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1

In this paper a finite element formulation of a geometric and material nonlinear analytical model for externally prestressed beams is illustrated. Differently from existing methods starting from the linear theory and then including the tendon eccentricity variation, the analytical model adopted is based on a nonlinear kinematical theory. Thus a complete description of the nonlinear interactions between tendon and beam

Alessandro Zona; Laura Ragni; Andrea Dall’Asta

2008-01-01

2

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

3

Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.

The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation. PMID:23927186

Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor

2013-08-01

4

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

NASA Astrophysics Data System (ADS)

The temporal evolution of a periodic ripple pattern on a silicon surface undergoing erosion by 30keV argon ion bombardment has been studied for two angles of ion incidence of 60° and 70° 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?tn , where n=0.47±0.02 for a 60° angle of ion incidence followed by a saturation. Wavelength coarsening was also observed for 70° but ordering in the periodic ripple pattern is destroyed quickly for 70° as compared to 60°. 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

2007-08-01

5

NASA Astrophysics Data System (ADS)

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

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

2013-09-01

6

MULTIPHASE WEAKLY NONLINEAR GEOMETRIC OPTICS ODINGER EQUATIONS

. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric referred to as wave mixing. The study of this nonlinear phenomena is of signi#12;cant mathematical of highly oscillatory waves in nonlinear Schrodinger equations, posed on Eu- clidean space or on the torus

Recanati, Catherine

7

Computational optimization of adhesive microstructures based on a nonlinear beam formulation

in objective function E Young's modulus G shear modulus H beam height / thickness Hmin admissible minimum beam contact mechan- ics, geometrically exact beam theory, nonlinear finite element methods List of important

8

Geometrically nonlinear analysis of adhesively bonded joints

NASA Technical Reports Server (NTRS)

A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-release rates (G1/G2) was found to be strongly affected by the adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements. Previously announced in STAR as N83-13497

Dattaguru, B.; Everett, R. A., Jr.; Whitcomb, J. D.; Johnson, W. S.

1984-01-01

9

Gaussian beam evolution in nonlinear inhomogeneous plasma

NASA Astrophysics Data System (ADS)

The method of nonlinear complex geometrical optics (NCGO) is proposed in this paper for description of the evolution of a spatially narrow Gaussian beam (GB) in an inhomogeneous nonlinear plasma. NCGO method deals with first-order ordinary differential equations for the complex curvature of the wave front and for GB amplitude and for second-order ordinary differential equation for GB width. Thus, NCGO simplifies the description of GB diffraction and self-focusing effects as compared to the known methods of plasma physics and this way it can be assumed to be attractive and comprehensive approach in problems of plasma heating by electromagnetic waves. Moreover, we demonstrate in this paper some regularity for nonlinear inhomogeneous plasma in the framework of which central ray of a GB is not subjected to nonlinear refraction within NCGO method boundary applicability. On the contrary, the beam width, wave front curvature, and GB amplitude are modified by diffraction and self-focusing processes. General properties of the beam propagation are illustrated with results of numerical modeling for two particular cases: GB diffraction and self-focusing along curvilinear trajectory with torsion in axially symmetric plasma column and GB reflection from nonlinear inhomogeneous plasma layer. We prove in this paper that NCGO is new effective method of plasma physics, which can be applied for improvement of ray tracing techniques and plasma diagnostics.

Berczynski, P.; Kravtsov, Yu. A.; Tikhonchuk, V.; Tikhonchuk

2014-04-01

10

Classical light beams and geometric phases.

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

11

MULTIPHASE WEAKLY NONLINEAR GEOMETRIC OPTICS FOR SCHRODINGER EQUATIONS

of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation on the res- onance of such waves, often referred to as wave mixing. The study of this nonlinear phenomena is of significant oscillatory waves in nonlinear SchrÂ¨odinger equations, posed on Eu- clidean space or on the torus. Our scaling

Dumas, Eric

12

MULTIPHASE WEAKLY NONLINEAR GEOMETRIC OPTICS FOR SCHRODINGER EQUATIONS

of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation on the res- onance of such waves, often referred to as wave mixing. The study of this nonlinear phenomena is of significant oscillatory waves in nonlinear Schr¨odinger equations, posed on Eu- clidean space or on the torus. Our scaling

Paris-Sud XI, Université de

13

Dynamic instabilities in coupled oscillators induced by geometrically nonlinear damping

The dynamics of a system of coupled oscillators possessing strongly nonlinear stiffness and damping is examined. The system\\u000a consists of a linear oscillator coupled to a strongly nonlinear, light attachment, where the nonlinear terms of the system\\u000a are realized due to geometric effects. We show that the effects of nonlinear damping are far from being purely parasitic and\\u000a introduce new

David Andersen; Yuli Starosvetsky; Alexander Vakakis; Lawrence Bergman

14

Gain scheduling for geometrically nonlinear flexible space structures

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

15

Influence of geometric nonlinearities on skin-stiffener interface stresses

NASA Technical Reports Server (NTRS)

A method for computing skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The results indicate that the inclusion of geometric nonlinearities is very important for an accurate determination of the interface stresses. Membrane flattening of the panel tends to reduce the tendency of the stiffener to separate.

Cohen, D.; Hyer, M. W.

1988-01-01

16

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

17

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

18

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

19

Stiffness design of geometrically nonlinear structures using topology optimization

. The paper deals with topology optimization of structures undergoing large deformations. The geometrically nonlinear behaviour\\u000a of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson\\u000a iterative scheme. The sensitivities of the objective functions are found with the adjoint method and the optimization problem\\u000a is solved using the Method of

T. Buhl; C. B. W. Pedersen; O. Sigmund

2000-01-01

20

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

21

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

22

Nonlinear optimization of beam lines

NASA Astrophysics Data System (ADS)

The current final focus systems of linear colliders have been designed based on the local compensation scheme proposed by Raimondi and Seryi. However, there exist remaining aberrations that deteriorate the performance of the system. This paper develops a general algorithm for the optimization of beam lines based on the computation of the high orders of the transfer map using MAD-X and Polimorphic Tracking Code. The algorithm is applied to the CLIC beam delivery system.

Tomás, R.

2006-08-01

23

A consistent interface element formulation for geometrical and material nonlinearities

NASA Astrophysics Data System (ADS)

Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with coupled material and geometrical nonlinearities. The present work proposes a consistent derivation of a new interface element for large deformation analyses. The resulting compact derivation leads to an operational formulation that enables the accommodation of any order of kinematic interpolation and constitutive behavior of the interface. The derived interface element has been implemented into the finite element codes FEAP and ABAQUS by means of user-defined routines. The interplay between geometrical and material nonlinearities is investigated by considering two different constitutive models for the interface (tension cut-off and polynomial cohesive zone models) and small or finite deformation for the continuum. Numerical examples are proposed to assess the mesh independency of the new interface element and to demonstrate the robustness of the formulation. A comparison with experimental results for peeling confirms the predictive capabilities of the formulation.

Reinoso, J.; Paggi, M.

2014-12-01

24

Nonlinear geometric influence on the mechanical behavior of shape memory alloy helical springs

NASA Astrophysics Data System (ADS)

This paper investigates the nonlinear geometric effect on the mechanical behavior of shape memory alloy (SMA) helical springs. First, the SMA wires are characterized, and then the design and fabrication of SMA helical springs are discussed. Experimental tensile tests are carried out to show the nonlinear geometric influence. Results show a coupling between constitutive and geometric nonlinearities that defines the spring stiffness. Two springs with different geometries are built from SMA wires to define springs with both weak and strong nonlinear geometric influence. Numerical analyses are developed, using the finite element method to confirm the general conclusions shown in our experimental observations.

Savi, Marcelo A.; Pacheco, Pedro Manuel C. L.; Garcia, Mauricio S.; Aguiar, Ricardo A. A.; de Souza, Luís Felipe G.; da Hora, Rodolpho B.

2015-03-01

25

Beams on nonlinear elastic foundation

NASA Astrophysics Data System (ADS)

In order to determination vertical deflections and rail bending moments the Winkler model (1867) is often used. This linear model neglects several conditions. For example, by using experimental results, it has been observed that there is a substantial increase in the maximum rail deflection and rail bending moment when considering the nonlinearity of the track support system. A deeper mathematical analysis of the models is necessary in order to obtain better methods for more accurate numerical solutions in the determination of deflections and rail bending moments. This paper is intended to be a small step in this direction.

Lukkassen, Dag; Meidell, Annette

2014-12-01

26

NASA Technical Reports Server (NTRS)

In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.

Muravyov, Alexander A.; Turner, Travis L.; Robinson, Jay H.; Rizzi, Stephen A.

1999-01-01

27

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

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

28

About nonlinear geometric optics Institut Fourier, UMR 5582 (CNRS-UJF)

About nonlinear geometric optics E. Dumas Institut Fourier, UMR 5582 (CNRS-UJF) 100 rue des Math We give an idea of the evolution of mathematical nonlinear geomet- ric optics from its foundation Geometric optics goes back at least to the XVIIth Century, with Fermat, Snell and Descartes, who described

Dumas, Eric

29

Cubic nonlinearity in shear wave beams with different polarizations

A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal. Comparisons are made with effects of quadratic nonlinearity in compressional wave beams. PMID:18529167

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

2008-01-01

30

Generation of Optical Vortex Beams by Nonlinear Wave Mixing

Generation of Optical Vortex Beams by Nonlinear Wave Mixing Alon Bahabad and Ady Arie School.0190) Nonlinear optics; (190.2620) Harmonic generation and mixing optical vortex beams; (190.4223) Nonlinear wave mixing. References and links 1. J. F. Nye and M. V. Berry, "Dislocations in Wave Trains," Royal Society

Arie, Ady

31

A geometric calibration method for cone beam CT systems

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

32

Beam stability and nonlinear dynamics. Summary report

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

33

Sensitive measurement of optical nonlinearities using a single beam

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

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

1990-01-01

34

Beam stability & nonlinear dynamics. Formal report

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

35

Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions

NASA Astrophysics Data System (ADS)

An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The first approximation solution of the non-resonance is obtained by means of the method of multiple scales. The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method. The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS. Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.

Ma, NiuJing; Wang, RongHui; Han, Qiang; Lu, YiGang

2014-08-01

36

Multiple-mode nonlinear free and forced vibrations of beams using finite element method

NASA Technical Reports Server (NTRS)

Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.

Mei, Chuh; Decha-Umphai, Kamolphan

1987-01-01

37

Finite Element Analysis of Shape Memory Alloy Adaptive Trusses with Geometrical Nonlinearities

This contribution deals with the nonlinear analysis of shape memory alloy (SMA) adaptive trusses employing the finite element method. Geometrical nonlinearities are incorporated into the formulation together with a constitutive model that describes different thermomechanical behaviors of SMA. It has four macroscopic phases (three variants of martensite and an austenitic phase), and considers different material properties for austenitic and martensitic

Eduardo Lutterbach Bandeira; Marcelo Amorim Savi; Paulo Cesar da Camara Monteiro; Theodoro Antoun Netto

2006-01-01

38

The purpose of this review paper is to summarize the results of design sensi- tivity analysis and optimization methods of elastic conservative systems considering geo- metrical nonlinearity. Although those results are presented mainly for finite dimensional structures, they are applicable to continua discretized by finite element methods. Difficul- ties related to geometrical nonlinearity are discussed in detains by using small

M. Ohsaki

39

Nonlinear self-reconstruction of truncated Bessel beam

It is demonstrated that by blocking of the part of Bessel light beam azimuthal aperture, a far field ring is completely reconstructed in azimuth and partially in intensity after the beam passes through a benzene cell. The phenomenon is explained as beam self-action (degenerate four-wave mixing) in the medium with Kerr nonlinearity. A qualitative agreement of the theoretical predictions with

R. Butkus; R. Gadonas; J. Janusonis; A. Piskarskas; K. Regelskis; V. Smilgevi?ius; A. Stabinis

2002-01-01

40

NASA Astrophysics Data System (ADS)

The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam (or column) has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplification in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji's method (AGM). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is not needed in most cases via AGM manner. Also, comparisons are made between AGM and numerical method (Runge-Kutta 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.

Akbari, M. R.; Nimafar, M.; Ganji, D. D.; Akbarzade, M. M.

2014-12-01

41

Nonlinear system identification of frictional effects in a beam with a bolted joint connection

NASA Astrophysics Data System (ADS)

We perform nonlinear system identification (NSI) of the effects of frictional connections in the dynamics of a bolted beam assembly. The methodology utilized in this work combines experimental measurements with slow-flow dynamic analysis and empirical mode decomposition, and reconstructs the dynamics through reduced-order models. These are in the form of single-degree-of-freedom linear oscillators (termed intrinsic modal oscillators—IMOs) with forcing terms derived directly from the experimental measurements through slow-flow analysis. The derived reduced order models are capable of reproducing the measured dynamics, whereas the forcing terms provide important information about nonlinear damping effects. The NSI methodology is applied to model nonlinear friction effects in a bolted beam assembly. A 'monolithic' beam with identical geometric and material properties is also tested for comparison. Three different forcing (energy) levels were considered in the tests in order to study the energy-dependencies of the damping nonlinearities induced in the beam from the bolted joint. In all cases, the NSI methodology employed was successful in identifying the damping nonlinearities, their spatial distributions and their effects of the vibration modes of the structural component.

