluate the advantages of anatomy-based inverse optimization (IO) in planning high-dose-rate (HDR) brachytherapy. Methods and Materials: A total of 114 patients who received HDR brachytherapy (9 Gy in two fractions) combined with hypofractionated external beam radiotherapy (EBRT) were analyzed. The dose distributions of HDR brachytherapy were optimized using geometric optimization (GO) in 70 patients and by anatomy-based IO in the remaining 44 patients. The correlation between the dose-volume histogram parameters, including the urethral dose and the incidence of acute genitourinary (GU) toxicity, was evaluated. Results: The averaged values of the percentage of volume receiving 80-150% of the prescribed minimal peripheral dose (V{sub 8}-V{sub 15}) of the urethra generated by anatomy-based IO were significantly lower than the corresponding values generated by GO. Similarly, the averaged values of the minimal dose received by 5-50% of the target volume (D{sub 5}-D{sub 5}) obtained using anatomy-based IO were significantly lower than those obtained using GO. Regarding acute toxicity, Grade 2 or worse acute GU toxicity developed in 23% of all patients, but was significantly lower in patients for whom anatomy-based IO (16%) was used than in those for whom GO was used (37%), consistent with the reduced urethral dose (p <0.01). Conclusion: The results of this study suggest that anatomy-based IO is superior to GO for dose optimization in HDR brachytherapy for prostate cancer.

Akimoto, Tetsuo [Department of Radiation Oncology, Gunma University Graduate School of Medicine, Maebashi, Gunma (Japan)]. E-mail: takimoto@showa.gunma-u.ac.jp; Katoh, Hiroyuki [Department of Radiation Oncology, Gunma University Graduate School of Medicine, Maebashi, Gunma (Japan); Kitamoto, Yoshizumi [Department of Radiation Oncology, Gunma University Graduate School of Medicine, Maebashi, Gunma (Japan); Shirai, Katsuyuki [Department of Radiation Oncology, Gunma University Graduate School of Medicine, Maebashi, Gunma (Japan); Shioya, Mariko [Department of Radiation Oncology, Gunma University Graduate School of Medicine, Maebashi, Gunma (Japan); Nakano, Takashi [Department of Radiation Oncology, Gunma University Graduate School of Medicine, Maebashi, Gunma (Japan)

2006-04-01

285

Tricritical-like behavior of the nonlinear optical refraction at the nematic-isotropic transition in the E7 thermotropic liquid crystal.  

PubMed

We use Z-scan technique to investigate the nonlinear optical response of the thermotropic liquid crystal E7 in the neighborhood of the nematic-isotropic phase transition. The analysis of the data for the nonlinear optical birefringence is compatible with an effective critical exponent of the order parameter, ? = 0.28 ± 0.03, which is close to the classical value, ? = 0.25 , for a tricritical point. The nonlinear optical absorption in the nematic range depends on the geometrical configuration of the nematic director with respect to the polarization beam, and vanishes in the isotropic phase. PMID:22270454

Lenart, V M; Gómez, S L; Bechtold, I H; Figueiredo Neto, A M; Salinas, S R

2012-01-01

286

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

287

Ion-beam-assisted deposition of Au nanocluster\\/Nb 2O 5 thin films with nonlinear optical properties  

Microsoft Academic Search

Gold nanocluster thin films (? 200 nm thickness) consisting of metal clusters ? 5 nm in size embedded in a matrix of Nb2O5 were deposited by ion beam-assisted deposition (IBAD) by coevaporation of Au and Nb with O2+ ion bombardment. The microstructure and optical characteristics of these films were examined as-deposited and after annealing at 600°C. Annealing crystallized the amorphous

C. M. Cotell; S. Schiestel; C. A. Carosella; S. Flom; G. K. Hubler; D. L. Knies

1997-01-01

288

The Effect of Basis Selection on Static and Random Acoustic Response Prediction Using a Nonlinear Modal Simulation  

NASA Technical Reports Server (NTRS)

An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.

Rizzi, Stephen A.; Przekop, Adam

2005-01-01

289

Wave description of geometric modes of a resonator  

NASA Astrophysics Data System (ADS)

By using both an operator and a geometric argument, we obtain a wave description of geometric modes of a degenerate optical resonator. This is done by considering the propagation of a displaced Gaussian beam inside the resonator. The round-trip Gouy phase, which is independent of the wavelength of the light, determines the properties of the Gaussian eigenmode. The extra freedom in the case of degeneracy allows for the existence of geometric modes.

Visser, Jorrit; Zelders, Niels J.; Nienhuis, Gerard

2005-08-01

290

Graphical user interface based computer simulation of self-similar modes of a paraxial slow self-focusing laser beam for saturating plasma nonlinearities  

NASA Astrophysics Data System (ADS)

The task for the present study is to make an investigation of self-similarity in a self-focusing laser beam both theoretically and numerically using graphical user interface based interactive computer simulation model in MATLAB (matrix laboratory) software in the presence of saturating ponderomotive force based and relativistic electron quiver based plasma nonlinearities. The corresponding eigenvalue problem is solved analytically using the standard eikonal formalism and the underlying dynamics of self-focusing is dictated by the corrected paraxial theory for slow self-focusing. The results are also compared with computer simulation of self-focusing by the direct fast Fourier transform based spectral methods. It is found that the self-similar solution obtained analytically oscillates around the true numerical solution equating it at regular intervals. The simulation results are the main ones although a feasible semianalytical theory under many assumptions is given to understand the process. The self-similar profiles are called as self-organized profiles (not in a strict sense), which are found to be close to Laguerre-Gaussian curves for all the modes, the shape being conserved. This terminology is chosen because it has already been shown from a phase space analysis that the width of an initially Gaussian beam undergoes periodic oscillations that are damped when any absorption is added in the model, i.e., the beam width converges to a constant value. The research paper also tabulates the specific values of the normalized phase shift for solutions decaying to zero at large transverse distances for first three modes which can, however, be extended to higher order modes.

Batra, Karuna; Mitra, Sugata; Subbarao, D.; Sharma, R. P.; Uma, R.

2005-01-01

291

Geometrization of Quantum Mechanics  

E-print Network

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.

J. F. Carinena; J. Clemente-Gallardo; G. Marmo

2007-01-19

292

Hierarchies of Geometric Entanglement  

E-print Network

We introduce and discuss a class of generalized geometric measures of entanglement. For pure quantum states of N elementary subsystems, these extended measures are defined as the distances from the sets of K-separable states (K = 2,...,N). In principle, the entire set of these geometric measures provides a complete quantification and a hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows to discriminate among the different contributions. The extended measures are applied in the study of entanglement for different classes of N-qubit pure states, including W, GHZ, and cluster states. In all these cases we introduce a general method for the computation of the different geometric entanglement com- ponents. The entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between GHZ and W states, clarifying the original result...

Blasone, M; De Siena, S; Illuminati, F

2007-01-01

293

Geometric Effects in an Elastic Tensegrity Structure  

Microsoft Academic Search

Tensegrity structures are under-constrained, 3-dimensional, self-stressing structural systems. They demonstrate an infinitesimal flex and when loaded they display a nonlinear geometric stiffening. In earlier work many examples of the resulting force–displacement relationship have been demonstrated numerically, and some aspects of the force–displacement relationship have been derived analytically. In this article an energy formulation is presented for the case of a

I. J. Oppenheim; W. O. Williams

2000-01-01

294

Geometric continuum regularization of quantum field theory  

SciTech Connect

An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.

Halpern, M.B. (California Univ., Berkeley, CA (USA). Dept. of Physics)

1989-11-08

295

A Survey of Geometric Algebra  

E-print Network

A Survey of Geometric Algebra and Geometric Calculus c Alan Macdonald Luther College, Decorah, IA is always available at my web page.) The principal argument for the adoption of geometric algebra and Geometric Algebra: http://faculty.luther.edu/~macdonal/laga/ Vector and Geometric Calculus: http

Harrington, J. Patrick

296

Nonlinear springs with applications to flow regulation valves and mechanisms  

E-print Network

This thesis focuses on the application of nonlinear springs for fluid flow control valves where geometric constraints, or fabrication technologies, limit the use of available solutions. Types of existing nonlinear springs ...

Freeman, David Calvin

2008-01-01

297

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

298

Discover Geometric Dimensioning & Tolerancing  

NSDL National Science Digital Library

Learn about Geometric Dimensioning & Tolerancing (GD&T) basics before applying it to DT-1200 course projects Geometric Dimensioning & Tolerancing is the science of size, shape, and form control. It is used in mechanical design to ensure proper fit and function of mating parts in mechanical assemblies. It addresses the following mechanical design challenges: 1. How does feature form, and not just size and location, affect ...

Manning, David

2005-11-21

299

Differential microscopy for fluorescence-detected nonlinear absorption linear anisotropy based on a staggered two-beam femtosecond Yb:KGW oscillator  

PubMed Central

We present a new laser system and nonlinear microscope, designed for differential nonlinear microscopy. The microscope features time-correlated single photon counting of multiphoton fluorescence generated by an alternating pulse-train of orthogonally polarized pulses. The generated nonlinear signal is separated using home-built electronics. Results are presented on fluorescence-detected nonlinear absorption linear anisotropy (FDNALA) of chloroplasts in Asparagus Sprengerii Regel and of Congo Red-stained cellulose. PMID:21258516

Sandkuijl, Daaf; Cisek, Richard; Major, Arkady; Barzda, Virginijus

2010-01-01

300

Optimization of piezoelectric cantilever energy harvesters including non-linear effects  

NASA Astrophysics Data System (ADS)

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

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

2014-08-01

301

Geometrical Aspects in Optical Wavepacket Dynamics  

E-print Network

We construct a semiclassical theory for propagation of an optical wavepacket in non-conducting media with periodic structures of dielectric permittivity and magnetic permeability, i.e., non-conducting photonic crystals. We employ a quantum-mechanical formalism in order to clarify its link to those of electronic systems. It involves the geometrical phase, i.e., Berry phase, in a natural way, and describes an interplay between orbital motion and the internal rotation. Based on the above theory, we discuss the geometrical aspects of the optical Hall effect. We also consider a reduction of the theory to a system without periodic structure and apply it to the transverse shift at an interface reflection/refraction. For generic incident beams with elliptic polarizations, an identical result for the transverse shift of each reflected/transmitted beam is given by the following different approaches; (i) analytic evaluation of wavepacket dynamics, (ii) total angular momentum (TAM) conservation {\\it for individual photon...

Onoda, M; Nagaosa, N; Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto

2006-01-01

302

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

303

MECHANICS AND NONLINEAR CONTROL: MAKING UNDERWATER VEHICLES  

E-print Network

MECHANICS AND NONLINEAR CONTROL: MAKING UNDERWATER VEHICLES RIDE AND GLIDE Naomi Ehrich Leonard \\Lambda \\Lambda Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544 naomi@princeton.edu Abstract: Methods from geometric mechanics and dynamical systems theory make

Leonard, Naomi

304

Geometrical integrity of micromold cavity sputtered by FIB using multilayer slicing approach  

Microsoft Academic Search

This paper discusses the investigation of geometrical integrity of micromold cavity produced by focused ion beam (FIB) sputtering slice by slice. Parabolic shaped micromold cavity was chosen as an example. Preliminary experiments were carried out to characterize the machine and select the optimum process parameters such as beam current, pixel spacing, aperture size, and dwell time. The geometrical integrity of

Mohammad Yeakub Ali; Yee Wei Loo

2007-01-01

305

Geometric Quantum Computation  

E-print Network

We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.

A. Ekert; M. Ericsson; P. Hayden; H. Inamori; J. A. Jones; D. K. L. Oi; V. Vedral

2000-04-04

306

Algebraic geometric codes  

NASA Technical Reports Server (NTRS)

The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.

Shahshahani, M.

1991-01-01

307

Wave function as geometric entity  

E-print Network

A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. Interference of electrons whose wave functions are represented by geometric entities is considered. New experiments concerning the geometric nature of electrons are proposed.

B. I. Lev

2011-02-10

308

The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation  

NASA Technical Reports Server (NTRS)

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.

Rizzi, Stephen A.; Przekop, Adam

2004-01-01

309

A framework for optimal temporal reduced order modeling of nonlinear dynamical systems  

NASA Astrophysics Data System (ADS)

An optimal temporal reduced order modeling framework is proposed for nonlinear dynamical systems. The governing equations are modified for an under-resolved simulation with an arbitrary scheme and a coarse temporal grid. Subgrid-scale models are developed to account for the unresolved temporal structure via inclusion of statistical information on a multi-point temporal stencil. These models are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. In order to validate the proposed framework, we investigate time-periodic solutions for a canonical Duffing oscillator using a coarse harmonic balance scheme. In order to demonstrate application of the proposed framework to a high dimensional nonlinear dynamical system, we also investigate a simply supported, geometrically nonlinear beam under the influence of time-periodic external forcing. For both problems, the subgrid-scale models are shown to significantly improve the accuracy of coarse-grained solutions.

LaBryer, A.; Attar, P. J.; Vedula, P.

2013-02-01

310

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

311

Tournaments and Geometric Sequences.  

ERIC Educational Resources Information Center

Proposes a novel method of introducing and promoting the topic of geometric sequences through the problem of calculating the number of games necessary to determine the winner of a single elimination tournament in which two, three, or more teams compete at a time. (MDH)

Schielack, Vincent P., Jr.

1993-01-01

312

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

313

PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism  

NASA Astrophysics Data System (ADS)

Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: ?SR measurements on single crystals Oren Ofer, Amit Keren, Jess H Brewer, Tianheng H Han and Young S Lee Classical topological order in kagome ice Andrew J Macdonald, Peter C W Holdsworth and Roger G Melko Magnetic phase diagrams of classical triangular and kagome antiferromagnets M V Gvozdikova, P-E Melchy and M E Zhitomirsky The ordering of XY spin glasses Hikaru Kawamura Dynamic and thermodynamic properties of the generalized diamond chain model for azurite Andreas Honecker, Shijie Hu, Robert Peters and Johannes Richter Classical height models with topological order Christopher L Henley A search for disorder in the spin glass double perovskites Sr2CaReO6 and Sr2MgReO6 using neutron diffraction and neutron pair distribution function analysis J E Greedan, Shahab Derakhshan, F Ramezanipour, J Siewenie and Th Proffen Order and disorder in the local and long-range structure of the spin-glass pyrochlore, Tb2Mo2O7 Yu Jiang, Ashfia Huq, Corwin H Booth, Georg Ehlers, John E Greedan and Jason S Gardner The magnetic phase diagram of Gd2Sn2O7 R S Freitas and J S Gardner Calculation of the expected zero-field muon relaxation rate in the geometrically frustrated rare earth pyrochlore Gd2Sn2O7 antiferromagnet P A McClarty, J N Cosman, A G Del Maestro and M J P Gingras Magnetic frustration in the disordered pyrochlore Yb2GaSbO7 J A Hodges, P Dalmas de Réotier, A Yaouanc, P C M Gubbens, P J C King and C Baines Titanium pyrochlore magnets: how much can be learned from magnetization measurements? O A Petrenko, M R Lees and G Balakrishnan Local susceptibility of the Yb2Ti2O7 rare earth pyrochlore computed from a Hamiltonian with anisotropic exchange J D Thompson, P A McClarty and M J P Gingras Slow and static spin correlations in Dy2 + xTi2 - xO7 - ? J S Gardner, G Ehlers, P Fouquet, B Farago and J R Stewart The spin ice Ho2Ti2O7 versus the spin liquid Tb2Ti2O7: field-induced magnetic structures A P Sazonov, A Gukasov and I Mirebeau Magnetic monopole dynamics in spin ice L D C Jaubert and P C W Holdsworth

Gardner, Jason S.

2011-04-01

314

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.

315

Nonlinear models Nonlinear Regression  

E-print Network

the framework implemented in the SPM function spm-nlsi-GN.m. It implements Bayesian estimation of nonlinear density References VL Posteriors The Variational Laplace (VL) algorithm, implemented in spm-nlsi

Penny, Will

316

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

317

Complex geometric optics for symmetric hyperbolic systems I: linear theory  

E-print Network

We obtain an asymptotic solution for $\\ep \\to 0$ of the Cauchy problem for linear first-order symmetric hyperbolic systems with oscillatory initial values written in the eikonal form of geometric optics with frequency $1/\\ep$, but with complex phases. For the most common linear wave propagation models, this kind on Cauchy problems are well-known in the applied literature and their asymptotic theory, referred to as complex geometric optics, is attracting interest for applications. In this work, which is the first of a series of papers dedicated to complex geometric optics for nonlinear symmetric hyperbolic systems, we develop a rigorous linear theory and set the basis for the subsequent nonlinear analysis.

Omar Maj

2008-02-12

318

Geometric phases in higher-order transverse optical modes  

NASA Astrophysics Data System (ADS)

We study the geometric origin of generalized Gouy phases in paraxial optical modes of arbitrary order. We focus on the specific case of cyclic beam transformations of non-astigmatic vortex beams, thereby, generalizing the well-known geometric phase shift for first-order beams with orbital angular momentum to modes of arbitrary order. Our method involves two pairs of bosonic ladder operators, which, analogous to the algebraic description of the quantum-mechanical harmonic oscillator in two dimensions, connect transverse modes of different order. Rather than studying the geometry of the infinite-dimensional space of higher-order modes, we focus on the space underlying the ladder operators. We identify overall phases of the ladder operators, thereby obtaining the phases of all higher-order modes, and show that the variation of these phases under optical elements and transformations has a geometric interpretation in terms of the other parameters involved.

Habraken, Steven J. M.; Nienhuis, Gerard

2010-02-01

319

A generative geometric kernel  

Microsoft Academic Search

We present the design and implementation of a generative geometric kernel. The kernel generator is generic, type-safe, parametrized by many design-level choices and extensible. The resulting code has minimal traces of the design abstractions. We achieve genericity through a layered design deriving concepts from affine geometry, linear algebra and abstract algebra. We achieve parametrization and type-safety by using OCaml's module

Jacques Carette; Mustafa Elsheikh; Spencer Smith

2011-01-01

320

Geometric Intersection Problems  

Microsoft Academic Search

We develop optimal algorithms for forming the intersection of geometric objects in the plane and apply them to such diverse problems as linear programming, hidden-line elimination, and wire layout. Given N line segments in the plane, finding all intersecting pairs requires O(N2) time. We give an O(N log N) algorithm to determine whether any two intersect and use it to

Michael Ian Shamos; Dan Hoey

1976-01-01

321

Nonlinear-optic IR radiation converters  

NASA Astrophysics Data System (ADS)

A new class of instruments, nonlinear-optic (parametric) IR-visible converters, is described. A geometrical optics approximation and the diffraction theory are presented, and an analysis is made of the converter efficiency, noise characteristics, and threshold sensitivity of IR nonlinear-optic IR detection schemes. The theoretically derived converter parameters are compared with experimental data.

Gainer, Aleksandr V.

322

A Level Set Method for Anisotropic Geometric Diffusion in 3D Image Processing  

Microsoft Academic Search

A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution prob- lems. Its aim is to smooth level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an

Martin Rumpf

2000-01-01

323

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. In this resource you can set up various geometric series and see a visual representation of the successive terms and the corresponding sum of those terms.

Mathematics, Illuminations N.

2010-05-26

324

Conic Geometric Programming Venkat Chandrasekaranc  

E-print Network

Conic Geometric Programming Venkat Chandrasekaranc and Parikshit Shahw c Departments of Computing introduce and study conic geometric programs (CGPs), which are convex optimiza- tion problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP

325

Representing geometrical knowledge.  

PubMed Central

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic. PMID:9304680

Anderson, J A

1997-01-01

326

Development of solution techniques for nonlinear structural analysis  

NASA Technical Reports Server (NTRS)

Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

Vos, R. G.; Andrews, J. S.

1974-01-01

327

Constructing matrix geometric means  

E-print Network

In this paper, we analyze the process of “assembling ” new matrix geometric means from existing ones, and show what new means can be found, and what cannot be done because of group-theoretical obstructions. We show that for n = 4 a new matrix mean exists which is simpler to compute than the existing ones. Moreover, we show that for n> 4 the existing strategies of composing matrix means and taking limits of iterations cannot provide a mean computationally simpler than the existing ones.

Federico Poloni

328

Causal And Geometric Relations  

E-print Network

, for one, rejoiced in Einstein's treatment of gravitation. With the adoption of non- Euclidean geometry, he observed, we no longer need to assume that the sun somehow "makes" the earth travel in an ellipse about it; the earth simply travels along... the natural geodesic prescribed by the geometry; no "forces" or "little pushes" are required to keep it on its orbit.7 It is not that we have excused ourselves from giving a causal explanation of the orbit—we are using geometrical considerations as our...

Shrader, Douglas W. Jr.

1977-06-01

329

Geometric phase in Bohmian mechanics  

SciTech Connect

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{pi}. 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, E-mail: chiachun@mail.utexas.ed [Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, TX 78712 (United States); Wyatt, Robert E., E-mail: wyattre@mail.utexas.ed [Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, TX 78712 (United States)

2010-10-15

330

Nonlinear aerostatic stability analysis of Jiang Yin suspension bridge  

Microsoft Academic Search

A nonlinear aerostatic stability analysis of the Jiang Yin suspension bridge over the Yangtse River in China is carried out in this paper. We propose a new nonlinear method to analyze aerostatic stability of suspension bridges, based on both the three components of wind loads and geometric nonlinearity. A computer program NASAB, based on the proposed method, has been developed.