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

2013-08-01

42

Effect of Kerr nonlinearity on an Airy beam

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

43

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

NASA Technical Reports Server (NTRS)

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

Hrinda, Glenn A.

2006-01-01

44

Geometric manipulation of light : from nonlinear optics to invisibility cloaks

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

NASA Astrophysics Data System (ADS)

The algebraic-geometrical solutions of three (2 + 1)-dimensional equations (including mKP equation and coupled mKP equation) are discussed by Hamiltonian approach. First, the Poisson structure on CN × RN is introduced to give a Hamiltonian system associated with the derivative nonlinear Schrödinger (DNLS) hierarchy. The Hamiltonian system is proved to be Liouville integrable, accordingly the solutions of three (2 + 1)-dimensional nonlinear equations can be solved by three compatible Hamiltonian flows. Second, the canonical separated variables and Hamilton-Jacobi theory is used to definite action-angle variables for Hamiltonian flows. At last, by Riemann-Jacobi inversion, the algebraic-geometrical solutions of three (2 + 1)-dimensional nonlinear equations are obtained. Besides, the algebraic-geometrical solutions of the first two DNLS equations are also given.

Du, Dianlou; Yang, Xiao

2015-02-01

46

We develop a geometric optics series expansion approximation to a model of phase-compensated whole-beam thermal blooming of high-power laser beams. The model consists of a nonlinear medium whose thermal blooming coupling coefficient decreases exponentially with the propagation distance from the laser and whose motion relative to the laser beam is taken to be unidirectional, a Gaussian high-power intensity profile at the laser, and a collimated beam boundary condition at an exit plane that is many e-folding scale lengths from the laser. The series expansion parameter is directly proportional to Smith's geometric optics distortion parameter. Expansion formulae are derived for both the intensity and phase at all propagation distances. The exit plane intensity profiles obtained from these formally qualitatively agree with numerical results obtained from the wave- optics thermal blooming code FOURD, except when the FOURD results indicate that caustics are forming; quantitative agreement is also excellent, except for small differences in fine structure near the downwind edge of the beam. FOURD's return-wave phase-compensation iteration provides an estimate that the r.m.s. error in the initial phase obtained from our series approximation truncated at third-order is approximately 0.5% over the range of values we investigated. 3 refs., 2 figs., 1 tab.

Gautesen, A.K.; Morris, J.R.

1988-09-12

47

Geometrical Nonlinear Analysis of Composite Structures by Zigzag Theory—A Review

NASA Astrophysics Data System (ADS)

Advances in manufacturing technologies of composites leads to its uses as main load carrying structures which essentially need to be thick structures. Thus it is becoming increasingly important to predict accurately interlaminar variations of stresses and displacements along thickness of the composites. A review of the recent development of finite element methods for geometrical nonlinear analysis of composite structures specifically using zigzag theory is presented in this paper. The literature review is devoted to the recently developed finite elements, theories based on zigzag function for carrying out geometrical nonlinear analysis of composite structures. The future research is summarized finally.

Shirbhate, N. J.; Tungikar, V. B.

2010-10-01

48

Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method

NASA Astrophysics Data System (ADS)

In the present work, effect of von Kàrmàn geometric nonlinearity on the vibration behavior of a single-walled boron nitride nanotube (SWBNNT) is investigated based on nonlocal piezoelasticity theory. The SWBNNT is considered as a nanobeam within the framework of Timoshenko beam (TB). Loading is composed of a temperature change and an imposed axially electric potential throughout the SWBNNT. The interactions between the SWBNNT and its surrounding elastic medium are simulated by Winkler and Pasternak foundation models. The higher order governing equations of motion are derived using Hamilton's principle and the numerical solution of equations is obtained using Differential Quadrature (DQ) method. The effects of geometric nonlinearity, elastic foundation modulus, electric potential field, temperature change and nonlocal parameter on the frequency of the SWBNNT are studied in detail.

Ghorbanpour Arani, A.; Atabakhshian, V.; Loghman, A.; Shajari, A. R.; Amir, S.

2012-07-01

49

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

50

Geometric nonlinear analysis of microbeam under electrostatic loading

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.

2001-01-01

51

Nonlinear and tangent stiffness of imperfect beam columns

NASA Technical Reports Server (NTRS)

A curved member under axial load is analyzed using beam column theory to determine nonlinear response and the tangent stiffness associated with small displacements from the nonlinear state. Such a result is suitable for incorporation into a general nonlinear analysis using a corotational coordinate system to describe the rigid body type motion of individual members. The method is applied to buckling problems. Several examples are given to show the accuracy of the method.

Anderson, M. S.

1982-01-01

52

Hybrid Analytical Technique for Nonlinear Vibration Analysis of Thin-Walled Beams

NASA Technical Reports Server (NTRS)

A two-step hybrid analytical technique is presented for the nonlinear vibration analysis of thin-walled beams. The first step involves the generation of various-order perturbation functions using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in-plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section. The solutions obtained using a single-spatial mode were compared with those obtained using multiple-spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single-spatial mode.

Noor, Ahmed K.; Hadian, Jafar M.; Andersen, Carl M.

1993-01-01

53

Simulations of the nonlinear Helmholtz equation: arrest of beam collapse,

Simulations of the nonlinear Helmholtz equation: arrest of beam collapse, nonparaxial solitons provide the first ever numerical evidence that nonparaxiality and backscat- tering can arrest the collapse. Soc. Am. B 5, 633 (1988). 9. G. Fibich, "Small beam nonparaxiality arrests self-focussing of optical

Fibich, Gadi

54

Ince Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Based on the Snyder-Mitchell model that describes the beam propagation in strongly nonlocal nonlinear media, the close forms of Ince-Gaussian (IG) beams have been found. The transverse structures of the IG beams are described by the product of the Ince polynomials and the Gaussian function. Depending on the input power of the beams, the IG beams can be either a soliton state or a breather state. The IG beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The IG vortex beams can be constructed by a linear combination of the even and odd IG beams. The transverse intensity pattern of IG vortex beams consists of elliptic rings, whose number and ellipticity can be controlled, and a phase displaying a number of in-line vortices, each with a unitary topological charge. The analytical solutions of the IG beams are confirmed by the numerical simulations of the nonlocal nonlinear Schr\\rm \\ddot{o} dinger equation.

Deng, Dongmei; Guo, Qi

2008-07-01

55

Geometrically derived anisotropy in cubically nonlinear dielectric composites

We consider an anisotropic homogenized composite medium (HCM) arising from isotropic particulate component phases based on ellipsoidal geometries. For cubically nonlinear component phases, the corresponding zeroth-order strong-permittivity-fluctuation theory (SPFT) (which is equivalent to the Bruggeman homogenization formalism) and second-order SPFT are established and used to estimate the constitutive properties of the HCM. The relationship between the component phase particulate geometry

Tom G. Mackay; James Clerk

2003-01-01

56

Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes

A class of 'assumed strain' mixed finite element methods for fully nonlinear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part, formulated in the context

J. C. Simo; F. Armero

1992-01-01

57

Shell Element for Geometrically Non-Linear Analysis of Composite Laminates and Sandwich Structures

Summary This paper deals with a finite element formulation of a 4-node element for geometrically non-linear (GNL) analysis of layered shell structures. The element employs the MITC approach proposed by Dvorkin & Bathe (1) in order to eliminate the problem of shear locking. It uses full numerical integration both in-plane and through the thickness. The formulation passes all patch tests

J. Stegmann; J. C. Rauhe; L. Rosgaard; E. Lund

58

Geometric scaling in inclusive e A reactions and nonlinear perturbative QCD

In this note we report on geometric scaling in inclusive e A scattering data from the NMC and E665 experiments. We show that this scaling, as well as nuclear shadowing, is expected in the framework of nonlinear pQCD at small x based on a simple rescaling argument for e p scattering.

A. Freund; K. Rummukainen; H. Weigert; A. Schaefer

2002-10-09

59

Nonlinear geometrically adaptive finite element model of the coilbox

Hot bar heat loss in the transfer table, the rolling stage between rougher stands and finishing stands in a hot mill, is of major concern for reasons for energy consumption, metallurgical uniformity, and rollability. A mathematical model, as well as the corresponding numerical solution, is presented for the evolution of temperature in a coiling and uncoiling bar in hot mills in the form of a parabolic partial differential equation for a shape-changing domain. The space discretization is achieved via a computationally efficient geometrically adaptive finite element scheme that accommodates the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Finally, some numerical results are presented.

Troyani, N. [Univ. de Oriente, Puerto La Cruz (Venezuela). Dept. de Mecanica

1996-12-01

60

Iterative nonlinear beam propagation method and its application in nonlinear devices

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

61

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

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

62

Geometric Phase of Phase Space Trajectories:Mobius Strip and Nonlinear Oscillators

NASA Astrophysics Data System (ADS)

We present a gauge invariant formulation of associating a geometric phase with classical phase space trajectories. This geometric phase which depends upon the integrated torsion of the trajectory, bears a close analogy to the generalized Berry phase associated with the time evolution of the quantum wave functions. This topological quantity serves as an order parameter signalling phase transitions including novel geometrical transitions. One of the interesting aspects seen in Duffing and other nonlinear oscillators is the sudden jumps in the geometric phase which is accompanied by the divergence of the local torsion and the vanishing of the local curvature. Intriguingly, the analogous phenomenon was seen in a mobius strip when the ratio of the width to the length of the strip exceeds beyound a critical value.

Balakrishnan, Radha; Satija, Indubala

2005-03-01

63

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

64

NASA Astrophysics Data System (ADS)

The instability of geometrically imperfect shape memory alloy (SMA) fibers reinforced with hybrid laminated composite (SMAHC) plates and subjected to a uniform thermal loading is analytically investigated. The material properties of the SMAHC plates are assumed to be functions of temperature. Nonlinear equations of the plates’ thermal stability are derived based on a higher order shear deformation theory incorporating von Karman geometrical nonlinearity via stationary potential energy. The structural recovery stress, which is generated by martensitic phase transformation of the prestrained SMA fibers, is calculated based on the one-dimensional thermodynamic constitutive model by Brinson. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, in which systems of equations are solved by introducing an analytical approach. Closed-form formulations are presented to determine the load-deflection path and critical buckling temperature of the plate. Based on the developed closed-form solutions, ample numerical results are presented to provide an insight into the effects of the volume fraction, prestrain, location and orientation of the SMA fibers, composite plate geometry, geometrical imperfection and temperature dependence on the stability of the SMAHC plates. It is shown that a proper application of SMA fibers results in a considerable delay of the thermal bifurcation and controllable thermal post-buckling deflection of the SMAHC plate.

Asadi, Hamed; Eynbeygi, Mehdi; Wang, Quan

2014-07-01

65

A nonlinear theory for spinning anisotropic beams using restrained warping functions

NASA Technical Reports Server (NTRS)

A geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.

Ie, C. A.; Kosmatka, J. B.

1993-01-01

66

NASA Astrophysics Data System (ADS)

A general low-order fluid-structure interaction model capable of evaluating the multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures is presented. Cross-flow motions due to unsteady lift forces of inclined sagged cables and tensioned beams in uniform currents are investigated. In contrast to a linear equation governing the transverse motion of straight beams or cables typically considered in the literature, coupled horizontal/vertical (axial/transverse) displacements and geometric nonlinearities of curved cable (straight beam) are accounted for. A distributed nonlinear wake oscillator is considered in the approximation of space-time varying hydrodynamics. This semi-empirical fluid force model in general depends on the mass-damping parameter and has further been modified to capture both the effects of varying initial curvatures of the inclined cylinder and the Reynolds number. Numerical simulations are performed in the case of varying flow velocities and parametric results highlight several meaningful aspects of vortex-induced vibrations of long flexible cylinders. These comprise multi-mode lock-in, sharing, switching and interaction features in the space and time domains, the estimated maximum modal and total amplitudes, the resonant nonlinear modes of flexible cylinders and their space-time modifications, and the influence of fluid/structure parameters. A shortcoming of single-mode or linear structural model is underlined. Some quantitative and qualitative comparisons of numerical/experimental results are discussed to demonstrate the validity and required improvement of the proposed modelling and analysis predictions.

Srinil, Narakorn

2010-10-01

67

Nonlinear Analysis of Shear Dominant Prestressed Concrete Beams using ANSYS

This study reports the details of the finite element analysis of eleven shear critical partially prestressed concrete T-beams having steel fibers over partial or full depth. Prestressed T-beams having a shear span to depth ratio of 2.65 and 1.59 that failed in shear have been analyzed using the 'ANSYS' program. The 'ANSYS' model accounts for the nonlinearity, such as, bond-slip

Job Thomas

68

NASA Astrophysics Data System (ADS)

For repeated transient solutions of geometrically nonlinear structures, the numerical effort often poses a major obstacle. Thus it may become necessary to introduce a reduced order model which accelerates the calculations considerably while taking into account the nonlinear effects of the full order model in order to maintain accuracy. This work yields an integrated method that allows for rapid, accurate and parameterisable transient solutions. It is applicable if the structure is discretised in time and in space and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced order model. Three approaches, each responding to one of the requirements of rapidity, accuracy and parameterisation, are united to form the integrated method. The polynomial formulation of the nonlinear terms renders the solution of the reduced order model autonomous from the finite element formulation and ensures a rapid solution. The update and augmentation of the reduced basis ensures the accuracy, because the simple introduction of a constant basis seems to be insufficient to account for the nonlinear behaviour. The interpolation of the reduced basis allows adapting the reduced order model to different external parameters. A Newmark-type algorithm provides the backbone of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method enables a rapid, accurate and parameterisable transient solution.