Jin Cheng; Jian-Jing Jiang; Ru-Cheng Xiao; Hai-Fan Xiang

2002-01-01

331

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

332

Geometric Brownian Motion Consider the geometric Brownian motion process  

E-print Network

Geometric Brownian Motion · Consider the geometric Brownian motion process Y (t) eX(t) ­ X(t) is a (µ, ) Brownian motion. · As Y/X = Y and 2 Y/X2 = Y , Ito's formula (51) on p. 453 implies dY Y = µ-Dauh Lyuu, National Taiwan University Page 459 Product of Geometric Brownian Motion Processes · Let d

Lyuu, Yuh-Dauh

333

Nonlinear Optics 2 Institute of Quantum Electronics  

E-print Network

of the Nonlinear Optics Laboratory in Conference Committees and Editorial Boards 5 MOLECULAR CRYSTALS, THIN FILMS of Novel Organic Nonlinear Optical Thin Films Grown by Molecular Beam Deposition 15 Fluorescence Phenomena, AND POLYMERS 7 Design, Synthesis, and Crystal Growth of Second-Order Nonlinear Optical Materials 7 Second

Imamoglu, Atac

334

Nonlinear optomechanical pressure  

E-print Network

A transparent material exhibits ultra-fast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, as optical manipulation, biophysics, cavity optomechanics, quantum optics, optical tractors, and is relevant in fundamental problems as the Abraham-Minkoswky dilemma, or the Casimir effect. Here we show that an ultra-fast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order of magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.

Claudio Conti; Robert Boyd

2014-03-08

335

Nonlinear optomechanical pressure  

NASA Astrophysics Data System (ADS)

A transparent material exhibits ultrafast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, such as optical manipulation, biophysics, cavity optomechanics, quantum optics, and optical tractors, and is relevant in fundamental problems such as the Abraham-Minkoswky dilemma or the Casimir effect. Here, we show that an ultrafast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order-of-magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.

Conti, Claudio; Boyd, Robert

2014-03-01

336

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

337

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

338

Geometrical pattern learning  

SciTech Connect

In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.

Goldberg, P.W.

1993-04-01

339

Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer  

NASA Technical Reports Server (NTRS)

This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \\ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

Pai, P. F.; Lee, S.-Y.

2003-01-01

340

The application of structural nonlinearity in the development of linearly tunable MEMS capacitors  

NASA Astrophysics Data System (ADS)

Electrostatically actuated parallel-plate tunable capacitors are the most desired MEMS capacitors because of their smaller sizes and higher Q-factors. However, these capacitors suffer from low tunability and exhibit high sensitivity near the pull-in voltage which counters the concept of tunability. In this paper, a novel design for parallel-plate tunable capacitors with high tunability and linear capacitance-voltage (C-V) response is developed. The design uses nonlinear structural rigidities to relieve intrinsic electrostatic nonlinearity in MEMS capacitors. Based on the force-displacement characteristic of an ideally linear capacitor, a real beam-like nonlinear spring model is developed. The variable stiffness coefficients of such springs improve the linearity of the C-V curve. Moreover, because the structural stiffness increases with deformations, the pull-in is delayed and higher tunability is achieved. Finite element simulations reveal that capacitors with air gaps larger than 4 µm and supporting beams thinner than 1 µm can generate highly linear C-V responses and tunabilities over 120%. Experimental results for capacitors fabricated by PolyMUMPs verify the effect of weak nonlinear geometric stiffness on improving the tunability for designs with a small air gap and relatively thick structural layers.

Shavezipur, M.; Khajepour, A.; Hashemi, S. M.

2008-03-01

341

Stabilization of LCD devices via geometric alteration.  

PubMed

Glass bending in LCD displays is an inherent problem that has challenged many engineers. As a solution to this problem, we propose a methodology that can tackle the root of the phenomenon in terms of linear elastic beam theory. Using this hypothesis, we devised a background theory and a solution. In this paper, we present a glass panel to which geometrical changes, such as furrow, groove, and curb have been applied. These geometrical changes are applied to the nonactive area of the glass panel. To confirm the validity of our approach, we conducted simulation tests as well as hands-on experiments to observe the thermo-mechanical behavior of the device under various conditions. The simulation results using the Ansys simulator show that the proposed technique can reduce the deformation level of panel bending by 40%. In the experiment using a bare cell with polarizer films attached and with performing the high temperature reliability test, the deformation level of panel bending is reduced by half compared to the reference glass panel without any geometric alteration. PMID:23434997

Jeon, Il; Yoon, MinSung; Lee, Je-Hoon

2013-02-20

342

Geometric Effects on Electron Cloud.  

National Technical Information Service (NTIS)

The development of an electron cloud in the vacuum chambers of high intensity positron and proton storage rings may limit the machine performances by inducing beam instabilities, beam emittance increase, beam loss, vacuum pressure increases and increased ...

A. Chao, J. Wei, L. Wang

2007-01-01

343

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

344

Geometric Relations Among Voronoi Diagrams  

Microsoft Academic Search

Two general classes of Voronoi diagrams are introduced and, along with their modifications to higher order, are shown to be geometrically related. This geometric background, on one hand, serves to analyze the size and the combinatorial structure, and on the other hand, implies general and efficient methods of construction, for various important types of Voronoi diagrams considered in the literature.

Franz Aurenhammer; Hiroshi Imai

1987-01-01

345

CORRESPONDENCE PROBLEMS IN GEOMETRIC VISION  

E-print Network

- Dimensional Vision, submitted to SIAM Journal on Imaging Sciences ­ Special Issue on Optimization in ImagingCORRESPONDENCE PROBLEMS IN GEOMETRIC VISION OLOF ENQVIST Faculty of Engineering CentreTryck, Lund 2009 #12;Preface This thesis concerns optimal methods for geometric vision problems. Two important

Lunds Universitet

346

A Primer on Geometric Mechanics  

E-print Network

Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance of the subject for an understanding of "mechanics".

Christian Lessig

2012-06-14

347

Nonlinear free vibration of piezoelectric nanobeams incorporating surface effects  

NASA Astrophysics Data System (ADS)

In this study, the nonlinear free vibration of piezoelectric nanobeams incorporating surface effects (surface elasticity, surface tension, and surface density) is studied. The governing equation of the piezoelectric nanobeam is derived within the framework of Euler-Bernoulli beam theory with the von Kármán geometric nonlinearity. In order to satisfy the balance conditions between the nanobeam bulk and its surfaces, the component of the bulk stress, ?zz, is assumed to vary linearly through the nanobeam thickness. An exact solution is obtained for the natural frequencies of a simply supported piezoelectric nanobeam in terms of the Jacobi elliptic functions using the free vibration mode shape of the corresponding linear problem. Then, the influences of the surface effects and the piezoelectric field on the nonlinear free vibration of nanobeams made of aluminum and silicon with positive and negative surface elasticity, respectively, have been studied for various properties of the piezoelectric field, various nanobeam sizes and amplitude ratios. It is observed that if the Young’s modulus of a nanobeam is lower, the effect of the piezoelectric field on the frequency ratios (FRs) of the nanobeam will be greater. In addition, it is seen that by increasing the nanobeam length so that the nanobeam cross section is set to be constant, the surface effects and the piezoelectric field with negative voltage values increases the FRs, whereas it is the other way around when the nanobeam cross section is assumed to be dependent on the length of the nanobeam.

Hosseini-Hashemi, Shahrokh; Nahas, Iman; Fakher, Mahmood; Nazemnezhad, Reza

2014-03-01

348

Encoding geometric and non-geometric information: a study with evolved agents  

Microsoft Academic Search

Vertebrate species use geometric information and non-geometric or featural cues to orient. Under some circumstances, when\\u000a both geometric and non-geometric information are available, the geometric information overwhelms non-geometric cues (geometric\\u000a primacy). In other cases, we observe the inverse tendency or the successful integration of both cues. In past years, modular\\u000a explanations have been proposed for the geometric primacy: geometric and

Michela Ponticorvo; Orazio Miglino

2010-01-01

349

Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings  

NASA Astrophysics Data System (ADS)

The major purpose of this study is to predict the dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings in the presence of rigid support movements, the target application being turbochargers of vehicles or rotating machines subject to seismic excitation. The proposed on-board rotor model is based on Timoshenko beam finite elements. The dynamic modeling takes into account the geometric asymmetry of shaft and/or rigid disk as well as the six deterministic translations and rotations of the rotor rigid support. Depending on the type of analysis used for the bearing, the fluid film forces computed with the Reynolds equation are linear/nonlinear. Thus the application of Lagrange's equations yields the linear/nonlinear equations of motion of the rotating rotor in bending with respect to the moving rigid support which represents a non-inertial frame of reference. These equations are solved using the implicit Newmark time-step integration scheme. Due to the geometric asymmetry of the rotor and to the rotational motions of the support, the equations of motion include time-varying parametric terms which can lead to lateral dynamic instability. The influence of sinusoidal rotational or translational motions of the support, the accuracy of the linear 8-coefficient bearing model and the interest of the nonlinear model for a hydrodynamic journal bearing are examined and discussed by means of stability charts, orbits of the rotor, time history responses, fast Fourier transforms, bifurcation diagrams as well as Poincaré maps.

Dakel, Mzaki; Baguet, Sébastien; Dufour, Régis

2014-05-01

350

Fluid-Structure Interaction Analysis of a High-Aspect Wing Considering Structural Nonlinearity  

NASA Astrophysics Data System (ADS)

In this research, fluid-structure interaction problem including geometric structural nonlinearity is studied for a high-aspect-ratio wing. When a high-aspect-ratio wing structure is interacted with external airload, geometric structural nonlinearity can be caused by large deflection of a wing. For the investigation of such a fluid-structure interaction problem, the transonic small disturbance theory for the aerodynamic analysis and the large deflection beam theory for the structural analysis are used, respectively. For the coupling between fluid and structure, the transformation of a displacement from the structural mesh to the aerodynamic grid is performed by a shape function which is used for the finite element and the inverse transformation of force by work equivalent load method. Static deformations in the vertical and twist deflections caused by gravity loading are compared with experimental results. Also, static aeroelastic analysis results are compared with experimental data. From the analysis results, effects of structural nonlinearity on static aeroelastic characteristics are investigated.

Kim, Kyung-Seok; Lim, In-Gyu; Lee, In; Yoo, Jae-Han

351

Nonlinear tension-bending deformation of a shape memory alloy rod  

NASA Astrophysics Data System (ADS)

Based on the measured shape memory alloy (SMA) stress-strain curve and the nonlinear large deformation theory of extensible beams (or rods), the first-order nonlinear governing equations of a SMA cantilever straight rod are established. They consist of a boundary-value problem of ordinary differential equations with a strong nonlinearity, in which seven unknown functions are contained and the arc length of the deformed axis is considered as one of the basic unknown functions. The shooting method combining with the Newton-Raphson iteration method is applied to solve the equations numerically. For a SMA cantilever rod subjected to a transverse uniformly distributed force, the deformation characteristics curves, the maximum strain and the maximum stress distribution curves along the longitudinal direction of rod, and the relation curves between deformation characteristic parameters and transverse uniformly force under different slenderness ratios are obtained. The effects of material nonlinearity, geometrical nonlinearity and slenderness ratio on the tension-bending deformation of the SMA cantilever rod are investigated. The numerical simulation results are in good agreement with the experimental data from the literature, verifying the soundness of the entire numerical simulation scheme.

Shang, Zejin; Wang, Zhongmin

2012-11-01

352

Nonlinear vibrational microscopy  

DOEpatents

The present invention is a method and apparatus for microscopic vibrational imaging using coherent Anti-Stokes Raman Scattering or Sum Frequency Generation. Microscopic imaging with a vibrational spectroscopic contrast is achieved by generating signals in a nonlinear optical process and spatially resolved detection of the signals. The spatial resolution is attained by minimizing the spot size of the optical interrogation beams on the sample. Minimizing the spot size relies upon a. directing at least two substantially co-axial laser beams (interrogation beams) through a microscope objective providing a focal spot on the sample; b. collecting a signal beam together with a residual beam from the at least two co-axial laser beams after passing through the sample; c. removing the residual beam; and d. detecting the signal beam thereby creating said pixel. The method has significantly higher spatial resolution then IR microscopy and higher sensitivity than spontaneous Raman microscopy with much lower average excitation powers. CARS and SFG microscopy does not rely on the presence of fluorophores, but retains the resolution and three-dimensional sectioning capability of confocal and two-photon fluorescence microscopy. Complementary to these techniques, CARS and SFG microscopy provides a contrast mechanism based on vibrational spectroscopy. This vibrational contrast mechanism, combined with an unprecedented high sensitivity at a tolerable laser power level, provides a new approach for microscopic investigations of chemical and biological samples.

Holtom, Gary R. (Richland, WA); Xie, Xiaoliang Sunney (Richland, WA); Zumbusch, Andreas (Munchen, DE)

2000-01-01

353

Geometric Phase and Nonadiabatic Effects in an Electronic Harmonic Oscillator  

NASA Astrophysics Data System (ADS)

Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.

Pechal, M.; Berger, S.; Abdumalikov, A. A., Jr.; Fink, J. M.; Mlynek, J. A.; Steffen, L.; Wallraff, A.; Filipp, S.

2012-04-01

354

Towards physically motivated proofs of the Poincaré and geometrization conjectures  

Microsoft Academic Search

Although the Poincaré and the geometrization conjectures were recently proved by Perelman, the proof relies heavily on properties of the Ricci flow previously investigated in great detail by Hamilton. Physical realization of such a flow can be found, for instance, in the work by Friedan [D. Friedan, Nonlinear models in 2+? dimensions, Ann. Phys. 163 (1985) 318–419]. In his work the renormalization

Arkady L. Kholodenko

2008-01-01

355

Chiral symmetry breaking as a geometrical process  

E-print Network

This article expands for spinor fields the recently developed Dynamical Bridge formalism which relates a linear dynamics in a curved space to a nonlinear dynamics in Minkowski space. Astonishingly, this leads to a new geometrical mechanism to generate a chiral symmetry breaking without mass, providing an alternative explanation for the undetected right-handed neutrinos. We consider a spinor field obeying the Dirac equation in an effective curved space constructed by its own currents. This way, both chiralities of the spinor field satisfy the same dynamics in the curved space. Subsequently, the dynamical equation is re-expressed in terms of the flat Minkowski space and then each chiral component behaves differently. The left-handed part of the spinor field satisfies the Dirac equation while the right-handed part is trapped by a Nambu-Jona-Lasinio (NJL) type potential.

Eduardo Bittencourt; Sofiane Faci; Mário Novello

2014-06-08

356

Chiral symmetry breaking as a geometrical process  

NASA Astrophysics Data System (ADS)

This paper is an extension for spinor fields the recently developed Dynamical Bridge formalism which relates a linear dynamics in a curved space to a nonlinear dynamics in Minkowski space. This leads to a new geometrical mechanism to generate a chiral symmetry breaking without mass, providing an alternative explanation for the absence of right-handed neutrinos. We analyze a spinor field obeying the Dirac equation in a curved space which is constructed by its own current. This way, both chiralities of the spinor field satisfy the same dynamics in the curved space. Afterward, the dynamical equation is re-expressed in terms of the flat Minkowski space and then each chiral component behaves differently. The left-handed part of the spinor field satisfies the Dirac equation while the right-handed part is trapped by a Nambu-Jona-Lasinio type potential.

Bittencourt, E.; Faci, S.; Novello, M.

2014-10-01

357

The Geometric Origin of the Madelung Potential  

E-print Network

Madelung's hydrodynamical forms of the Schrodinger equation and the Klein-Gordon equation are presented. The physical nature of the quantum potential is explored. It is demonstrated that the geometrical origin of the quantum potential is in the scalar curvature of the of the metric that defines the kinetic energy density for an extended particle and that the quantization of circulation (Bohr-Sommerfeld) is a consequence of associating an SO(2)-reduction of the Lorentz frame bundle with wave motion. The Madelung equations are then cast in a basis-free form in terms of exterior differential forms in such a way that they represent the equations for a timelike solution to the conventional wave equations whose rest mass density satisfies a differential equation of the "Klein-Gordon minus nonlinear term" type. The role of non-zero vorticity is briefly examined.

D. H. Delphenich

2002-11-19

358

March 18, 1998 2:43 pm. Geometrically Intrinsic Nonlinear  

E-print Network

the problem of tracking and intercepting a target, using sensors based on a moving missile. Compu- tational Tracking DÃ?Souza, McClure, and Cloutier [8], [9] consider the following tactical air-to-air missile-rate, all mea- sured from a missile with known position, velocity, and acceleration. The goal of filtering

Sekhon, Jasjeet S.

359

Geometrical non-linear analysis of tensegrity systems  

Microsoft Academic Search

A calculation method for structures with large deformations and displacements, based on works by Bathe [7–9], is developed so as to determine the tangent stiffness matrix and the internal stress vector. The formulation is established for a `bar' element. Application of this method for tensegrity systems allowed the study of behaviour for a simple self-stressed system, the four-strut tensegrity system,

K. Kebiche; M. N. Kazi-Aoual; R. Motro

1999-01-01

360

A Geometric Approach to Nonlinear Fault Detection and Isolation  

E-print Network

-95-1-0232, by DARPA, AFRL, AFMC, under grant F30602-99-2-0551, and by MURST. The U.S. Government is authorized as necessarily representing the official policies or endorsements, either expressed or implied, of DARPA, of AFRL

De Persis, Claudio

361

March 18, 1998 3:14 pm. Geometrically Intrinsic Nonlinear  

E-print Network

. Darling 1 1. University of South Florida. E-mail: darling@math.usf.edu For updates, see Report 512 at http algorithm presented in the companion paper, Darling [3]. The results can be summarized as follows. 1.1 State

Sekhon, Jasjeet S.

362

Geometric nonlinearity and mechanical anisotropy in strained helical nanoribbons  

NASA Astrophysics Data System (ADS)

Fabrication and synthesis of helical nanoribbons have received increasing attention because of the broad applications of helical nanostructures in nano-elecromechanical/micro-electromechanical systems (NEMS/MEMS), sensors, active materials, drug delivery, etc. In this paper, I study the mechanical principles used in designing strained helical nanoribbons, and propose the use of a full three-dimensional finite element method to simulate the coexistence of both left- and right-handed segments in the same strained nanoribbon. This work can both help understand the large deformation behaviours of such nanostructures and assist in the design of helical nanostructures for engineering applications.

Chen, Z.

2014-07-01

363

Geometric nonlinearity and mechanical anisotropy in strained helical nanoribbons.  

PubMed

Fabrication and synthesis of helical nanoribbons have received increasing attention because of the broad applications of helical nanostructures in nano-elecromechanical/micro-electromechanical systems (NEMS/MEMS), sensors, active materials, drug delivery, etc. In this paper, I study the mechanical principles used in designing strained helical nanoribbons, and propose the use of a full three-dimensional finite element method to simulate the coexistence of both left- and right-handed segments in the same strained nanoribbon. This work can both help understand the large deformation behaviours of such nanostructures and assist in the design of helical nanostructures for engineering applications. PMID:24837718

Chen, Z

2014-08-21

364

Optimization of biotechnological systems through geometric programming  

PubMed Central

Background In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. Results A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. Conclusion GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus, efficient methods for optimizing GMA systems have multifold appeal. PMID:17897440

Marin-Sanguino, Alberto; Voit, Eberhard O; Gonzalez-Alcon, Carlos; Torres, Nestor V

2007-01-01

365

Nonlinear evolution equations in QCD  

E-print Network

The following lectures are an introduction to the phenomena of partonic saturation and nonlinear evolution equations in Quantum Chromodynamics. After a short introduction to the linear evolution, the problems of unitarity bound and parton saturation are discussed. The nonlinear Balitsky-Kovchegov evolution equation in the high energy limit is introduced, and the progress towards the understanding of the properties of its solution is reviewed. We discuss the concepts of the saturation scale, geometrical scaling and the lack of the infrared diffusion. Finally, we give a brief summary of current theoretical developments which extend beyond the Balitsky-Kovchegov equation.

A. M. Stasto

2004-12-06

366

Fine correction of nonlinearity in homodyne interferometry  

NASA Astrophysics Data System (ADS)

In a typical homodyne interferometer with 4-channel detectors, the nonlinearity resulting from beam power drifting couldn't be thoroughly suppressed by Heydemann correction. This study presents an analysis of the nonlinearity resulting from beam power drifting. From a theoretical approach, the nonlinearity model before and after conventional Heydemann correction is built. And a fine correction method involving Heydemann correction with partial data is introduced. The experimental results indicate that, the proposed method suppresses the nonlinearity in a homodyne interferometer to 0.18 nm, which would be 1.49 nm with conventional Heydemann correction.

Hu, Peng-cheng; Pollinger, Florian; Meiners-Hagen, Karl; Yang, Hong-xing; Abou-Zeid, Ahmed

2010-08-01

367

Nonlinear left-handed metamaterials  

E-print Network

We analyze nonlinear properties of microstructured materials with negative refraction, the so-called left-handed metamaterials. We demonstrate that the hysteresis-type dependence of the magnetic permeability on the field intensity allows changing the material properties from left- to right-handed and back. Using the finite-difference time-domain simulations, we study wave transmission through the slab of nonlinear left-handed material, and predict existence of temporal solitons in such materials. We demonstrate also that nonlinear left-handed metamaterials can support both TE- and TM-polarized self-trapped localized beams, spatial electromagnetic solitons. Such solitons appear as single- and multi-hump beams, being either symmetric or antisymmetric, and they can exist due to the hysteresis-type magnetic nonlinearity and the effective domains of negative magnetic permeability.

Ilya V. Shadrivov; Alexander A. Zharov; Nina A. Zharova; Yuri S. Kivshar

2004-10-24

368

Waldyr Muniz Oliva Geometric Mechanics  

E-print Network

Waldyr Muniz Oliva Geometric Mechanics February 1, 2002 Springer Berlin Heidelberg New mechanics : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 51 4.1 Galilean space-time structure and Newton equations . . . . . . . . 51 4.2 Critical remarks on Newtonian mechanics

Natário, José

369

Geometrical optics in general relativity  

E-print Network

General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.