Lülf, Fritz Adrian; Tran, Duc-Minh; Matthies, Hermann G.; Ohayon, Roger

2015-02-01

69

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

70

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

71

NASA Technical Reports Server (NTRS)

A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed, In this context. the first-order transversely shearable plate theory in conjunction with von-Karman geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic field disturbances within the plate, the assumptions proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e. the ones by Faraday, Ampere, Ohm, Maxwell and Lorentz), the modified Fourier's law of heat conduction and on the elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2- D one. The theory developed herein provides a foundation for the investigation, both analytical and numerical, of the interacting effects among the magnetic, thermal and elastic fields in multi-layered thin plates made of anisotropic materials.

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

2006-01-01

72

Beam-plasma instabilities and nonlinear electron waves in a helical-beam, magnetic mirror plasma

The possibility of using the plasma produced by a helical electron beam in a magnetic mirror geometry to study large amplitude electron plasma waves was investigated in the Allis mode. Results indicate that the helical-beam system is not suitable for nonlinear electron wave studies. Suggestions are made for certain modification on the apparatus so that it could be used to

E. P. Scannell

1976-01-01

73

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

74

Nonlinear optical catastrophe from a smooth initial beam.

We observed an optical cusp diffraction catastrophe with an initially smooth but elongated Gaussian beam with an aspect ratio of 2:1. Nonlinear and linear diffraction regimes account for the near-field elliptical annulus and the far-field spatially complex astroid. PMID:18073991

Deykoon, A M; Soskin, M S; Swartzlander, G A

1999-09-01

75

A Simple Model for Nonlinear Confocal Ultrasonic Beams

NASA Astrophysics Data System (ADS)

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

2007-01-01

76

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

77

Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals

space propagation of an Airy beam. This beam is generated by a nonlinear wave mixing process waves. The Y com- ponent of the nonlinear coefficient modulation imposes a cu- bic phaseControl of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals

Arie, Ady

78

Three wave mixing of airy beams in a quadratic nonlinear photonic crystals and Ady Arie

Three wave mixing of airy beams in a quadratic nonlinear photonic crystals Ido Doleva and Ady Arie three wave mixing processes of accelerating Airy beams in quadratic nonlinear crystals. In order Recently nonlinear optical generation of one- dimensional 1D Airy beams by a three-wave mixing pro- cess

Arie, Ady

79

Switching the acceleration direction of Airy beams by a nonlinear optical process

beams generated by nonlinear three- wave mixing processes in an asymmetrically poled nonlinear photonic3 x,y exp ik3x , the 2D nonlinear wave equation takes the form A2 x,y + k2 2 A2 x,y = - A3A1 *Switching the acceleration direction of Airy beams by a nonlinear optical process Ido Dolev,1

Arie, Ady

80

Nonlinear transmission line based electron beam driver

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

81

Nonlinear analysis of a relativistic beam-plasma cyclotron instability

NASA Technical Reports Server (NTRS)

A self-consistent set of nonlinear and relativistic wave-particle equations are derived for a magnetized beam-plasma system interacting with electromagnetic cyclotron waves. In particular, the high-frequency cyclotron mode interacting with a streaming and gyrating electron beam within a background plasma is considered in some detail. This interaction mode may possibly find application as a high-power source of coherent short-wavelength radiation for laboratory devices. The background plasma, although passive, plays a central role in this mechanism by modifying the dielectric properties in which the magnetized electron beam propagates. For a particular choice of the transverse beam velocity (i.e., the speed of light divided by the relativistic mass factor), the interaction frequency equals the nonrelativistic electron cyclotron frequency times the relativistic mass factor. For this choice of transverse beam velocity the detrimental effects of a longitudinal beam velocity spread is virtually removed. Power conversion efficiencies in excess of 18 percent are both analytically calculated and obtained through numerical simulations of the wave-particle equations. The quality of the electron beam, degree of energy and pitch angle spread, and its effect on the beam-plasma cyclotron instability is studied.

Sprangle, P.; Vlahos, L.

1986-01-01

82

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

83

Development of geometrically-nonlinear finite element analysis for marine risers

the Second Piola-Kirchofi' stress ten- sor B. s: (2. 2) where P, i is the Second Piola-Kirchoff stress tensor evaluated at time t + At with respect to time t, , S, J is the incremental Second Piola-Kirchofi' stress tensor from time t to time t+ Dt, and r... , 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

1987-01-01

84

We analyze the convergence to equilibrium of solutions to the nonlinear Berger plate evolution equation in the presence of localized interior damping (also referred to as geometrically constrained damping). Utilizing the results in (Geredeli et al. in J. Differ. Equ. 254:1193–1229, 2013), we have that any trajectory converges to the set of stationary points N . Employing standard assumptions from the theory of nonlinear unstable dynamics on the set N , we obtain the rate of convergence to an equilibrium. The critical issue in the proof of convergence to equilibria is a unique continuation property (which we prove for the Berger evolution) that provides a gradient structure for the dynamics. We also consider the more involved von Karman evolution, and show that the same results hold assuming a unique continuation property for solutions, which is presently a challenging open problem.

Geredeli, Pelin G., E-mail: pguven@hacettepe.edu.tr [Hacettepe University (Turkey); Webster, Justin T., E-mail: websterj@math.oregonstate.edu [Oregon State University (United States)

2013-12-15

85

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

86

Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods

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

87

NASA Astrophysics Data System (ADS)

A new laser induced breakdown spectroscopy (LIBS) based on single-beam-splitting (SBS) and proper optical geometric configuration has been initially explored in this work for effective signal enhancement. In order to improve the interaction efficiency of laser energy with the ablated material, a laser beam operated in pulse mode was divided into two streams to ablate/excite the target sample in different directions instead of the conventional one beam excitation in single pulse LIBS (SP-LIBS). In spatial configuration, the laser beam geometry plays an important role in the emission signal enhancement. Thus, an adjustable geometric configuration with variable incident angle between the two splitted laser beams was constructed for achieving maximum signal enhancement. With the optimized angles of 60° and 70° for Al and Cu atomic emission lines at 396.15 nm and 324.75 nm respectively, about 5.6- and 4.8-folds signal enhancements were achieved for aluminum alloy and copper alloy samples compared to SP-LIBS. Furthermore, the temporal analysis, in which the intensity of atomic lines in SP-LIBS decayed at least ten times faster than the SBS-LIBS, proved that the energy coupling efficiency of SBS-LIBS was significantly higher than that of SP-LIBS.

Yang, Guang; Lin, Qingyu; Ding, Yu; Tian, Di; Duan, Yixiang

2015-01-01

88

A new laser induced breakdown spectroscopy (LIBS) based on single-beam-splitting (SBS) and proper optical geometric configuration has been initially explored in this work for effective signal enhancement. In order to improve the interaction efficiency of laser energy with the ablated material, a laser beam operated in pulse mode was divided into two streams to ablate/excite the target sample in different directions instead of the conventional one beam excitation in single pulse LIBS (SP-LIBS). In spatial configuration, the laser beam geometry plays an important role in the emission signal enhancement. Thus, an adjustable geometric configuration with variable incident angle between the two splitted laser beams was constructed for achieving maximum signal enhancement. With the optimized angles of 60° and 70° for Al and Cu atomic emission lines at 396.15?nm and 324.75?nm respectively, about 5.6- and 4.8-folds signal enhancements were achieved for aluminum alloy and copper alloy samples compared to SP-LIBS. Furthermore, the temporal analysis, in which the intensity of atomic lines in SP-LIBS decayed at least ten times faster than the SBS-LIBS, proved that the energy coupling efficiency of SBS-LIBS was significantly higher than that of SP-LIBS. PMID:25557721

Yang, Guang; Lin, Qingyu; Ding, Yu; Tian, Di; Duan, Yixiang

2015-01-01

89

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-03-01

90

We develop a geometric optics series expansion approximation to a model of phase-compensated whole-beam thermal blooming of high-power laser beams. The model consists of a nonlinear medium whose thermal blooming coupling coefficient decreases exponentially with the propagation distance from the laser and whose motion relative to the laser beam is taken to be unidirectional, a Gaussian high-power intensity profile at the laser, and a collimated beam boundary condition at an exit plane that is many e-folding scale lengths from the laser. The series expansion parameter is directly proportional to Smith's geometric optics distortion parameter. Expansion formulae are derived for both the intensity and phase at all propagation distances. The exit plane intensity profiles obtained from these formulae qualitatively agree with numerical results obtained from the wave-optics thermal blooming code FOURD, except when the FOURD results indicate that caustics are forming; quantitative agreement is also excellent, except for small differences in fine structure near the downwind edge of the beam. FOURD's return-wave phase-compensation iteration provides an estimate that the rms error in the initial phase obtained from our series approximation truncated at third-order is approximately 0.5% over the range of values we investigated. 3 refs., 2 figs., 1 tab.

Gautesen, A.K.; Morris, J.R.

1988-01-01

91

NASA Technical Reports Server (NTRS)

An analytical study of interlaminar stresses in unsymmetrically laminated plates is presented. The study examines the linear elastic, large deflection response of square laminated composite plates subjected to uniform thermal loading. Both cross-ply and angle-ply, symmetric and unsymmetric, laminates are examined to evaluate the effects of mismatch between adjacent layers in elastic constants and coefficients of thermal expansion. A geometrically nonlinear kinematic description is used to predict the large out-of-plane (transverse) deflections. The nonlinear, three-dimensional boundary value problems are formulated from elasticity theory and approximate solutions are determined using the finite element method. A global/local analysis procedure is used to obtain improved free edge stress predictions. For the laminates and loading conditions considered, the results indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses. These deflections also reduce interlaminar normal stresses in some laminates and increase these stresses for others. The results indicate that as the out-of-plane deflections become large, the differences in interlaminar stress predictions between linear and nonlinear theory can become quite large.

Norwood, D. S.; Shuart, Mark J.; Herakovich, Carl T.

1991-01-01

92

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

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

93

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

. The nonlinear spring connection module and the three dimensional beam module are added to appropriately solve the structural connection problem. The nonlinear spring connection module includes the hydro-pneumatic tensioner module with the friction & stick...

Yang, Chan K.

2010-07-14

94

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

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. PMID:25198790

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

2014-10-01

95

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

96

NASA Astrophysics Data System (ADS)

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.

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

2014-11-01

97

Two new 2+1 dimensional nonlinear evolution equations are presented. The 2+1 dimensional equations closely relate with a hierarchy of 1+1 dimensional soliton equations. Through nonlinearizing of Lax pairs, the 1+1 dimensional evolution equations are decomposed to the finite dimensional integrable Hamiltonian systems. Finally by applying Riemann–Jacobi inversion technique, the algebro-geometric solutions of the 1+1 dimensional soliton equation hierarchy as well

Jinbing Chen

2004-01-01

98

NASA Astrophysics Data System (ADS)

A geometric framework for the automatic extraction of channels and channel networks from high-resolution digital elevation data is introduced in this paper. The proposed approach incorporates nonlinear diffusion for the preprocessing of the data, both to remove noise and to enhance features that are critical to the network extraction. Following this preprocessing, channels are defined as curves of minimal effort, or geodesics, where the effort is measured on the basis of fundamental geomorphological characteristics such as flow accumulation area and isoheight contours curvature. The merits of the proposed methodology, and especially the computational efficiency and accurate localization of the extracted channels, are demonstrated using light detection and ranging (lidar) data of the Skunk Creek, a tributary of the South Fork Eel River basin in northern California.

Passalacqua, Paola; Do Trung, Tien; Foufoula-Georgiou, Efi; Sapiro, Guillermo; Dietrich, William E.

2010-03-01

99

Practical geometric calibration for helical cone-beam industrial computed tomography.

In helical cone-beam industrial computed tomography (ICT), the reconstructed images may be interfered by geometry artifacts due to the presence of mechanical misalignments. To obtain artifact-free reconstruction images, a practical geometric calibration method for helical scan is investigated based on Noo's analytic geometric calibration method for circular scan. The presented method is implemented by first dividing the whole ascending path of helical scan into several pieces, then acquiring the projections of a dedicated calibration phantom in circular scan at each section point, of which geometry parameters are calculated using Noo's analytic method. At last, the geometry parameters of each projection in a piece can be calculated by those of the two end points of the piece. We performed numerical simulations and real data experiments to study the performance of the presented method. The experimental results indicated that the method can obtain high-precision geometry parameters of helical scan and give satisfactory reconstruction images. PMID:24463383

Zhang, Feng; Yan, Bin; Li, Lei; Xi, Xiaoqi; Jiang, Hua

2014-01-01

100

Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.