A. Loinger

2006-09-19

370

GEOMETRIC FOKKER-PLANCK EQUATIONS  

Microsoft Academic Search

We study the large deviation function and small time asymptotics near the diagonal for the heat equation associated to Geometric Fokker-Planck equations (GFK) on the cotangent bundle ? = TX of a Riemannian smooth compact connected variety X.

Gilles Lebeau

2005-01-01

371

Geometric Analysis and General Relativity  

E-print Network

This article discusses methods of geometric analysis in general relativity, with special focus on the role of "critical surfaces" such as minimal surfaces, marginal surface, maximal surfaces and null surfaces.

Lars Andersson

2005-12-23

372

Crystal-Like geometric modeling  

E-print Network

geometry. The tiered extrusion method, along with a face grouping technique, simplifies the creation of complex, intricate faceted shapes. In combination with remeshing, these methods provide the capability to generate geometric shapes exhibiting planar...

Landreneau, Eric Benjamin

2006-08-16

373

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

374

Algorithms of NCG geometrical module  

NASA Astrophysics Data System (ADS)

The methods and algorithms of the versatile NCG geometrical module used in the MCU code system are described. The NCG geometrical module is based on the Monte Carlo method and intended for solving equations of particle transport. The versatile combinatorial body method, the grid method, and methods of equalized cross sections and grain structures are used for description of the system geometry and calculation of trajectories.

Gurevich, M. I.; Pryanichnikov, A. V.

2012-12-01

375

Optical antennas : linear and nonlinear excitation and emission.  

E-print Network

??The linear and nonlinear resonance behaviour of optical antennas (metallic nanostructures showing resonance behaviour at optical frequencies) made of gold and aluminum using electron-beam lithography… (more)

Wissert, Matthias Dominik

2011-01-01

376

Nonlinear analysis of anisotropic shells of revolution  

E-print Network

of solutions of technically The citations on the following pages follow the style of NASA CR-909. important shell problems as well as with critical reappraisal and contributions to the foundations of the theory upon which these so'lutions are based... 1965, pp. 506-510. 3. Ball, R. E. , "A Geometrically Nonlinear Analysis of Arbitrarily Loaded Shells of Revolution", NASA Contractor Report, DR-909. 4. Sanders, Jr. , J. Syell, "Nonlinear Theories for Thin Shells", quart. Appl. Math. , Volume 21, g8...

Kelley, William Rhea

2012-06-07

377

Assumed--stress hybrid elements with drilling degrees of freedom for nonlinear analysis of composite structures  

NASA Technical Reports Server (NTRS)

The goal of this research project is to develop assumed-stress hybrid elements with rotational degrees of freedom for analyzing composite structures. During the first year of the three-year activity, the effort was directed to further assess the AQ4 shell element and its extensions to buckling and free vibration problems. In addition, the development of a compatible 2-node beam element was to be accomplished. The extensions and new developments were implemented in the Computational Structural Mechanics Testbed COMET. An assessment was performed to verify the implementation and to assess the performance of these elements in terms of accuracy. During the second and third years, extensions to geometrically nonlinear problems were developed and tested. This effort involved working with the nonlinear solution strategy as well as the nonlinear formulation for the elements. This research has resulted in the development and implementation of two additional element processors (ES22 for the beam element and ES24 for the shell elements) in COMET. The software was developed using a SUN workstation and has been ported to the NASA Langley Convex named blackbird. Both element processors are now part of the baseline version of COMET.

Knight, Norman F., Jr. (Principal Investigator)

1996-01-01

378

Nonlinear transformat  

NASA Technical Reports Server (NTRS)

A technique for designing automatic flight controllers for aircraft which utilizes the transformation theory of nonlinear systems to linear systems is presently being developed at NASA Ames Research Center. A method is considered in which a given nonlinear is transformed to a controllable linear system in Brunovsky canonical form. A linear approximation is introduced to the nonlinear system called the modified tangent model. This model is easily computed. Constructing the transformation for this model enables the designer to find an approximate transformation for the nonlinear system.

Ford, H.; Hunt, L. R.; Su, R.

1983-01-01

379

Accurate electrostatic and van der Waals pull-in prediction for fully clamped nano/micro-beams using linear universal graphs of pull-in instability  

NASA Astrophysics Data System (ADS)

In spite of the fact that pull-in instability of electrically actuated nano/micro-beams has been investigated by many researchers to date, no explicit formula has been presented yet which can predict pull-in voltage based on a geometrically non-linear and distributed parameter model. The objective of present paper is to introduce a simple and accurate formula to predict this value for a fully clamped electrostatically actuated nano/micro-beam. To this end, a non-linear Euler-Bernoulli beam model is employed, which accounts for the axial residual stress, geometric non-linearity of mid-plane stretching, distributed electrostatic force and the van der Waals (vdW) attraction. The non-linear boundary value governing equation of equilibrium is non-dimensionalized and solved iteratively through single-term Galerkin based reduced order model (ROM). The solutions are validated thorough direct comparison with experimental and other existing results reported in previous studies. Pull-in instability under electrical and vdW loads are also investigated using universal graphs. Based on the results of these graphs, non-dimensional pull-in and vdW parameters, which are defined in the text, vary linearly versus the other dimensionless parameters of the problem. Using this fact, some linear equations are presented to predict pull-in voltage, the maximum allowable length, the so-called detachment length, and the minimum allowable gap for a nano/micro-system. These linear equations are also reduced to a couple of universal pull-in formulas for systems with small initial gap. The accuracy of the universal pull-in formulas are also validated by comparing its results with available experimental and some previous geometric linear and closed-form findings published in the literature.

Tahani, Masoud; Askari, Amir R.

2014-09-01

380

Nonlinear interaction of plane elastic waves  

SciTech Connect

The paper presents basic first order results of nonlinear elastic theory by Murnaghan for elastic wave propagation in isotropic solids. The authors especially address the problem of resonant scattering of two collimated beams and present analytical solutions for amplitudes of all possible types of resonant interactions for elastic plane waves. For estimation of nonlinear scattered waves they use measured elastic parameters for sandstone. The most profound nonlinear effect is expected for interactions of two SH waves generating compressional P wave at sum frequency. Estimations show that nonlinear phenomena is likely to be observed in seismic data. Basic equations of nonlinear five-constant theory by Murnaghan are also presented.

Korneev, V.A.; Nihei, K.T.; Myer, L.R.

1998-06-01

381

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

382

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

383

Geometric modeling basic examples Toric surface patches  

E-print Network

Tutorial John B. Little Department of Mathematics and Computer Science College of the Holy Cross July 29-31, 2013 John B. Little Toric Varieties in Geometric Modeling #12;Geometric modeling ­ basic examples Toric and connections with statistics John B. Little Toric Varieties in Geometric Modeling #12;Geometric modeling

Little, John B.

384

Geometric phases in astigmatic optical modes of arbitrary order  

SciTech Connect

The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.

Habraken, Steven J. M.; Nienhuis, Gerard [Leiden Institute of Physics, P.O. Box 9504, 2300 RA Leiden (Netherlands)

2010-08-15

385

Geometric phases in astigmatic optical modes of arbitrary order  

NASA Astrophysics Data System (ADS)

The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schrödinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.

Habraken, Steven J. M.; Nienhuis, Gerard

2010-08-01

386

Geometric structures of vectorial type  

NASA Astrophysics Data System (ADS)

We study geometric structures of W4-type in the sense of A. Gray on a Riemannian manifold. If the structure group G?SO(n) preserves a spinor or a non-degenerate differential form, its intrinsic torsion ? is a closed 1-form (Proposition 2.1 and Theorem 2.1). Using a G-invariant spinor we prove a splitting theorem (Proposition 2.2). The latter result generalizes and unifies a recent result obtained in [S. Ivanov, M. Parton, P. Piccinni, Locally conformal parallel G- and Spin(7)-structures, mathdg/0509038], where this splitting has been proved in dimensions n=7,8 only. Finally we investigate geometric structures of vectorial type and admitting a characteristic connection ?. An interesting class of geometric structures generalizing Hopf structures are those with a ?-parallel intrinsic torsion ?. In this case, ? induces a Killing vector field (Proposition 4.1) and for some special structure groups it is even parallel.

Agricola, I.; Friedrich, T.

2006-12-01

387

Parametric Study on the Response of Compression-Loaded Composite Shells With Geometric and Material Imperfections  

NASA Technical Reports Server (NTRS)

The results of a parametric study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thinwalled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The imperfections considered include initial geometric shell-wall midsurface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these imperfections on the nonlinear responses and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable response characteristics.

Hilburger, Mark W.; Starnes, James H., Jr.

2004-01-01

388

A nonlinear algorithm for speckle reduction  

Microsoft Academic Search

A nonlinear image processing algorithm called geometric filtering is demonstrated. This technique, originally developed for reducing the speckle in synthetic aperture radar imagery, is an iterative-rule based method which uses a pixel's nearest neighbors to decide if an intensity modification is required. By applying the rule, rapid fluctuations in pixel intensity caused by speckle are more quickly eliminated than true

L. J. Busse; D. R. Dietz

1991-01-01

389

Geometrical Optics of Dense Aerosols  

SciTech Connect

Assembling a free-standing, sharp-edged slab of homogeneous material that is much denser than gas, but much more rare ed than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed fi eld, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the nite particle density reduces the eff ective Stokes number of the flow, a critical result for controlled focusing. __________________________________________________

Hay, Michael J.; Valeo, Ernest J.; Fisch, Nathaniel J.

2013-04-24

390

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

391

Soliton mode locking by nonlinear Faraday rotation  

NASA Astrophysics Data System (ADS)

We propose nonlinear Faraday rotation as a mechanism for achieving stable polarization mode locking of a soliton laser. We analyze by perturbation theory and beam-propagation simulations the interplay between bandwidth-limited gain, gain dichroism, and linear and nonlinear Faraday rotation. .

Wabnitz, S.; Westin, E.; Frey, R.; Flytzanis, C.

1996-11-01

392

Identifying parameters of multi-degree-of-freedom nonlinear structural dynamic systems using linear time periodic approximations  

NASA Astrophysics Data System (ADS)

The authors recently presented a new nonlinear system identification method, here dubbed the NL-LTP method, in which the system of interest is forced harmonically so that it responds in a stable periodic orbit, and then it is perturbed slightly and its response is recorded as it returns to the orbit. Under mild assumptions the response about the periodic orbit can be approximated using a linear time periodic system model, which can be identified from the measurements using techniques that are akin to linear modal analysis. While the prior work focused on simulated measurements from single degree-of-freedom systems, this work presents several tools that are needed in order to use this approach on multi-degree-of-freedom systems and focuses on applying the method to experimental hardware. The proposed system identification methodology is unique in that it identifies both the order of the nonlinear system and a mathematical model for the nonlinear restoring forces without assuming the mathematical form for the nonlinearities a priori. Towards these ends, this work explains how to extract the underlying nonlinear system model, or nonlinear restoring force versus displacement relationships, from the time periodic model that governs deviations of the system from its periodic orbit, and presents various metrics that can be used to determine which terms in the model are meaningful. These new tools are used to apply the identification method to a continuous, multi-degree-of-freedom structure with a discrete geometric nonlinearity, using both simulated and experimental measurements. The experimental hardware consists of a cantilever beam with a nonlinear spring attached to its tip, which is driven in a periodic limit cycle by an electromagnetic shaker.