Lin, Tai-Chia, E-mail: tclin@math.ntu.edu.tw [Institute of Applied Mathematical Sciences and Mathematics Division, National Center for Theoretical Sciences (NCTS) at Taipei, National Taiwan University, Taipei 10617, Taiwan (China)] [Institute of Applied Mathematical Sciences and Mathematics Division, National Center for Theoretical Sciences (NCTS) at Taipei, National Taiwan University, Taipei 10617, Taiwan (China); Beli?, Milivoj R. [Texas A and M University at Qatar, P.O. Box 23874, Doha (Qatar)] [Texas A and M University at Qatar, P.O. Box 23874, Doha (Qatar); Petrovi?, Milan S. [Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia)] [Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia); Chen, Goong [Texas A and M University at Qatar, P.O. Box 23874, Doha (Qatar) [Texas A and M University at Qatar, P.O. Box 23874, Doha (Qatar); Department of Mathematics and Institute for Quantum Science and Engineering, Texas A and M University, College Station, Texas 77843 (United States)

2014-01-15

101

Combination instabilities and non-linear vibratory interactions in beam systems

As an extension of previously reported work on effects of internal resonance on non-linear vibration of beams, it has been shown that for blade-like beams excited parametrically by support motion in the plane of maximum ...

Cartmell, Matthew Phillip

102

Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST) code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton (e-p) two-stream instability observed in

Hong Qin; Ronald C. Davidson; W. Wei-Li Lee

2000-01-01

103

Geometrical non-linearity of the laminated element has not been realized so far in the widely known commercial finite element method packages such as ABAQUS, ALGOR, ANSYS, COSMOS although researches in that field are actively carried out. On the other hand, there is a lot of problems where large displacements and deformations must be dealt with to obtain a precise decision.A

V. Kulini?

2001-01-01

104

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

105

Geometric nonlinear analysis of self-anchored cable-stayed suspension bridges.

Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed. PMID:24282388

Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang

2013-01-01

106

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

107

Geometric Nonlinear Analysis of Self-Anchored Cable-Stayed Suspension Bridges

Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800?m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800?m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed. PMID:24282388

Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang

2013-01-01

108

Numerical results of the nonlinear evolution of longitudinal instabilities of bunched beams are presented. Only a pure-dipole instability is considered which appears for the short-bunch, long-wavelength-of-impedance situation, when the wake-field force is a linear function of the coordinate. An argument is made for a rescaling of multibunch dynamics to a single-bunch case for the case of a narrow-band impedance exciting a single coupled-bunch mode. Saturation effects due to the decoherence caused by tune spread are categorized according to the magnitude and type of impedances. The phenomenon of a nonsaturating instability (beam splitting) is described. A slow decay of instabilities after saturation with randomlike bunch-centroid oscillations ( beam turbulence'') is observed and discussed.

Gerasimov, A. (Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510 (United States))

1994-03-01

109

This paper studies the effect of nonlinear left-hand polarized waves supported by a proton beam on the linear circularly polarized instabilities driven by the same beam. It shows that the nonlinear wave can either stabilize or destabilize the linear instabilities. The effects depend on the amplitude of the nonlinear wave and on the temperature of the system. It also shows that purely electrostatic ion-acoustic-like waves, can be destabilized by the large amplitude wave. The latter instabilities do not occur in the absence of the nonlinear waves.

Gomberoff, L.; Hoyos, J. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santigo (Chile)

2005-09-15

110

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

111

NASA Technical Reports Server (NTRS)

The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.

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

2002-01-01

112

Self-action of Bessel light beams in medium with large nonlinearity

The modifications of an angular spectrum of the intense Bessel J0 and J1 beams caused by self-action in the medium with large cubic nonlinearity are investigated. The appearance of an outer ring of triple radius was observed. The phenomenon can be explained as Bragg diffraction of Bessel beam on Bessel lattice in nonlinear medium. Experimental results are in qualitative agreement

V. Pyragaite; K. Regelskis; V. Smilgevicius; A. Stabinis

2006-01-01

113

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

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

1996-01-01

114

Direct determination of geometric alignment parameters for cone-beam scanners

This paper describes a comprehensive method for determining the geometric alignment parameters for cone-beam scanners (often called calibrating the scanners or performing geometric calibration). The method is applicable to x-ray scanners using area detectors, or to SPECT systems using pinholes or cone-beam converging collimators. Images of an alignment test object (calibration phantom) fixed in the field of view of the scanner are processed to determine the nine geometric parameters for each view. The parameter values are found directly using formulae applied to the projected positions of the test object marker points onto the detector. Each view is treated independently, and no restrictions are made on the position of the cone vertex, or on the position or orientation of the detector. The proposed test object consists of 14 small point-like objects arranged with four points on each of three orthogonal lines, and two points on a diagonal line. This test object is shown to provide unique solutions for all possible scanner geometries, even when partial measurement information is lost by points superimposing in the calibration scan. For the many situations where the cone vertex stays reasonably close to a central plane (for circular, planar, or near-planar trajectories), a simpler version of the test object is appropriate. The simpler object consists of six points, two per orthogonal line, but with some restrictions on the positioning of the test object. This paper focuses on the principles and mathematical justifications for the method. Numerical simulations of the calibration process and reconstructions using estimated parameters are also presented to validate the method and to provide evidence of the robustness of the technique. PMID:19242049

Mennessier, C; Clackdoyle, R; Noo, F

2009-01-01

115

Light beams with general direction and polarization: Global description and geometric phase

We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S{sup 2} of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S{sup 2}×C{sup 2}?(0), the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S{sup 2}×S{sup 2} which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana’s mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP{sup 2}, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S{sup 2}×S{sup 2}. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework. -- Highlights: • We construct a polarization basis for light which is smooth in all directions. • Proof that the manifold of all polarizations and directions is S{sup 2}×S{sup 2}. • Formula for the geometric phase for paths in S{sup 2}×S{sup 2}, generalizing earlier work.

Nityananda, R., E-mail: rajaram@ncra.tifr.res.in [TIFR Centre for Interdisciplinary Sciences, 21, Brundavan colony, Narsingi, Hyderabad 500 089 (India); National Centre for Radio Astrophysics, TIFR, Pune 411 007 (India); Sridhar, S., E-mail: ssridhar@rri.res.in [Raman Research Institute, Sadashivanagar, Bangalore 560 080 (India)

2014-02-15

116

Fast Calculations in Nonlinear Collective Models of Beam/Plasma Physics

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

117

Integrability and chaos in nonlinearly coupled optical beams

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

118

Charged-particle beams are employed for a number of scientific and technological applications. The conventional description of their collective behavior is usually given in terms of the Vlasov equation. In the last 15 years some alternative descriptions have been developed in terms of a nonlinear Schrödinger equation governing the collective dynamics of the beam while interacting with the surrounding medium. This

Renato Fedele; Dusan Jovanovic

2004-01-01

119

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

120

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

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

2001-11-08

121

NASA Astrophysics Data System (ADS)

Product quality is a main concern today in manufacturing; it drives competition between companies. To ensure high quality, a dimensional inspection to verify the geometric properties of a product must be carried out. High-speed non-contact scanners help with this task, by both speeding up acquisition speed and increasing accuracy through a more complete description of the surface. The algorithms for the management of the measurement data play a critical role in ensuring both the measurement accuracy and speed of the device. One of the most fundamental parts of the algorithm is the procedure for fitting the substitute geometry to a cloud of points. This article addresses this challenge. Three relevant geometries are selected as case studies: a non-linear least-squares fitting of a circle, sphere and cylinder. These geometries are chosen in consideration of their common use in practice; for example the sphere is often adopted as a reference artifact for performance verification of a coordinate measuring machine (CMM) and a cylinder is the most relevant geometry for a pin-hole relation as an assembly feature to construct a complete functioning product. In this article, an improvement of the initial point guess for the Levenberg-Marquardt (LM) algorithm by employing a chaos optimization (CO) method is proposed. This causes a performance improvement in the optimization of a non-linear function fitting the three geometries. The results show that, with this combination, a higher quality of fitting results a smaller norm of the residuals can be obtained while preserving the computational cost. Fitting an ‘incomplete-point-cloud’, which is a situation where the point cloud does not cover a complete feature e.g. from half of the total part surface, is also investigated. Finally, a case study of fitting a hemisphere is presented.

Moroni, Giovanni; Syam, Wahyudin P.; Petrò, Stefano

2014-08-01

122

NASA Technical Reports Server (NTRS)

A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.

Hrinda, Glenn A.; Nguyen, Duc T.

2008-01-01

123

NASA Astrophysics Data System (ADS)

Based on the element-free Galerkin (EFG) method, an analysis-independent density variable approach is proposed for topology optimization of geometrically nonlinear structures. This method eliminates the mesh distortion problem often encountered in the finite element analysis of large deformations. The topology optimization problem is formulated on the basis of point-wise description of the material density field. This density field is constructed by a physical meaning-preserving interpolation with the density values of the design variable points, which can be freely positioned independently of the field points used in the displacement analysis. An energy criterion of convergence is used to resolve the well-known convergence difficulty, which would be usually encountered in low density regions, where displacements oscillate severely during the optimization process. Numerical examples are given to demonstrate the effectiveness of the developed approach. It is shown that relatively clear optimal solutions can be achieved, without exhibiting numerical instabilities like the so-called "layering" or "islanding" phenomena even in large deformation cases. This study not only confirms the potential of the EFG method in topology optimization involving large deformations, but also provides a novel topology optimization framework based on element-free discretization of displacement and density fields, which can also easily incorporate other meshless analysis methods for specific purposes.

He, Qizhi; Kang, Zhan; Wang, Yiqiang

2014-09-01

124

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

125

NASA Astrophysics Data System (ADS)

We have demonstrated an original ultrafast laser beam shaping technique for material processing using a spatial light modulator (SLM). Complicated and time-consuming diffraction far-field phase hologram calculations based on Fourier transformations are avoided, while simple and direct geometric masks are used to shape the incident beam at diffraction near-field. Various beam intensity shapes, such as square, triangle, ring and star, are obtained and then reconstructed at the imaging plane of an f-theta lens. The size of the shaped beam is approximately 20 ?m, which is comparable to the beam waist at the focal plane. A polished stainless steel sample is machined by the shaped beam at the imaging plane. The shape of the ablation footprint well matches the beam shape.

Kuang, Zheng; Li, Jiangning; Edwardson, Stuart; Perrie, Walter; Liu, Dun; Dearden, Geoff

2015-07-01

126

In this report we describe an experiment which was conducted at the SPS to observe the combined effects of a single isolated high-order nonlinear resonance, nonlinear detuning, and tune modulation. The nonlinear resonance, as well as the nonlinear detuning, was driven by a nonlinear lens, which had been previously used at the SPS for the study of the beam-beam interactions. The nonlinear motion of a particle in the field of the lens is discussed.

Cornacchia, M.; Evans, L.

1982-10-07

127

NASA Technical Reports Server (NTRS)

Multiple-mode nonlinear analysis is carried out for beams subjected to acoustic excitation. Effects of both nonlinear damping and large-deflection are included in the analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening of the strain response peaks and the increase of modal frequency. An amplitude dependent nonlinear damping model is used in the anlaysis to study the effects and interactions of multiple modes, nonlinear stiffness and nonlinear damping on the random response of beams. Mean square maximum deflection, mean square maximum strain, and spectral density function of maximum strain for simple supported and clamped beams are obtained. It is shown analytically that nonlinear damping contributes significantly to the broadening of the response peak and to the mean square deflection and strain.

Prasad, C. B.; Mei, Chuh

1987-01-01

128

Spatial Distributions Of Acoustic Parameters In Nonlinear Focused Beams Of Various Geometry

NASA Astrophysics Data System (ADS)

In this work, numerical simulations are performed and spatial distributions of specific parameters of nonlinear focused ultrasound beams of various geometry are compared. The numerical algorithm is based on the solution of the Khokhlov-Zabolotskaya (KZ) equation. Focused acoustic beams of periodic waves with an initially uniform amplitude distribution, typical for medical therapeutic transducers, and with Gaussian amplitude shading are considered. Numerical solutions are obtained and analyzed for nonlinear acoustic field in various regimes of linear, quasilinear, and nonlinear propagation when shock fronts are developed in the waveform close to the focus and while propagating to the focus of the beam.

Bessonova, Olga V.; Khokhlova, Vera A.

2008-06-01

129

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

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

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

2011-03-04

130

Collective processes in intense charged particle beams described self-consistently by the Vlasov- Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST) code is used to simulate the non- linear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton (e-p) two-stream instability

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

2000-01-01

131

NON-LINEAR VIBRATIONS OF A BEAM-MASS SYSTEM UNDER DIFFERENT BOUNDARY CONDITIONS

An Euler-Bernoulli beam and a concentrated mass on this beam are considered as a beam-mass system. The beam is supported by immovable end conditions, thus leading to stretching during the vibrations. This stretching produces cubic non-linearities in the equations. Forcing and damping terms are added into the equations. The dimensionless equations are solved for five different set of boundary conditions.