Sracic, Michael W.; Allen, Matthew S.

2014-06-01

393

Vibrational Control of a Nonlinear Elastic Panel  

NASA Technical Reports Server (NTRS)

The paper is concerned with the stabilization of the nonlinear panel oscillation by an active control. The control is actuated by a combination of additive and parametric vibrational forces. A general method of vibrational control is presented for stabilizing panel vibration satisfying a nonlinear beam equation. To obtain analytical results, a perturbation technique is used in the case of weak nonlinearity. Possible application to other types of problems is briefly discussed.

Chow, P. L.; Maestrello, L.

1998-01-01

394

Multiscale geometric modeling of macromolecules I: Cartesian representation  

PubMed Central

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the polarized curvature, for the prediction of protein binding sites. PMID:24327772

Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo Wei

2013-01-01

395

Celestial mechanics with geometric algebra  

NASA Technical Reports Server (NTRS)

Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

Hestenes, D.

1983-01-01

396

Sublinear Geometric Algorithms # Bernard Chazelle  

E-print Network

University and NEC Laboratories America, Inc. chazelle@cs.princeton.edu Ding Liu Department of Computer for geo­ metric problems in two and three dimensions. We give opti­ mal algorithms for intersection.5 [Computational Geometry and Object Modeling]: Geometric algorithms, languages, and systems General Terms

Magen, Avner

397

Geometrical Methods in Gauge Theory  

E-print Network

In this work we explore the geometrical interpretation of gauge theories through the formalism of fiber bundles. Moreover, we conduct an investigation in the topology of fiber bundles, providing a proof of the Classification Theorem. In the last chapter we present some applications, such as electromagnetism and generalized Kaluza-Klein Theory.

Henrique de A. Gomes

2006-10-25

398

Exploring young children's geometrical strategies  

Microsoft Academic Search

This study explores young children's strategies while transforming polygons, through the use of geometrical models. Data were collected from 291 children ranging from 4 to 8 years of age in Cyprus. Children were asked to draw a stairway of specific poly- gons, with each shape being bigger or smaller than its preceding one. Relationships between children's responses in the transformation

ATHANASIOS GAGATSIS; BHARATH SRIRAMAN; ILIADA ELIA; MODESTINA MODESTOU

399

Vergence, Vision, and Geometric Optics  

ERIC Educational Resources Information Center

Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…

Keating, Michael P.

1975-01-01

400

Algorithmic + Geometric characterization of CAR  

E-print Network

Algorithmic + Geometric characterization of CAR (Coarsening at Random) Richard Gill - Utrecht but independent) CCAR 3 door problem X=door with car behind Y=two doors still closed = {your first choice, other door left closed} 3 door problem X=door with car behind Y=(your first choice, other door left closed

Gill, Richard D.

401

Discrete nonlinear wave propagation in Kerr nonlinear media  

NASA Astrophysics Data System (ADS)

Discrete optical systems are a subgroup of periodic structures in which the evolution of a continuous electromagnetic field can be described by a discrete model. In this model, the total field is the sum of localized, discrete modes. Weakly coupled arrays of single mode channel waveguides have been known to fall into this class of systems since the late 1960's. Nonlinear discrete optics has received a considerable amount of interest in the last few years, triggered by the experimental realization of discrete solitons in a Kerr nonlinear AlGaAs waveguide array by H. Eisenberg and coworkers in 1998. In this work a detailed experimental investigation of discrete nonlinear wave propagation and the interactions between beams, including discrete solitons, in discrete systems is reported for the case of a strong Kerr nonlinearity. The possibility to completely overcome "discrete" diffraction and create highly localized solitons, in a scalar or vector geometry, as well as the limiting factors in the formation of such nonlinear waves is discussed. The reversal of the sign of diffraction over a range of propagation angles leads to the stability of plane waves in a material with positive nonlinearity. This behavior can not be found in continuous self-focusing materials where plane waves are unstable against perturbations. The stability of plane waves in the anomalous diffraction region, even at highest powers, has been experimentally verified. The interaction of high power beams and discrete solitons in arrays has been studied in detail. Of particular interest is the experimental verification of a theoretically predicted unique, all optical switching scheme, based on the interaction of a so called "blocker" soliton with a second beam. This switching method has been experimentally realized for both the coherent and incoherent case. Limitations of such schemes due to nonlinear losses at the required high powers are shown.

Meier, Joachim

402

Rigorous derivation of the nonlinear Schrodinger equation and Davey-Stewartson systems from quadratic  

E-print Network

Rigorous derivation of the nonlinear Schr¨odinger equation and Davey-Stewartson systems from@math.u-bordeaux.fr Abstract: In this paper, we derive rigorously the nonlinear Schr¨odinger equation and Davey, and which satisfy a "transparency" hypothesis. Key words: Geometric optics, nonlinear Schr¨odinger equation

Colin, Thierry

403

Nonlinear Response of Laminated Cylindrical Shell Panels Subjected to Thermomechanical Loads  

Microsoft Academic Search

The nonlinear response of multi-layered composite cylindrical shell panels subjected to thermomechanical loads are studied in this article. The structural model is based on the first order shear deformation theory incorporating geometric nonlinearities. The nonlinear equilibrium paths are traced using the arc-length control algorithm within the framework of finite element method. Hashin's failure criterion has been adopted to predict the

Maloy K. Singh; L. S. Ramachandra; J. N. Bandyopadhyay

2006-01-01

404

Time-resolved Z-scan measurements of optical nonlinearities  

Microsoft Academic Search

We introduce a temporal delay in one beam of the two-color Z-scan apparatus, which measures nondegenerate nonlinear absorption and nondegenerate nonlinear refraction. This technique allows us to time resolve separately the sign and the magnitude of the nonlinear absorption and refraction at frequency p that are due to the presence of a strong excitation at frequency oe. For example, in

Jiangwei Wang; Mansour Sheik-Bahae; A. A. Said; David J. Hagan; Eric W. van Stryland

1994-01-01

405

Nonlinear opto-mechanical pressure  

E-print Network

A transparent material exhibits ultra-fast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, as optical manipulation, biophysics, cavity optomechanics, quantum optics, optical tractors, and is relevant in fundamental problems as the Abraham-Minkoswky dilemma, or the Casimir effect. Here we show that an ultra-fast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order of magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.

Conti, Claudio

2014-01-01

406

Study on the Geometric Distortion Correction Algorithm for Circular-Scanning SAR Imaging  

Microsoft Academic Search

The images generated by a circular-scanning synthetic aperture radar (SAR) can provide precise guiding information though image-matching post-processing, which necessitates their high precision in geometry. However, due to the irregular motion of the radar platform and the circular scanning antenna beam, the inevitable geometric distortion in the focused images is necessarily to be corrected. In this paper, a two-dimensional geometric

Yong Li; Daiyin Zhu; Ling Wang

2008-01-01

407

Optimal spatiotemporal reduced order modeling for nonlinear dynamical systems  

NASA Astrophysics Data System (ADS)

Proposed in this dissertation is a novel reduced order modeling (ROM) framework called optimal spatiotemporal reduced order modeling (OPSTROM) for nonlinear dynamical systems. The OPSTROM approach is a data-driven methodology for the synthesis of multiscale reduced order models (ROMs) which can be used to enhance the efficiency and reliability of under-resolved simulations for nonlinear dynamical systems. In the context of nonlinear continuum dynamics, the OPSTROM approach relies on the concept of embedding subgrid-scale models into the governing equations in order to account for the effects due to unresolved spatial and temporal scales. Traditional ROMs neglect these effects, whereas most other multiscale ROMs account for these effects in ways that are inconsistent with the underlying spatiotemporal statistical structure of the nonlinear dynamical system. The OPSTROM framework presented in this dissertation begins with a general system of partial differential equations, which are modified for an under-resolved simulation in space and time with an arbitrary discretization scheme. Basic filtering concepts are used to demonstrate the manner in which residual terms, representing subgrid-scale dynamics, arise with a coarse computational grid. Models for these residual terms are then developed by accounting for the underlying spatiotemporal statistical structure in a consistent manner. These subgrid-scale models are designed to provide closure by accounting for the dynamic interactions between spatiotemporal macroscales and microscales which are otherwise neglected in a ROM. For a given resolution, the predictions obtained with the modified system of equations are optimal (in a mean-square sense) as the subgrid-scale models are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. Methods are suggested for efficient model construction, appraisal, error measure, and implementation with a couple of well-known time-discretization schemes. Four nonlinear dynamical systems serve as testbeds to demonstrate the technique. First we consider an autonomous van der Pol oscillator for which all trajectories evolve to self-sustained limit cycle oscillations. Next we investigate a forced Duffing oscillator for which the response may be regular or chaotic. In order to demonstrate application for a problem in nonlinear wave propagation, we consider the viscous Burgers equation with large-amplitude inflow disturbances. For the fourth and final system, we analyze the nonlinear structural dynamics of a geometrically nonlinear beam under the influence of time-dependent external forcing. The practical utility of the proposed subgrid-scale models is enhanced if it can be shown that certain statistical moments amongst the subgrid-scale dynamics display to some extent the following properties: spatiotemporal homogeneity, ergodicity, smooth scaling with respect to the system parameters, and universality. To this end, we characterize the subgrid-scale dynamics for each of the four problems. The results in this dissertation indicate that temporal homogeneity and ergodicity are excellent assumptions for both regular and chaotic response types. Spatial homogeneity is found to be a very good assumption for the nonlinear beam problem with models based upon single-point but not multi-point spatial stencils. The viscous Burgers flow, however, requires spatially heterogeneous models regardless of the stencil. For each of the four problems, the required statistical moments display a functional dependence which can easily be characterized with respect to the physical parameters and the computational grid. This observed property, in particular, greatly simplifies model construction by way of moment estimation. We investigate the performance of the subgrid-scale models with under-resolved simulations (in space and time) and various discretization schemes. For the canonical Duffing and van der Pol oscillators, the subgrid-scale models are found to improve the accuracy of under-resolved time-marching and time-s

LaBryer, Allen

408

Fast and Robust Projective Matching for Fingerprints using Geometric Hashing Rintu Boro Sumantra Dutta Roy  

E-print Network

Fast and Robust Projective Matching for Fingerprints using Geometric Hashing Rintu Boro Sumantra, sumantra}@ee.iitb.ac.in Abstract Fingerprint matching is the most important module in automatic person recognition using fingerprints. We model the nonlinear distortions and noise obtained during the fin- gerprint

Banerjee, Subhashis

409

Integrated multidisciplinary design optimization using discrete sensitivity analysis for geometrically complex aeroelastic configurations  