E. Özkaya; M. Pakdemirli; H. R. Öz

1997-01-01

132

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

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 (Xs,Ys,Zs), detector (Xd,Yd,Zd), piercing point (Uo,Vo), and detector rotation angles (?,?,?) 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 (?4 h) and long-term (?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 ?Uo=15.8 mm and ?Vo=9.8 mm (for the piercing point), ?X and ?Y=6–8 mm and ?Z=1 mm (for the source and detector), and ???2.9°, ???1.9°, and ???0.8° (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° 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 (?) between calibration and image acquisition: FWHM=0.62, 0.63, 0.66, 0.71, and 0.72 mm at ?=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 (Uo,Vo) and in-plane positions of the source (Xs,Ys) and detector (Xd,Yd). Errors in the out-of-plane position of the source (Zs) and detector (Zd) and the detector angles (?,?,?) 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.

2008-01-01

133

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

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

134

NASA Astrophysics Data System (ADS)

Generation of ELF/VLF radio waves (300 Hz to 10 kHz) is achievable via modulation of natural currents in the lower ionosphere with high-power HF (2-10 MHz) heating. Recently, Cohen et al. (2008b) put forth an alternative to conventional amplitude HF power modulation, therein referred to as geometric modulation, in which the HF ionospheric heating beam is geometrically steered at the desired ELF/VLF frequency, and found 7-11 dB enhanced amplitudes, and ˜14 dB directional dependence for the thus generated ELF/VLF waves, compared to vertical amplitude modulation. In this paper, we quantitatively compare amplitude modulation, geometric modulation, and a previously proposed technique known as beam painting, wherein the HF beam is rapidly moved over a wide area during the on portion of amplitude modulation in order to create a larger heated region in the ionosphere. We experimentally analyze both the total generation and the directionality, i.e., the suitability of each technique to direct signals along a chosen azimuth. Among the three methods, geometric modulation is found to be uniquely well suited for both goals. We also conduct experiments to investigate two particular physical effects and their role in generation efficacy: that of heat-cool duty cycle and the oblique angle of the HF heating beam. It is found that both duty cycle and the oblique angle of the beam have small but counteracting impacts, consistent with the notion that the primary physical process responsible for generation enhancement in geometric modulation is that of formation of an effective multielement phased array.

Cohen, M. B.; Inan, U. S.; Go?kowski, M.; McCarrick, M. J.

2010-02-01

135

Effect of the interaction of spatial modes on the nonlinear dynamics of sound beams

NASA Astrophysics Data System (ADS)

Propagation of an acoustic beam in a medium with a combined second-and third-order nonlinearity is studied. The derivation of the dynamics equations and the determination of modes is performed using the orthogonal-projection operator technique. The problem on the beam evolution considered with allowance for weak nonlinearity, diffraction, and dissipation leads to a set of equations describing the interaction of directed waves and a quasi-stationary (thermal) mode. In the conditions of a directed beam, the inclusion of the interaction leads to a modified Khokhlov-Zabolotskaya-Kuznetsov equation with quadratic and cubic nonlinearities. The solutions to the problem are obtained in the region near the beam axis, in the form of series expansions in the transverse coordinate up to the focal point. The results of calculations are represented in graphical form for different nonlinearity combinations.

Vereshchagina, I. S.; Perelomova, A. A.

2002-03-01

136

Collective processes in intense charged particle beams for heavy ion fusion are studied using a 3D multispecies nonlinear perturbative particle simulation method, which solves self-consistently the nonlinear Vlasov–Maxwell equations. The newly-developed Beam Equilibrium Stability and Transport code is used to simulate the nonlinear stability properties of intense beam propagation, surface and body eigenmodes in a high-intensity beam, and the electron-ion

Hong Qin; Ronald C. Davidson; W. Wei-li Lee; Roman Kolesnikov

2001-01-01

137

Propagation of four-petal Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

The propagation of four-petal Gaussian beams in strongly nonlocal nonlinear media has been studied. The analytical solution and the analytical second-order moment beam width are obtained. For the off-waist incident and the waist incident cases, the intensity pattern evolves periodically during propagation in strongly nonlocal nonlinear media. Under the off-waist incident condition, the second-order moment beam width varies periodically during propagation, whatever the input power is. But under the waist incident condition, there exists a critical power. When the input power equals the critical power, the second-order moment beam width remains invariant, otherwise the second-order moment beam width varies periodically. Numerical simulations based on the nonlocal nonlinear Schrödinger equation are carried out for comparison with the theoretical predictions. The results show that the numerical simulations are in good agreement with the analytical results in the case of strong nonlocality.

Yang, Zhenjun; Lu, Daquan; Deng, Dongmei; Li, Shaohua; Hu, Wei; Guo, Qi

2010-02-01

138

Nonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor S. Skupin,1

stretching from nonlinear optics to plasmas and ultracold atomic gases [1,2]. The structure and stability 0 and 00 depend on atomic parameters. We assume a two-level atomic model for which the scatteringNonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor S. Skupin,1 M. Saffman,2

Skupin, Stefan

139

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

NASA Astrophysics Data System (ADS)

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

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

2008-07-01

140

Effects of Geometric Azimuthal Asymmetries of the PPM Stack on Electron Beam Characteristics

NASA Technical Reports Server (NTRS)

The effects of geometric azimuthally asymmetric properties of a periodic permanent magnet (PPM) focusing stack on electron beam characteristics obtained using a fully three dimensional (3D) particle-in-cell (PIC) code will be presented. The simulation model, using MAFIA (Solution of MAxwell's equations by the Finite-Integration-Algorithm), incorporates 3D behavior of the beam immersed in static fields calculated directly from the exact geometry and material properties of the 3D magnetic focusing structure. The Hughes 8916H, 18-40 GHz helical TWT for the millimeter-wave power module (MMPM) was used as a prototype. Firstly, the effects of C-magnets used at the input and output of the TWT to allow for coupling of the RF signal into and out of the tube are considered. The 8916H input and output C-magnets differ because coaxial couplers are used at the input and waveguide couplers are used at the output The repositioning of the beam from its central axis due to the inclusion of the output C-magnet was found to be most significant. The modeled output C-magnet and its orientation in the Cartesian coordinate system is shown, and a two-dimensional beam profile including the output C-magnet is also shown. A table presents the shift of the beam center off the central axis relative to the average radius of the beam at the longitudinal points A, B and C designated on an enclosed figure. Secondly, the addition of shunts, or rectangular iron pieces applied manually by a skilled technician in order to improve beam transmission, is considered. The shunts are applied to the top of the tube; thus, azimuthal symmetry of the focusing stack is interrupted. Although shunts are typically added during RF focusing, they are also typically added at the input section of the tube where RF forces are minimal, making an electron optics analysis meaningful. Because several shunts are usually applied to one pole piece, the simulations have been simplified by modeling a half washer with the same radius and longitudinal length as a shunt over the entire x, positive-y half of the transverse plane. A modeled pole piece and shunt as described are shown. Lastly, in order to study the effects of magnet misalignments, a magnet in the PPM stack was arbitrarily chosen and adjusted so that its central axis was shifted both 0.7 percent and 1.0 percent of the magnet outer diameter in the positive-y direction. In practice, positioning the magnets so that their central axis is accurately aligned with the central axis of the tube is challenging. Thus, it is a strong possibility that one or more magnets will be misaligned relative to the tube central axis.

Kory, Carol L.

2000-01-01

141

The objective of this paper is to apply He's homotopy perturbation method (HPM) to analyze nonlinear free vibration of simply supported Timoshenko beams considering the effects of rotary inertia and shear deformation. First, the equation governing the nonlinear free vibration of a Timoshinko beam is nondimensionalized. Galerkin's projection method is utilized to reduce the governing nonlinear partial differential equation to

Mahdi Mojahedi; Hamid Moeenfard; Mohammad Taghi Ahmadian

2011-01-01

142

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

Nonlinear charge and current neutralization of an ion beam pulse in a pre-formed plasma Igor D pulse by the background plasma. The electric and magnetic fields generated by the ion beam are studied. Kaganovich,a) Gennady Shvets, Edward Startsev, and Ronald C. Davidson Plasma Physics Laboratory, Princeton

Kaganovich, Igor

143

For the high intensity accelerators and beam transport systems of practical interest for heavy ion fusion and high energy and nuclear physics applications, it is increasingly important to develop an improved theoretical understanding of the influence of the intense self fields produced by the beam space charge and current. For this purpose, a three-dimensional multispecies nonlinear perturbative particle simulation method

Hong Qin; Ronald C. Davidson; W. Wei-Li Lee; Roman Kolesnikov

2000-01-01

144

Non-linear processes in the gas cluster ion beam modification of solid surfaces

The unique characteristics of gas cluster ion beam processing are reviewed. Cluster ion beams consisting of hundreds to thousands of atoms have been generated from various kinds of gas materials. Multiple collisions during the impact of accelerated cluster ions upon the substrate surfaces produce fundamentally non-linear bombarding processes. These bombarding characteristics can be applied to shallow ion implantation, high yield

I Yamada; J Matsuo; N Toyoda; T Aoki; E Jones; Z Insepov

1998-01-01

145

NASA Astrophysics Data System (ADS)

Poly bis(glycine)cadmium chloride (BGCC) crystals of both undoped and doped with thiourea (Tu) were grown from saturated solutions by a slow evaporation technique. The geometrical isomerism of the octahedral BGCC molecule is investigated using single crystal XRD, powder XRD and FT-IR. The significant difference between the two isomers namely facial ( fac) and meridional ( mer), is explained in terms of the different point group symmetries of C3 and C1, respectively. The loss of point group symmetry from C3 to C1 is attributed for the observed powder second-harmonic generation (SHG). Semi-empirical calculations from the optimized geometrical parameters also supported non-linear optical properties of the material.

Raju, B.; Saritha, A.; Jotani, Mukesh M.; Prasad, P. S. R.; Hussain, K. A.

2012-01-01

146

A Solving Module of an Expert System for Nonlinear Beam Dynamics

NASA Astrophysics Data System (ADS)

This paper presents a methodological essay on building expert systems based on mathematical modelling of particle beams nonlinear behavior. This type of expert systems can be very useful because there are very many problems appeared in accelerator physics. Two basic sets of problems are pointed out. The first set is connected with the nature of objects under study - particle beam and control systems for beam forming and transportation (beam lines). The second set has mathematical nature. In this paper we describe basic concepts which are took as a base of an expert system for an investigation of nonlinear behavior of particle beams. Modelling process for beam line design is based on the matrix formalism for Lie algebraic tools and computer algebra methods. This allows to use object-oriented approach for describing both physical and mathematical objects.

Andrianov, Serge; Dvoeglazov, Andrew

1997-05-01

147

Self-reconstruction of Bessel beam in Kerr nonlinear medium

There has been much interest in the applications of Bessel beams due to their strongly peaked pump intensity distribution over relatively long distance in the media. An observation of self-reconstruction (SR) of an intense Bessel beam in different liquids was reported. Truncated in azimuth Bessel beam was reconstructed when its power reached a threshold value. The SR was preceded by

R. Butkus; R. Gadonas; J. Janusshkonis; A. Piskarskas; K. Regelskis; V. Smilgevicius; A. Stabinis

2002-01-01

148

Collective instabilities in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The electron-proton (e-p) two-stream instability is observed in the simulations carried out with the newly-developed Beam Equilibrium Stability and Transport (BEST) code. This code provides an effective numerical tool to investigate collective instabilities, periodically-focused beam propagation

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

1999-01-01

149

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

150

NASA Astrophysics Data System (ADS)

In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1–S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1–S2 and S2–S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo–Hooke and Mooney–Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.

Rauter, N.; Lammering, R.

2015-04-01

151

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

152

Nonlinear beam-based vibration energy harvesters and load cells

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

153

In this paper, a modified Jeffcott model is proposed and studied in order to shed light into the dynamics of a complex system, the Short Electrodynamic Tether (SET), which is similar to an unbalanced rotor. Due to the internal damping, a geometrically linear SET model appears to be unstable as predicted by the linear rotordynamics theory. Some studies in the

J. Valverde; J. L. Escalona; E. Freire; J. Domínguez

2005-01-01

154

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

155

Beam-shape effects in nonlinear Compton and Thomson scattering

We discuss intensity effects in collisions between beams of optical photons from a high-power laser and relativistic electrons. Our main focus is on the modifications of the emission spectra due to realistic finite-beam geometries. By carefully analyzing the classical limit we precisely quantify the distinction between strong-field QED Compton scattering and classical Thomson scattering. A purely classical, but fully covariant,

T. Heinzl; D. Seipt; B. Kämpfer

2010-01-01

156

BEAM-BASED NON-LINEAR OPTICS CORRECTIONS IN COLLIDERS.

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

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

2005-05-16

157

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

NASA Astrophysics Data System (ADS)

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

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

2012-10-01

158

A wide range of collective effects in high intensity charged particle beams have been numerically studied using the nonlinear delta-f particle simulation method implemented in the Beam Equilibrium Stability and Transport (BEST) code. For the electron-ion two-stream instability in high intensity accelerators and storage rings, the secondary electron yield effects are self-consistently studied by coupling the secondary electron yield library

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

2004-01-01

159

Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium

It is revealed that orbital angular momentum can be conserved within the spontaneous parametric down-conversion of higher-order Bessel beam. That is the result of strong transverse selection of spontaneously arising optical fields in optical parametric generator pumped by Bessel beam due to transverse phase-matching of interacting waves in nonlinear medium. A qualitative agreement of theoretical predictions with experimental results is

V. Pyragaite; A. Piskarskas; K. Regelskis; V. Smilgevicius; A. Stabinis; S. Mikalauskas

2004-01-01

160

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

161

NASA Astrophysics Data System (ADS)

We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.

Ella, Lior; Yuvaraj, D.; Suchoi, Oren; Shtempluk, Oleg; Buks, Eyal

2015-01-01

162

Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection

Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on von Kármán's plate

Shi-Rong Li; Jing-Hua Zhang; Yong-Gang Zhao

2007-01-01

163

Precise quantification of femur strength and accurate assessment of hip fracture risk would help physicians to identify individuals with high risk and encourage them to take preventive interventions. A major contributing factor of hip fracture is the reduction of hip strength, determined by the bone quality. Bone mineral density (BMD) alone cannot determine bone strength accurately. In this paper, subject-specific quantitative computer tomography (QCT) image-based finite element analyses were conducted to identify the quantitative relationships between femoral strength and BMD, material distribution and geometric morphology. Sixty-six subjects with QCT data of hip region were selected from the MrOS cohorts in Hong Kong. Subject-specific nonlinear finite element models were developed to predict strengths of proximal femurs. The models took non-linear elasto-plasticity and heterogeneity of bone tissues into consideration and derived bone strengths with proper bone failure criteria. From finite element analysis (FEA), relationships between femoral strength and BMD, material distribution, and geometric parameters were determined. Results showed that FEA-predicted femoral strength was highly correlated with BMD, material distribution, height, weight, diameters of femoral head (HD), and femoral neck (ND), as well as the moment arm for femoral neck bending-offset (OFF). Through principal components analysis, three independent principal components (PCs) were extracted. PC1 was the component of bone material quality. PC2 included height, weight, HD, and ND. PC3 mainly represented OFF. Multivariate linear regression showed that the PCs were strongly predictive of the FEA-predicted strength. This study provided quantitative information regarding the contributing factors of proximal femur strength and showed that such a biomechanical approach may have clinical potential in noninvasive assessment of hip fracture risk. PMID:22258889

Gong, He; Zhang, Ming; Fan, Yubo; Kwok, Wai Leung; Leung, Ping Chung

2012-07-01

164

Beam loading in the nonlinear regime of plasma-based acceleration.

A theory that describes how to load negative charge into a nonlinear, three-dimensional plasma wakefield is presented. In this regime, a laser or an electron beam blows out the plasma electrons and creates a nearly spherical ion channel, which is modified by the presence of the beam load. Analytical solutions for the fields and the shape of the ion channel are derived. It is shown that very high beam-loading efficiency can be achieved, while the energy spread of the bunch is conserved. The theoretical results are verified with the particle-in-cell code OSIRIS. PMID:18851537

Tzoufras, M; Lu, W; Tsung, F S; Huang, C; Mori, W B; Katsouleas, T; Vieira, J; Fonseca, R A; Silva, L O

2008-10-01

165

Nonlinear plasma waves excitation by intense ion beams in background plasma

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

166

The nonlinear interaction of two-crossed focussed ultrasonic beams in the presence of turbulence

This paper examines the scattering of a nonlinearly generated sum frequency acoustic wave component from a region of turbulence defined by the overlap volume of two mutually perpendicular crossed focussed ultrasonic beams. The scattered sum frequency pressure amplitude is measured at different radial scan positions across the jet flow stream providing conclusions that explain some qualitative results governing the sum

Stephen C. Rife

1988-01-01

167

1 Reshaping the trajectory and spectrum 2 of nonlinear Airy beams

1 Reshaping the trajectory and spectrum 2 of nonlinear Airy beams 3 Yi Hu,1,2, * Zhe Sun,2 Domenico Bongiovanni,1 Daohong Song,2 Cibo Lou,2 Jingjun Xu,2 4 Zhigang Chen,2,3 and Roberto Morandotti1 5 1 Université

Chen, Zhigang

168

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.

Michael Spata

2012-08-01

169

On simple and accurate finite element models for nonlinear bending analysis of beams and plates

. . . . . . . . . . . . . . . . . . . . . . . . . 58 V.2. Linear bending analysis . . . . . . . . . . . . . . . . . . 61 V.3. Nonlinear bending analysis . . . . . . . . . . . . . . . . 77 VI SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS : 94 VI.1. Summary and conclusions... moment resultants) when compared to classical plate elements (three displacements, two rotations and three moment resultants). A similar formulation for laminated beams based on a high- order shear deformation theory was proposed by Singh et. al [77...

Urthaler Lapeira, Yetzirah Yksya

2007-09-17

170

Mechanisms for saturation of nonlinear pulsed and periodic signals in focused acoustic beams

NASA Astrophysics Data System (ADS)

Acoustic fields of powerful ultrasound sources with Gaussian spatial apodization and initial excitation in the form of a periodic wave or single pulse are examined based on the numerical solution of the Khokhlov-Zabolotskaya-Kuznetsov equation. The influence of nonlinear effects on the spatial structure of focused beams, as well as on the limiting values of the acoustic field parameters is compared. It is demonstrated that pressure saturation in periodic fields is mainly due to the effect of nonlinear absorption at a shock front, while in pulsed fields is due to the effect of nonlinear refraction. The limiting attainable values for the peak positive pressure in periodic fields turned out to be higher than the analogous values in pulsed acoustic fields. The total energy in a beam of periodic waves decreases with the distance from the source faster than in the case of a pulsed field, but it becomes concentrated within much smaller spatial region in the vicinity of the focus. These special features of nonlinear effect manifestation provide an opportunity to use pulsed beams for more efficient delivery of wave energy to the focus and to use periodic beams for attaining higher values of pressure in the focal region.

Karzova, M. M.; Averiyanov, M. V.; Sapozhnikov, O. A.; Khokhlova, V. A.

2012-01-01

171

Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams

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

172

Mimicking the cochlear amplifier in a cantilever beam using nonlinear velocity feedback control

NASA Astrophysics Data System (ADS)

The mammalian cochlea exhibits a nonlinear amplification which allows mammals to detect a large range of sound pressure levels while maintaining high frequency sensitivity. This work seeks to mimic the cochlea’s nonlinear amplification in a mechanical system. A nonlinear, velocity-based feedback control law is applied to a cantilever beam with piezoelectric actuators. The control law reduces the linear viscous damping of the system while introducing a cubic damping term. The result is a system which is positioned close to a Hopf bifurcation. Modelling and experimental results show that the beam with this control law undergoes a one-third amplitude scaling near the resonance frequency and an amplitude-dependent bandwidth. Both behaviors are characteristic of data obtained from the mammalian cochlea. This work could provide insight on the biological cochlea while producing bio-inspired sensors with a large dynamic range and sharp frequency sensitivity.

Joyce, Bryan S.; Tarazaga, Pablo A.

2014-07-01

173

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method,

S. Kitipornchai; J. Yang; K. M. Liew

2004-01-01

174

NASA Technical Reports Server (NTRS)

The use of stress predictions from equivalent linearization analyses in the computation of high-cycle fatigue life is examined. Stresses so obtained differ in behavior from the fully nonlinear analysis in both spectral shape and amplitude. Consequently, fatigue life predictions made using this data will be affected. Comparisons of fatigue life predictions based upon the stress response obtained from equivalent linear and numerical simulation analyses are made to determine the range over which the equivalent linear analysis is applicable.

Rizzi, Stephen A.

2003-01-01

175

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

176

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

177

Nonlinear Interaction of a Powerful Oblique Wave Beam with the Ionosphere Layer F2.

NASA Astrophysics Data System (ADS)

The presentation is devoted to modeling oblique sounding of the ionosphere layer F2 by powerful wave beams. Part of its energy propagates trough the ionospheric layer, the other part goes back along a downward trajectory. However, nonlinearity leads to further stratification of the ionospheric layer. A new feature, in comparison with the linear case, is appearing a narrow waveguide beneath the F2 layer maximum which traps a small part of the beam energy. • We study the relationship between these parts of the wave field in a simplified model of parabolic F2 layer, with nonlinearity caused by thermal plasma expulsion from the high field intensity region. • We model and analyze of the interaction of a powerful obliquely incident wave beam of decameter radio waves with the ionospheric layer F2. Oblique propagation of a powerful HF wave beam in the ionospheric F2 layer leads to additional plasma stratification, in particular to the formation of an artificial waveguide controlled by the beam intensity. We show that formation of the artificial waveguide is a nonlinear effect. The problem of efficient feeding the artificial waveguide depends on the ability to create in the F2 layer high values of the HF electric field compared with the characteristic "plasma fields". Analytical results are supplemented with numerical estimates of the effects. The proposed investigation can be used in Space Weather Services.

Atamaniuk, Barbara; Rothkaehl, Hanna; Anatolevich Molotkov, Ivan; Popov, Alexei

2013-04-01

178

White-Noise and Geometrical Optics Limits of Wigner-Moyal Equation for Wave Beams in Turbulent Media

Starting with the Wigner distribution formulation for beam wave propagation in H\\"{o}lder continuous non-Gaussian random refractive index fields we show that the wave beam regime naturally leads to the white-noise scaling limit and converges to a Gaussian white-noise model which is characterized by the martingale problem associated to a stochastic differential-integral equation of the It\\^o type. In the simultaneous geometrical optics the convergence to the Gaussian white-noise model for the Liouville equation is also established if the ultraviolet cutoff or the Fresnel number vanishes sufficiently slowly. The advantage of the Gaussian white-noise model is that its $n$-point correlation functions are governed by closed form equations.

Albert C. Fannjiang

2004-03-05

179

Numerical methods for axisymmetric and 3D nonlinear beams

NASA Astrophysics Data System (ADS)

Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.

Pinton, Gianmarco F.; Trahey, Gregg E.

2005-04-01

180

NASA Astrophysics Data System (ADS)

This investigation deals with the free vibration characteristics of circular higher-order shear deformable nanoplates around the postbuckling configuration incorporating surface effects. Using the Gurtin-Murdoch elasticity theory, a size-dependent higher-order shear deformable plate model is developed which takes account all surface effects including surface elasticity, surface stress and surface density. Geometrical nonlinearity is considered based on the von Karman type nonlinear strain-displacement relationships. Also, in order to satisfy the balance conditions between bulk and surfaces of nanoplate, it is assumed that the normal stress is distributed cubically through the thickness of nanoplate. Hamilton's principle is utilized to derive non-classical governing differential equations of motion and related boundary conditions. Afterwards, an efficient numerical methodology based on a generalized differential quadrature (GDQ) method is employed to solve numerically the problem so as to discretize the governing partial differential equations along various edge supports using Chebyshev-Gauss-Lobatto grid points and pseudo arc-length continuation technique. A comparison between the results of present non-classical model and those of the classical plate theory is conducted. It is demonstrated that in contrast to the prebuckling domain, for a specified value of axial load in the postbuckling domain, increasing the plate thickness leads to higher frequencies.

Sahmani, S.; Bahrami, M.; Ansari, R.

2014-12-01

181

Propagation dynamics of modified hollow Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

We investigate here a new class of optical beams: modified hollow Gaussian beams (MHGBs) in strongly nonlocal nonlinear media (SNNM). A set of analytical expressions for the propagation properties is deduced and some numerical simulations are also carried out to illustrate the propagation properties. It is found that the evolution of the MHGBs in SNNM is periodical, which is the result of the competition between nonlinearity and diffraction. The second-order moment beam width of the MHGBs can keep invariant during propagation like a soliton when the input power equals the critical power, otherwise it varies periodically like a breather. However, the patterns of transverse intensity are always changing with the propagation distance increasing, which is different from solitons or breathers. It is also found that the evolution curve of on-axis intensity may manifest itself in a concave, a platform, or a Gaussian-like shape depending on the input power.

Dai, Zhiping; Yang, Zhenjun; Zhang, Shumin; Pang, Zhaoguang; You, Kaiming

2015-02-01

182

influences the sensitivity of load increments. Figures 10 and 11 show that, for lower I/A ratios, the load increments should be reduced. 3. From Figures 10 through 13, it may be observed that the present formulation yields displacement responses which... are stiffer than those given by the Total Lagrangian formulation in the region of moderate rotations. However, full scale testing is recommended to determine which formulation yields results closer to the "true" solution. 4. The cantilevered beam and bent...

Cheung, Shing Tak

1974-01-01

183

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

184

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

NASA Astrophysics Data System (ADS)

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

Zhang, Likun; Marston, Philip L.

2011-09-01

185

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

Lee, S. Y.

2014-04-07

186

Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionisation

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

Vlasov, R A [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus); Khasanov, O Kh; Smirnova, T V [Institute of Solid-State and Semiconductor Physics, National Academy of Sciences of Belarus, Minsk (Belarus)

2005-10-31

187

NASA Astrophysics Data System (ADS)

Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.

Egorov, E. N.; Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E.

2013-11-01

188

Multiple beam two-plasmon decay: linear threshold to nonlinear saturation in three dimensions.