Microsoft Academic Search

The first two steps in the development of an integrated multidisciplinary design optimization procedure capable of analyzing the nonlinear fluid flow about geometrically complex aeroelastic configurations have been accomplished in the present work. For the first step, a three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed. The advantage of unstructured grids, when compared

James Charles Newman III

1997-01-01

410

Geometric inequalities via a duality between certain quasilinear PDEs and Fokker-Planck equations  

E-print Network

Geometric inequalities via a duality between certain quasilinear PDEs and Fokker-Planck equations M and stationary solutions of Fokker-Planck equations u t = div{u (F (u) + V )}, where V is an appro- priate convex­and yields convergence rates for -generalized- entropies of degenerate nonlinear Fokker-Planck equations

Agueh, Martial

411

On Anisotropic Geometric Diffusion in 3D Image Processing and Image Sequence Analysis  

Microsoft Academic Search

A morphological multiscale method in 3D image and 3D image sequence processing is discussed which identifies edges on level sets and the motion of features in time. Based on these indicator evaluation the image data is processed applying nonlinear diffusion and the theory of geometric evolution problems. The aim is to smooth level sets of a 3D image while preserving

Karol Mikula; Martin Rumpf; Fiorella Sgallari

2002-01-01

412

A MODEL BASED APPROACHTO IMPROVE THE PERFORMANCE OF THE GEOMETRIC FILTERMG SPECKLE REDUCTION ALGORITHM  

E-print Network

to ultrasound imaging The geometricfiltering method is an iterative algorithm for speckle reduction which the effective algorithms This paper describes how a specific speckle detection) and display (e images4 of contrast resolution phantomsand it was The geometric filteris a nonlinear, iterative algorithm

Fienup, James R.

413

The verdict geometric quality library.  

SciTech Connect

Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. The geometric qualities of these regions is usually strongly tied to the accuracy these solvers are able to obtain in their approximations. The subroutines are written in C++ and have a simple C interface. Each metric may be evaluated individually or in combination. When multiple metrics are evaluated at once, they share common calculations to lower the cost of the evaluation.

Knupp, Patrick Michael; Ernst, C.D. (Elemental Technologies, Inc., American Fork, UT); Thompson, David C. (Sandia National Laboratories, Livermore, CA); Stimpson, C.J. (Elemental Technologies, Inc., American Fork, UT); Pebay, Philippe Pierre

2006-03-01

414

Bouncing Balls and Geometric Series  

NSDL National Science Digital Library

The introduction to this intriguing exercise and article begins "If a ball bounces an infinite number of times, it must take an infinite amount of time to finish bouncing!" This piece appeared in The Journal of Online Mathematics and Its Applications in May 2007, and it was authored by Robert Styer and Morgan Besson of Villanova University. This particular article and its accompanying teaching module "explore the time and distance of a bouncing ball and leads to a study of the geometric series." Along with the actual article, this site also includes a video clip and several interactive Flash mathlets. It's a fun way to get students thinking about geometric series, and mathematics educators will definitely want to tell colleagues about the site as well. [KMG

Besson, Morgan; Styer, Robert

2007-05-01

415

Geometrical modelling of textile reinforcements  

NASA Technical Reports Server (NTRS)

The mechanical properties of textile composites are dictated by the arrangement of yarns contained within the material. Thus, to develop a comprehensive understanding of the performance of these materials, it is necessary to develop a geometrical model of the fabric structure. This task is quite complex, as the fabric is made from highly flexible yarn systems which experience a certain degree of compressibility. Furthermore there are tremendous forces acting on the fabric during densification typically resulting in yarn displacement and misorientation. The objective of this work is to develop a methodology for characterizing the geometry of yarns within a fabric structure including experimental techniques for evaluating these models. Furthermore, some applications of these geometric results to mechanical property predictions models are demonstrated.

Pastore, Christopher M.; Birger, Alexander B.; Clyburn, Eugene

1995-01-01

416

Geometric Modeling and Industrial Geometry  

NSDL National Science Digital Library

The Geometric Modeling and Industrial Geometry group is part of the Institute of Discrete Mathematics and Geometry at the Vienna University of Technology. The group's goal is "to bridge the gap between academic and industrial research in geometry" by "performing application oriented fundamental research and industrial research closely connected to geometry." Its work currently emphasizes the recognition, inspection, manipulation, and design of geometric shapes. Short descriptions of the group's work and some articles are available on the academic research, covering topics such as Computational Line Geometry, Laguerre Geometry, approximation in the space of planes, the isophotic metric, and swept volumes. Visitors can also read about the group's industrial research on 3-D Computer Vision, reverse Engineering, and Industrial Inspection. The Application Areas section includes more articles and provides actual data from some of the objects it has scanned along with the resulting 3-D images.

2005-11-03

417

Nonlinear channelizer  

NASA Astrophysics Data System (ADS)

The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.

In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio

2012-12-01

418

Nonlinear channelizer.  

PubMed

The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz. PMID:23278100

In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio

2012-12-01

419

Parametric FEM for geometric biomembranes  

NASA Astrophysics Data System (ADS)

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 a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations.

Bonito, Andrea; Nochetto, Ricardo H.; Sebastian Pauletti, M.

2010-05-01

420

Geometric compression through topological surgery  

Microsoft Academic Search

The abundance and importance of complex 3-D data bases in major industry segments, the affordability of interactive 3-D rendering for office and consumer use, and the exploitation of the Internet to distribute and share 3-D data have intensified the need for an effective 3-D geometric compression technique that would significantly reduce the time required to transmit 3-D models over digital

Gabriel Taubin; Jarek Rossignac

1998-01-01

421

Geometric structures of vectorial type  

Microsoft Academic Search

We study geometric structures of W4-type in the sense of A. Gray on a Riemannian manifold. If the structure group G?SO(n) preserves a spinor or a non-degenerate differential form, its intrinsic torsion ? is a closed 1-form (Proposition 2.1 and Theorem 2.1). Using a G-invariant spinor we prove a splitting theorem (Proposition 2.2). The latter result generalizes and unifies a

Ilka Agricola; Thomas Friedrich

2006-01-01

422

Geometric phases of water waves  

E-print Network

Recently, Banner et al. (2014) highlighted a new fundamental property of open ocean wave groups, the so-called crest slowdown. For linear narrowband waves, this is related to the geometric phase associated with the parallel transport through the principal fiber bundle of the wave motion with U(1) group symmetry. The theoretical predictions are shown to be in fair agreement with ocean field observations.

Fedele, Francesco

2014-01-01

423

Geometrical methods in learning theory  

NASA Astrophysics Data System (ADS)

The methods of information theory provide natural approaches to learning algorithms in the case of stochastic formal neural networks. Most of the classical techniques are based on some extremization principle. A geometrical interpretation of the associated algorithms provides a powerful tool for understanding the learning process and its stability and offers a framework for discussing possible new learning rules. An illustration is given using sequential and parallel learning in the Boltzmann machine.

Burdet, G.; Combe, Ph.; Nencka, H.

2001-02-01

424

Scaling properties of geometric parallelization  

NASA Astrophysics Data System (ADS)

We present a universal scaling law for all geometrically parallelized computer simulation algorithms. For algorithms with local interaction laws we calculate the scaling exponents for zero and infinite lattice size. The scaling is tested on local (cellular automata, Metropolis Ising) as well as cluster (Swendsen-Wang) algorithms. The practical aspects of the scaling properties lead to a simple recipe for finding the optimum number of processors to be used for the parallel simulation of a particular system.

Jakobs, A.; Gerling, R. W.

1992-01-01

425

Great Gobs of Geometric Games!  

NSDL National Science Digital Library

These games help you review shapes, make shapes, and transform shapes! First, use the online Geoboard to make your own shapes, just for fun. Now, review your geometric vocabulary and match the shape with its name in the memory game Matching Shapes. Transformational Geometry is loads of fun. You'll have to use your knowledge of translation and rotation for this game. Can you make the ...

Hearne, Miss

2009-04-30

426

Geometrical factor correction in grazing incident x-ray fluorescence experiment  

SciTech Connect

The geometrical factor in the grazing incident x-ray fluorescence analysis is an important angle-dependent term, which can have a great effect on the measured data. In this paper, the effects of the geometrical factor on the florescence yield have been demonstrated. A formula is presented to estimate the geometrical factor, which includes the experimental parameters of the beam and setup. The validity of this formula is proven by the good agreement between the calculated fluorescence yields with the experimental results in grazing incident x-ray fluorescence analysis.

Li Wenbin; Zhu Jingtao; Ma Xiaoying; Li Haochuan; Wang Hongchang; Wang Zhanshan [Key Laboratory of Advanced Micro-Structured Materials, MOE, Institute of Precision Optical Engineering, Department of Physics, Tongji University, Shanghai 200092 (China); Sawhney, Kawal J. S. [Diamond Light Source Ltd., Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE (United Kingdom)

2012-05-15

427

Geometrical content of Leslie coefficients  

NASA Astrophysics Data System (ADS)

In this work, we will study how the effective geometry acquired by nematic molecules under thermal vibration contribute to the determination of the Leslie coefficients. To do this, we will divide this work in two sections. In the first section, we present the geometrical fundamentals of the so-called Hess-Baalss (HB) approach [D. Baalss and S. Hess, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.57.86 57, 86 (1986)] where we show that its basic assumptions can be understood as a geometrical interpretation of de Gennes’ passage from the microscopic to the macroscopic order parameter. In the second section, we use an extended version of the HB approach [M. Simões, K. Yamaguti, and A. J. Palangana, Phys. Rev. EPHRVAO1539-375510.1103/PhysRevE.80.061701 80, 061701 (2009)] to obtain the geometrical contribution to each Leslie coefficient. Our results will be compared with experimental data, and we will show that the Miesowicz’s coefficients are connected as long as the ratio ?3/?4 between these Leslie coefficients can be considered small.

Simões, M.; da Silva, J. L. Correia

2011-05-01

428

Geometric mean for subspace selection.  

PubMed

Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions. PMID:19110492

Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

2009-02-01

429

GEOMETRIC HOMOGENEITY AND STABILIZATION MATTHIAS KAWSKI \\Lambda  

E-print Network

GEOMETRIC HOMOGENEITY AND STABILIZATION MATTHIAS KAWSKI \\Lambda \\Lambda Center for Systems Science of homogeneity, for vector fields (differential equations and control systems), functions, differential forms and endomorphisms. The fundamental observation is that homogeneity is an intrinsic, geometric property. Accordingly

Kawski, Matthias

430

Nonlinear Dynamos  

NASA Astrophysics Data System (ADS)

This paper discusses nonlinear dynamos where the nonlinearity arises directly via the Lorentz force in the Navier-Stokes equation, and leads to a situation where the Lorentz force and the velocity and the magnetic field are in direct competition over substantial regions of the flow domain. Filamentary and non-filamentary dynamos are contrasted, and the concept of Alfvénic dynamos with almost equal magnetic and kinetic energies is reviewed via examples. So far these remain in the category of toy models; the paper concludes with a discussion of whether similar dynamos are likely to exist in astrophysical objects, and whether they can model the solar cycle.