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. PMID:25238364

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

2014-09-01

189

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

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

190

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

191

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

We study the cyclotron maser instability (CMI) driven by an energetic ring-beam distribution by a particle simulation to explain possible generation mechanisms of intense radiation phenomena observed in space. The main objective is to understand the nonlinear processes that control saturation of the emission process. Our study reveals new issues that have been overlooked in past literature. It is found that electrostatic wave modes excited by the electron beam instability compete with the electromagnetic waves excited by the CMI. Nonlinear effects of these electrostatic modes tend to redistribute the energy of the energetic electrons and make the physics more complicated. The CMI can be much less effective in a realistic case than it is anticipated theoretically.

Lee, K. H.; Lee, L. C.; Wu, C. S. [Institute of Space Science, National Central University, Taoyuan, Taiwan (China); Omura, Y. [Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto (Japan)

2009-09-04

192

Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. Besides a detailed understanding of the driving forces and mode structures of the collective processes, the fully kinetic description and simulations also provide a theoretical framework to investigate important kinetic effects due to wave-particle interactions. The

Hong Qin; Ronald C. Davidson

2000-01-01

193

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

194

Slender sharp-edged flexible beams such as flapping wings of micro air vehicles (MAVs), piezoelectric fans and insect wings typically oscillate at moderate-to-high values of non-dimensional frequency parameter beta with amplitude as large as their widths resulting in Keulegan-Carpenter (KC) numbers or order one. Their oscillations give rise to aerodynamic damping forces which vary nonlinearly with the oscillation amplitude and frequency;

Rahul A. Bidkar; Mark Kimber; Arvind Raman; Anil K. Bajaj; Suresh V. Garimella

2009-01-01

195

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

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

196

Stimulated Raman Scattering and Nonlinear Focusing of High-Power Laser Beams Propagating in Water

The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. While discussed here in the context of propagation in water, the gain-focusing phenomenon is general to any medium supporting nonlinear focusing and stimulated forward Raman scattering.

Hafizi, B; Penano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D

2015-01-01

197

Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water.

The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown, and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. The phenomenon of gain-focusing discussed here for propagation in water is expected to be of general occurrence applicable to any medium supporting nonlinear focusing and stimulated Raman scattering. PMID:25831383

Hafizi, B; Palastro, J P; Peñano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D

2015-04-01

198

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

199

Generation of nonlinear Alfvén and magnetosonic waves by beam-plasma interaction

NASA Astrophysics Data System (ADS)

One-dimensional (1-D) and two-dimensional (2-D) hybrid simulations are carried out to study the interaction between a background plasma and an ion beam, whose velocity is parallel to the ambient magnetic field B0. It is found that the beam-plasma interaction and the associated wave evolution can be divided into four phases. The simulation results in phase 1 in the early stage of wave evolution are consistent with the linear theory. Right-hand nonresonant instabilities are present and dominant in cases with a relatively strong ion beam (e.g., the ratio of beam ion density to background ion density >0.06 for beam velocity =10VA, where VA is the Alfvén speed), while right-hand resonant instabilities are present in the weak beam cases. During phases 2 and 3, the waves grow to form nonlinear structure, and are then saturated. A detailed analysis shows that the wave evolution in these phases is through secondary instabilities associated with parametric decay or the wave modulation. In addition, it is shown for the first time from the self-consistent simulation that in the final phase, nonlinear shear Alfvén waves with right-hand polarization in the magnetic field are generated. The magnetohydrodynamic (MHD) wave conditions of the Alfvén mode are satisfied. These Alfvén waves propagate mainly with k?B0>0, and the dispersion relation ?=kVA cos ? is satisfied, where ? is the angle between the wave vector k and B0. On the other hand, fast magnetosonic/whistler waves and slow mode waves are formed in the final phase of weak beam cases. In the 2-D simulations, field-aligned filaments (with k˜k?) in the density and magnetic field can be present due to the 2-D effects, in addition to the Alfvén, fast, and slow modes. The heating rate of background ions and its dependence on the wave propagation direction are also examined.

Wang, X. Y.; Lin, Y.

2003-09-01

200

Purpose: Misregistration artifact is the major cause of image degradation in digital subtraction angiography (DSA). The purpose of this study was to evaluate the efficacy of a newly developed nonlinear geometric warping method to reduce misregistration artifact in DSA. Methods: The processing of the images was carried out on a workstation with a fully automatic computerized program. After making differential images with a lapracian filter, 49 regions of interest (ROIs) were set in the image to be processed. Each ROI of the live image scanned the corresponding ROI of the mask image searching for the best position to match itself. Each pixel of the mask image was shifted individually following the data calculated from the shifts of the ROIs. Five radiologists compared the images produced by the conventional parallel shift technique and those processed with this new method in 16 series of cerebral DSA. Results: In 14 of 16 series (88%), more radiologists judged the images processed with the new method to be better in quality. Small arteries near the skull base and veins of low density were clearly visualized in the images processed by the new method. Conclusion: This newly proposed method could be a simple and practical way to automatically reduce misregistration artifacts in DSA.

Hayashi, Nobushige; Sakai, Toyohiko; Kitagawa, Manabu; Inagaki, Rika; Sadato, Norihiro; Ishii, Yasushi; Nishimoto, Yasuhiro; Tanaka, Masato; Fukushima, Tetsuya; Komuro, Hiroyuki [Department of Radiology, Fukui Medical School, 23 Shimoaizuki, Matsuoka-cho, Yoshida-gun, Fukui 910-11 (Japan); Ogura, Hisakazu [Department of Information Science, University of Fukui, 3-9-1 Bunkyou, Fukui 910 (Japan); Kobayashi, Hidenori; Kubota, Toshihiko [Department of Neurosurgery, Fukui Medical School, 23 Shimoaizuki, Matsuoka-cho, Yoshida-gun, Fukui 910-11 (Japan)

1998-03-15

201

Ultrahigh Brilliance Multi-MeV ? -Ray Beams from Nonlinear Relativistic Thomson Scattering

NASA Astrophysics Data System (ADS)

We report on the generation of a narrow divergence (??<2.5 mrad ), multi-MeV (Emax?18 MeV ) and ultrahigh peak brilliance (>1.8 ×1020 photons s-1 mm-2 mrad-2 0.1% BW) ? -ray beam from the scattering of an ultrarelativistic laser-wakefield accelerated electron beam in the field of a relativistically intense laser (dimensionless amplitude a0?2 ). The spectrum of the generated ? -ray beam is measured, with MeV resolution, seamlessly from 6 to 18 MeV, giving clear evidence of the onset of nonlinear relativistic Thomson scattering. To the best of our knowledge, this photon source has the highest peak brilliance in the multi-MeV regime ever reported in the literature.

Sarri, G.; Corvan, D. J.; Schumaker, W.; Cole, J. M.; Di Piazza, A.; Ahmed, H.; Harvey, C.; Keitel, C. H.; Krushelnick, K.; Mangles, S. P. D.; Najmudin, Z.; Symes, D.; Thomas, A. G. R.; Yeung, M.; Zhao, Z.; Zepf, M.

2014-11-01

202

NASA Astrophysics Data System (ADS)

In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji's method (AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method (Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration ( A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure. Therefore, AGM can be considered as a significant progress in nonlinear sciences.

Akbari, M. R.; Ganji, D. D.; Rostami, A. K.; Nimafar, M.

2015-03-01

203

NASA Astrophysics Data System (ADS)

In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji's method (AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method (Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration (A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure. Therefore, AGM can be considered as a significant progress in nonlinear sciences.

Akbari, M. R.; Ganji, D. D.; Rostami, A. K.; Nimafar, M.

2015-01-01

204

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

Ernesto Grande; Maura Imbimbo; Elio Sacco

2011-01-01

205

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

206

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

207

We investigated second order optical nonlinearity of zinc oxide thin films, grown on glass substrates by the dual ion beam sputtering technique under different deposition conditions. Linear optical characterization of the films was carried out by spectrophotometric optical transmittance and reflectance measurements, giving the complex refractive index dispersion. Resistivity of the films was determined using the four-point probe sheet resistance method. Second harmonic generation measurements were performed by means of the Maker fringes technique where the fundamental beam was originated by nanosecond laser at {lambda}=1064 nm. We found a relatively high nonlinear optical response, and evidence of a dependence of the nonlinear coefficient on the deposition parameters for each sample. Moreover, the crystalline properties of the films were investigated by x-ray diffraction measurements and correlation with second order nonlinearity were analyzed. Finally, we investigated the influence of the oxygen flow rate during the deposition process on both the second order nonlinearity and the structural properties of the samples.

Larciprete, M.C.; Passeri, D.; Michelotti, F.; Paoloni, S.; Sibilia, C.; Bertolotti, M.; Belardini, A.; Sarto, F.; Somma, F.; Lo Mastro, S. [INFM at Dipartimento di Energetica, Universita di Roma 'La Sapienza', Via A.Scarpa 16 00161 Rome (Italy); INFM at Dipartimento di Energetica, Universita di Roma 'La Sapienza', Via A.Scarpa 16 00161 Rome (Italy); Department of Physics and UdR INFM, University of Roma Tre, Via della Vasca Navale 84, 00146 Rome (Italy); ENEA, Division of Advanced Physics Technologies, Via Anguillarese, 301-00060 Rome (Italy); Department of Physics and UdR INFM, University of Roma Tre, Via della Vasca Navale 84, 00146 Rome (Italy); Department of Geology, University of Roma Tre, Largo S.L. Murialdo 1, 00146 Rome (Italy)

2005-01-15

208

Nonlinear dynamics of an intense circularly polarized laser beam interacting with a hot magnetized plasma is investigated. Using a relativistic fluid model, a modified nonlinear Schrödinger equation is derived based on a quasineutral approximation, which is valid for hot plasma. Using a three-dimensional model, spatial-temporal development of the laser pulse is investigated. The occurrence of some nonlinear phenomena such as self-focusing, self-modulation, light trapping, and filamentation of the laser pulse is discussed. Also the effect of polarization and external magnetic field on the nonlinear evolution of these phenomena is studied. PMID:24229288

Sepehri Javan, N; Adli, F

2013-10-01

209

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

NASA Technical Reports Server (NTRS)

This paper presents an approach for the approximate input-output linearization of nonlinear systems, particularly those for which relative degree is not well defined. It is shown that there is a great deal of freedom in the selection of an approximation and that, by designing a tracking controller based on the approximating system, tracking of reasonable trajectories can be achieved with small error. The approximating system is itself a nonlinear system, with the difference that it is input-output linearizable by state feedback. Some properties of the accuracy of the approximation are demonstrated and, in the context of the ball and beam example, it is shown to be far superior to the Jacobian approximation. The results are focused on finding regular SISO systems which are close to systems which are not regular and controlling these approximate regular systems.

Hauser, John; Sastry, Shankar; Kokotovic, Petar

1989-01-01

210

Derivation of nonlinear wave equations for ultrasound beam in nonuniform bubbly liquids

NASA Astrophysics Data System (ADS)

Weakly nonlinear propagation of diffracted ultrasound beams in a nonuniform bubbly liquid is theoretically studied based on the method of multiple scales with the set of scaling relations of some physical parameters. It is assumed that the spatial distribution of the number density of bubbles in an initial state at rest is a slowly varying function of space coordinates and the amplitude of its variation is small compared with a mean number density. As a result, a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with dispersion and nonuniform effects for a low frequency case and a nonlinear Schrödinger (NLS) equation with dissipation, diffraction, and nonuniform effects for a high frequency case, are derived from the basic equations of bubbly flows.

Kanagawa, Tetsuya; Yano, Takeru; Kawahara, Junya; Kobayashi, Kazumichi; Watanabe, Masao; Fujikawa, Shigeo

2012-09-01

211

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

212

Calibration of a Non-Linear Beam Position Monitor Electronics by Switching Electrode Signals

Button electrode signals from beam position monitors embedded into new LHC collimators will be individually processed with front-end electronics based on compensated diode detectors and digitized with 24-bit audio-range ADCs. This scheme allows sub-micrometre beam orbit resolution to be achieved with simple hardware and no external timing. As the diode detectors only operate in a linear regime with large amplitude signals, offset errors of the electronics cannot be calibrated in the classical way with no input. This paper describes the algorithms developed to calibrate the offset and gain asymmetry of these nonlinear electronic channels. Presented algorithm application examples are based on measurements performed with prototype diode orbit systems installed on the CERN SPS and LHC machines.

Gasior, M

2013-01-01

213

Nonlinear Interaction of the Beat-Photon Beams with the Brain Neurocenters: Laser Neurophysics

NASA Astrophysics Data System (ADS)

I propose a novel mechanism for laser-brain interaction: Nonlinear interaction of ultrashort pulses of beat-photon, (?1-- ?2), or double-photon, (?1+?2), footnotetextMaria Goeppert-Mayer, "Uber Elementarakte mit zwei Quantenspr"ungen, Ann Phys 9, 273, 95. (1931). beams with the corrupted brain neurocenters, causing a particular neurological disease. The open-scull cerebral tissue can be irradiated with the beat-photon pulses in the range of several 100s fs, with the laser irradiances in the range of a few mW/cm^2, repetition rate of a few 100s Hz, and in the frequency range of 700-1300nm generated in the beat-wave driven free electron laser.footnotetextV. Alexander Stefan, The Interaction of Photon Beams with the DNA Molecules: Genomic Medical Physics. American Physical Society, 2009 APS March Meeting, March 16-20, 2009, abstract #K1.276; V. Stefan, B. I. Cohen, and C. Joshi, Nonlinear Mixing of Electromagnetic Waves in Plasmas Science 27 January 1989:Vol. 243. no. 4890, pp. 494 -- 500 (January 1989). This method may prove to be an effective mechanism in the treatment of neurological diseases: Parkinson's, Lou Gehrig's, and others.