Galloway, David

2011-08-01

431

Geometric Algebra and Physics Anthony Lasenby  

E-print Network

Geometric Algebra and Physics Anthony Lasenby Astrophysics Group, Cavendish Laboratory, Cambridge Microwave Background, and early universe Why am I here talking about `Geometric Algebra'? Came across effectively extends them to the relativistic domain And via `conformal geometric algebra' gives a whole new

Hart, Gus

432

CRYSTAL-LIKE GEOMETRIC MODELING ERIC LANDRENEAU  

E-print Network

CRYSTAL-LIKE GEOMETRIC MODELING A Thesis by ERIC LANDRENEAU Submitted to the Office of Graduate OF SCIENCE May 2005 Major Subject: Computer Science #12;CRYSTAL-LIKE GEOMETRIC MODELING A Thesis by ERIC Science #12;iii ABSTRACT Crystal-Like Geometric Modeling. (May 2005) Eric Landreneau, B.S., Texas A

Keyser, John

433

Introduction to Pauli Geometric Algebra M. Berrondo  

E-print Network

Introduction to Pauli Geometric Algebra M. Berrondo May 9, 2009 #12;Pauli Algebra Geometric Algebras Geometric algebras (also called Cliord algebras) are used to endow physical spaces with a useful algebraic structure. By analyzing the physical system within this context, we can nd alternate

Hart, Gus

434

GEOMETRIC MEASUREMENT COMPARISONS FOR ROCKWELL DIAMOND INDENTERS  

Microsoft Academic Search

In the uncertainty budget of Rockwell C hardness (HRC) tests, geometric error of the Rockwell diamond indenter is a major contributor. The geometric calibration of Rockwell diamond indenters has been a key issue for Rockwell hardness standardization. The National Institute of Standards and Technology (NIST) developed a microform calibration system based on a stylus instrument for the geometric calibration of

John Song; Samuel Low; Alan Zheng

435

Geometrically frustrated magnets Arnab Sen, TIFR  

E-print Network

, 10786 (1992) f= |cw|/T* Arnab Sen, TIFR Geometrically frustrated magnets #12;Materials TriangularGeometrically frustrated magnets Arnab Sen, TIFR Theoretical Physics Colloquium Collaborators: K and A. Vishwanath, PRL 100, 097202 (2008). July 7, 2009 Arnab Sen, TIFR Geometrically frustrated magnets

436

Towards modeling of nonlinear laser-plasma interactions with hydrocodes: the thick-ray approach.  

PubMed

This paper deals with the computation of laser beam intensity in large-scale radiative hydrocodes applied to the modeling of nonlinear laser-plasma interactions (LPIs) in inertial confinement fusion (ICF). The paraxial complex geometrical optics (PCGO) is adapted for light waves in an inhomogeneous medium and modified to include the inverse bremsstrahlung absorption and the ponderomotive force. This thick-ray model is compared to the standard ray-tracing (RT) approach, both in the chic code. The PCGO model leads to different power deposition patterns and better diffraction modeling compared to standard RT codes. The intensity-reconstruction technique used in RT codes to model nonlinear LPI leads to artificial filamentation and fails to reproduce realistic ponderomotive self-focusing distances, intensity amplifications, and density channel depletions, whereas PCGO succeeds. Bundles of Gaussian thick rays can be used to model realistic non-Gaussian ICF beams. The PCGO approach is expected to improve the accuracy of ICF simulations and serve as a basis to implement diverse LPI effects in large-scale hydrocodes. PMID:24730950

Colaïtis, A; Duchateau, G; Nicolaï, P; Tikhonchuk, V

2014-03-01

437

Towards modeling of nonlinear laser-plasma interactions with hydrocodes: The thick-ray approach  

NASA Astrophysics Data System (ADS)

This paper deals with the computation of laser beam intensity in large-scale radiative hydrocodes applied to the modeling of nonlinear laser-plasma interactions (LPIs) in inertial confinement fusion (ICF). The paraxial complex geometrical optics (PCGO) is adapted for light waves in an inhomogeneous medium and modified to include the inverse bremsstrahlung absorption and the ponderomotive force. This thick-ray model is compared to the standard ray-tracing (RT) approach, both in the chic code. The PCGO model leads to different power deposition patterns and better diffraction modeling compared to standard RT codes. The intensity-reconstruction technique used in RT codes to model nonlinear LPI leads to artificial filamentation and fails to reproduce realistic ponderomotive self-focusing distances, intensity amplifications, and density channel depletions, whereas PCGO succeeds. Bundles of Gaussian thick rays can be used to model realistic non-Gaussian ICF beams. The PCGO approach is expected to improve the accuracy of ICF simulations and serve as a basis to implement diverse LPI effects in large-scale hydrocodes.

Colaïtis, A.; Duchateau, G.; Nicolaï, P.; Tikhonchuk, V.

2014-03-01

438

Geometrical and physical parameters for electromagnetic relativistic sources  

E-print Network

The electromagnetic field is typically measured by the charged particle motion observation. Generally in the experiments, position, velocity and other physical parameters concerning relativistic particle beams, are estimated evaluating the actual distance between the moving source and the detector, at even given time (typically appointing the reference time to the minimum distance between the two points). So to describe faithfully a physical scenario, fixing a spatial reference system is a very troublesome act as well as evaluating the geometrical parameters and relative time evolution. In the present note, within a simple experimental context, avoiding as much as possible complex mathematical formalisms, the intensity field evolution is predicted at a given point, using fundamental geometrical assertions. The result is consistent with the special relativity law.

Modestino, Giuseppina

2014-01-01

439

Nonlinear Mode-Coupling in Nanomechanical Systems  

PubMed Central

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

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

2013-01-01

440

Categorical geometric skew Howe duality  

E-print Network

We categorify the R-matrix isomorphism between tensor products of minuscule representations of U_q(sl(n)) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of U_q(sl(2)) which are related to representations of U_q(sl(n)) by quantum skew Howe duality. The resulting equivalence is part of the program of algebro-geometric categorification of Reshitikhin-Turaev tangle invariants developed by the first two authors.

Cautis, Sabin; Licata, Anthony

2009-01-01

441

Science, art and geometrical imagination  

NASA Astrophysics Data System (ADS)

From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental rôle of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Dürer, Kepler, Escher, Grisey or the author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as on beauty, conciseness and an emotional approach of the world.

Luminet, Jean-Pierre

2011-06-01

442

Geometrical setting of solid mechanics  

NASA Astrophysics Data System (ADS)

The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation.

Fiala, Zden?k

2011-08-01

443

Geometric phases of water waves  

NASA Astrophysics Data System (ADS)

Recently, Banner et al. (Phys. Rev. Lett., 112 (2014) 114502) highlighted a new fundamental property of open ocean wave groups, the so-called crest slowdown. For linear narrow-band waves, this is related to the geometric and dynamical phase velocities Ud and Ug associated with the parallel transport through the principal fiber bundle of the wave dynamics with U(1) symmetry. The theoretical predictions are shown to be in fair agreement with ocean field observations, from which the average crest speed c=U_d+Ug with c/U_d?0.8 and Ug/U_d?-0.2 .

Fedele, Francesco

2014-09-01

444

Geometric analysis of wing sections  

NASA Technical Reports Server (NTRS)

This paper describes a new geometric analysis procedure for wing sections. This procedure is based on the normal mode analysis for continuous functions. A set of special shape functions is introduced to represent the geometry of the wing section. The generators of the NACA 4-digit airfoils were included in this set of shape functions. It is found that the supercritical wing section, Korn airfoil, could be well represented by a set of ten shape functions. Preliminary results showed that the number of parameters to define a wing section could be greatly reduced to about ten. Hence, the present research clearly advances the airfoil design technology by reducing the number of design variables.

Chang, I.-CHUNG; Torres, Francisco J.; Tung, Chee

1995-01-01

445

Geometric methods in quantum computation  

NASA Astrophysics Data System (ADS)

Recent advances in the physical sciences and engineering have created great hopes for new computational paradigms and substrates. One such new approach is the quantum computer, which holds the promise of enhanced computational power. Analogous to the way a classical computer is built from electrical circuits containing wires and logic gates, a quantum computer is built from quantum circuits containing quantum wires and elementary quantum gates to transport and manipulate quantum information. Therefore, design of quantum gates and quantum circuits is a prerequisite for any real application of quantum computation. In this dissertation we apply geometric control methods from differential geometry and Lie group representation theory to analyze the properties of quantum gates and to design optimal quantum circuits. Using the Cartan decomposition and the Weyl group, we show that the geometric structure of nonlocal two-qubit gates is a 3-Torus. After further reducing the symmetry, the geometric representation of nonlocal gates is seen to be conveniently visualized as a tetrahedron. Each point in this tetrahedron except on the base corresponds to a different equivalent class of nonlocal gates. This geometric representation is one of the cornerstones for the discussion on quantum computation in this dissertation. We investigate the properties of those two-qubit operations that can generate maximal entanglement. It is an astonishing finding that if we randomly choose a two-qubit operation, the probability that we obtain a perfect entangler is exactly one half. We prove that given a two-body interaction Hamiltonian, it is always possible to explicitly construct a quantum circuit for exact simulation of any arbitrary nonlocal two-qubit gate by turning on the two-body interaction for at most three times, together with at most four local gates. We also provide an analytic approach to construct a universal quantum circuit from any entangling gate supplemented with local gates. Closed form solutions have been derived for each step in this explicit construction procedure. Moreover, the minimum upper bound is found to construct a universal quantum circuit from any Controlled-Unitary gate. A near optimal explicit construction of universal quantum circuits from a given Controlled-Unitary is provided. For the Controlled-NOT and Double-CNOT gate, we then develop simple analytic ways to construct universal quantum circuits with exactly three applications, which is the least possible for these gates. We further discover a new quantum gate (named B gate) that achieves the desired universality with minimal number of gates. Optimal implementation of single-qubit quantum gates is also investigated. Finally, as a real physical application, a constructive way to implement any arbitrary two-qubit operation on a spin electronics system is discussed.

Zhang, Jun

446

Buildings, spiders, and geometric Satake  

E-print Network

Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case G = SL(3), non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0).

Fontaine, Bruce; Kuperberg, Greg

2011-01-01

447

Graphene with geometrically induced vorticity  

E-print Network

At half filling, the electronic structure of graphene can be modelled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field, an everywhere-real Kekule modulation of the hopping matrix elements can correspond to a non-real Higgs field with non-trivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes. For fullerene-like molecules we employ the index theorem to demonstrate the existence of six low-lying states that do not depend strongly on the Kekule-induced mass gap.

Jiannis K. Pachos; Michael Stone; Kristan Temme

2007-10-03

448

Geometric phases of water waves  

E-print Network

Recently, Banner et al. (2014) highlighted a new fundamental property of open ocean wave groups, the so-called crest slowdown. For linear narrowband wav