Stefan, V. Alexander

2010-03-01

214

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

215

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

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

216

Hydrophone area-averaging correction factors in nonlinearly generated ultrasonic beams

NASA Astrophysics Data System (ADS)

The nonlinear propagation of an ultrasonic wave can be used to produce a wavefield rich in higher frequency components that is ideally suited to the calibration, or inter-calibration, of hydrophones. These techniques usually use a tone-burst signal, limiting the measurements to harmonics of the fundamental calibration frequency. Alternatively, using a short pulse enables calibration at a continuous spectrum of frequencies. Such a technique is used at PTB in conjunction with an optical measurement technique to calibrate devices. Experimental findings indicate that the area-averaging correction factor for a hydrophone in such a field demonstrates a complex behaviour, most notably varying periodically between frequencies that are harmonics of the centre frequency of the original pulse and frequencies that lie midway between these harmonics. The beam characteristics of such nonlinearly generated fields have been investigated using a finite difference solution to the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a focused field. The simulation results are used to calculate the hydrophone area-averaging correction factors for 0.2 mm and 0.5 mm devices. The results clearly demonstrate a number of significant features observed in the experimental investigations, including the variation with frequency, drive level and hydrophone element size. An explanation for these effects is also proposed.

Cooling, M. P.; Humphrey, V. F.; Wilkens, V.

2011-02-01

217

NASA Astrophysics Data System (ADS)

A time-domain numerical code (the so-called Texas code) that solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation has been extended from an axis-symmetric coordinate system to a three-dimensional (3D) Cartesian coordinate system. The code accounts for diffraction (in the parabolic approximation), nonlinearity and absorption and dispersion associated with thermoviscous and relaxation processes. The 3D time domain code was shown to be in agreement with benchmark solutions for circular and rectangular sources, focused and unfocused beams, and linear and nonlinear propagation. The 3D code was used to model the nonlinear propagation of diagnostic ultrasound pulses through tissue. The prediction of the second-harmonic field was sensitive to the choice of frequency-dependent absorption: a frequency squared f2 dependence produced a second-harmonic field which peaked closer to the transducer and had a lower amplitude than that computed for an f1.1 dependence. In comparing spatial maps of the harmonics we found that the second harmonic had dramatically reduced amplitude in the near field and also lower amplitude side lobes in the focal region than the fundamental. These findings were consistent for both uniform and apodized sources and could be contributing factors in the improved imaging reported with clinical scanners using tissue harmonic imaging. .

Yang, Xinmai; Cleveland, Robin O.

2005-01-01

218

Geometric Effects on Electron Cloud

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

219

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

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

2006-06-15

220

Nonlinear-optical method for combining high-power laser beams in gases or plasmas. Final report

The purpose is to investigate concepts for laser-controlled optics via near-resonance nonlinear dispersion, so that a laser-induced index grating which is capable of high-power laser beam combining might be produced and demonstrated. The principle of coherent addition of several input laser beams into one output beam had been demonstrated by the use of binary phase gratings. Properly shaped phase gratings had been etched onto a solid surface, establishing that multiple laser beams can be combined into a single beam with good conversion efficiency. For high-power beams, the limited damage thresholds and maximum permissible thermal loading of solid-state devices encouraged a search for more satisfactory working media. Gases and plasmas appeared to offer better solutions as working media. It had been predicted that two laser fields of differing wavelengths interacting with a collision-dominated atomic or molecular system with three effective energy levels could influence one another in a nonreciprocal manner; the creation of and interaction with a grating via near-resonance nonlinear dispersion thus should provide a method for low power laser beams to create a grating in which other beams combined to form a high-power beam.

Chivian, J.S.; Cantrell, C.D.; Glosson, C.A.; Cotten, W.D.; DiMarco, S.F.

1988-05-31

221

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

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

222

In this work, we consider sensitivity of the beam to small, steady-state perturbations whose characteristic size is small compared to the beam diameter. Therefore, on the ground the intensity of beam is taken to be a Gaussian times a function which differs from one by a small perturbation that is sinusoidal in the coordinate transverse to the wind. We also require that the beam be collimated at the end of the propagation path, which in this work is taken to be at a finite distance. We use a geometric optics approximation and develop a solution as a power series in a small parameter. The terms in this series are computed using the symbolic manipulating computer program MACSYMA. 4 refs., 1 fig.

Gautesen, A.; Morris, J.R.

1989-03-15

223

The nonlinear refractive-index (n(2)) spectrum of ZnSe near the band gap (lambda(gap) approximately 450 nm) at 77 K was measured for the first time to our knowledge by using self-bending of a pulsed laser beam. The maximum nonlinearity, n(2) approximately 1.9 x 10(-8) cm(2)/W, measured by us is anomalously large, which cannot be explained by conventional thermally induced band-gap shrinkage. PMID:19771112

Ding, Y J; Guo, C L; Swartzlander, G A; Khurgin, J B; Kaplan, A E

1990-12-15

224

NASA Astrophysics Data System (ADS)

This Letter reports an out-of-resonance vibro-acoustic modulation (VAM) effect in nonlinear ultrasonic evaluation of a microcracked cantilever beam. We design a model to involve the microcracked cantilever beam in a nonlinear oscillator system whose dynamics is introduced to extend the operating vibration excitation band of the VAM out of resonance. The prototype model exhibits an effective bandwidth four times that of the traditional linear model. The reported VAM effect allows efficiently enhancing the detection, localization, and imaging of various types of microcracks in solid materials at out-of-resonance vibration excitation frequencies.

He, Qingbo; Xu, Yanyan; Lu, Siliang; Dai, Daoyi

2014-04-01

225

This Letter reports an out-of-resonance vibro-acoustic modulation (VAM) effect in nonlinear ultrasonic evaluation of a microcracked cantilever beam. We design a model to involve the microcracked cantilever beam in a nonlinear oscillator system whose dynamics is introduced to extend the operating vibration excitation band of the VAM out of resonance. The prototype model exhibits an effective bandwidth four times that of the traditional linear model. The reported VAM effect allows efficiently enhancing the detection, localization, and imaging of various types of microcracks in solid materials at out-of-resonance vibration excitation frequencies.

He, Qingbo, E-mail: qbhe@ustc.edu.cn; Xu, Yanyan; Lu, Siliang; Dai, Daoyi [Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei, Anhui 230026 (China)

2014-04-28

226

Effect of nonlinear radiofrequency electromagnetic fields on the emittance of bunched beams

NASA Astrophysics Data System (ADS)

Gap transformations are frequently used in ion Linac codes, to efficiently describe the particle dynamics. Using similar approach, we analyze the uniformly bunched beam passing through an axis-symmetric radiofrequency (RF) cavity. The method can be used for other distributions as well using a similar six dimensional analysis. The effect of non-linear RF field in radial and axial directions in an RF cavity and the finite phase width of the bunch, on the transverse and longitudinal emittance growth have been studied. The expressions obtained have been verified for the two types of cavity cells namely the zero mode DTL and pi mode CCL type used frequently in ion linacs. The results are seen to be valid for the entire maximum phase acceptance up to 360 degrees. Simulations with the equivalent beams of non-uniform distributions namely Waterbag and Gaussian show that at synchronous phases closer to the wave crest, the results give a good approximation of emittance growth in both planes for non-uniform beams.

Phadte, D. S.; Patidar, C. B.

2013-07-01

227

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

NASA Astrophysics Data System (ADS)

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

Korman, Murray S.

2000-07-01

228

The coaxial gyrotron with two electron beams. I. Linear theory and nonlinear theory

NASA Astrophysics Data System (ADS)

The coaxial gyrotron with two electron beams (CGTB) is proposed and investigated in this paper. This paper consists of two parts: the linear theory and nonlinear theory of CGTB are presented in part I and the investigation on the dual frequency operation, a special operation state of CGTB, is given in part II. The magnetron injection gun with two electron beams has been developed, and simulations show that it may work well. It may guarantee that both the electric potential and the ratio of vertical to longitudinal velocities of two electron beams are equal. The results of the calculation show that CGTB has some distinguished advantages: mode competition is improved and output power is enhanced. Thus CGTB may be capable of providing 2-4MW continuous-wave (CW) at 170GHz to meet the demand of very high radio frequency CW power 1-2MW in the ITER [ITER EDA Agreement and Protocol 2 (IAEA, Vienna, 1994)] program and other applications.

Liu, Shenggang; Yuan, Xuesong; Fu, Wengjie; Yan, Yang; Zhang, Yaxin; Li, Hongfu; Zhong, Renbin

2007-10-01

229

NASA Technical Reports Server (NTRS)

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

Ball, R. E.

1972-01-01

230

We depict a new approach for the localized creation in three dimensions (3D) of a highly demanded nonlinear optical function for integrated optics, namely second harmonic generation. We report on the nonlinear optical characteristics induced by single-beam femtosecond direct laser writing in a tailored silver-containing phosphate glass. The original spatial distribution of the nonlinear pattern, composed of four lines after one single laser writing translation, is observed and modeled with success, demonstrating the electric field induced origin of the second harmonic generation. These efficient second-order nonlinear structures (with ?{sub eff}{sup (2)}???0.6?pm V{sup ?1}) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired.

Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L. [Univ. Bordeaux, LOMA, UMR 5798, F-33400 Talence, France and CNRS, LOMA, UMR 5798, F-33400 Talence (France); Petit, Y., E-mail: yannick.petit@u-bordeaux1.fr [Univ. Bordeaux, LOMA, UMR 5798, F-33400 Talence, France and CNRS, LOMA, UMR 5798, F-33400 Talence (France); CNRS, ICMCB, UPR 9048, F-33608 Pessac, France and Univ. Bordeaux, ICMCB, UPR 9048, F-33400 Pessac (France); Dussauze, M.; Rodriguez, V. [Univ. Bordeaux, ISM, UMR 5255, F-33400 Talence, France and CNRS, ISM, UMR 5255, F-33400 Talence (France); Cardinal, T. [CNRS, ICMCB, UPR 9048, F-33608 Pessac, France and Univ. Bordeaux, ICMCB, UPR 9048, F-33400 Pessac (France)

2014-03-21

231

The nonlinear dynamics of the instability of a straight high-density relativistic electron beam under the conditions of the stimulated Cherenkov effect in a plasma waveguide is studied both analytically and numerically. It is shown that, for a beam of sufficiently high density such that the stabilizing factors are nonlinear frequency shifts and for a plasma described in a linear approximation, the basic equations have soliton-like solutions and the electron beam after saturation of the instability relaxes to its initial, weakly perturbed state, provided that only one harmonic of the plasma and the beam density is taken into account. The analytical solutions obtained here for this case correlate well with the numerical ones. A more general model that accounts for the generation of higher harmonics of the plasma and the beam density does not yield soliton-like solutions for the time evolution of the amplitudes of the plasma and beam waves. In such a model, the instability will be collective again: it can be described analytically (at least, up to the time at which it saturates) by using equations with cubic nonlinearities and the method of expansion of the electron trajectories and momenta.

Bobylev, Yu. V. [L.N. Tolstoy Tula State Pedagogical University (Russian Federation); Kuzelev, M. V. [Moscow State University (Russian Federation); Rukhadze, A. A. [Russian Academy of Sciences, Prokhorov Institute of General Physics (Russian Federation)

2009-06-15

232

Producing an intense collimated beam of sound via a nonlinear ultrasonic array

NASA Astrophysics Data System (ADS)

We have designed and built an ultrasonic parametric array with an emphasis on creating an intense, collimated beam of low frequency sound. With this device, we can insonify a small area of ground or a small target at range and induce vibrations. These vibrations can be synchronously detected with any stand-off device such as a laser-Doppler vibrometer or the millimeter wave vibrometer we describe in Smith et al. [J. Appl. Physics 108, 024902 (2010)]. Despite nonlinear conversion losses, the array produces sound pressure levels in excess of 90 dB at 1 kHz, 1.5 m in front of the array using 25 low-cost 40 KHz transducers.

Gibson, Daniel; Smith, Martin; Scales, John; Zadler, Brian

2012-06-01

233

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

234

A nonlinear lens may be used to study the effect of high-order multipolar field imperfections on a stored proton beam. Such a nonlinear lens is particulary suitable to simulate field imperfections of the types encountered in coil dominated superconducting magnets. We have studied experimentally at the SPS the effect of high order (5th and 8th) single isolated resonances driven by the nonlinear lens. The width of these resonances is of the order one expects to be caused by field errors in superconducting magnets of the SSC type. The experiment shows that, in absence of tune modulation, these resonances are harmless. Slow crossings of the resonance, on the other hand, have destructive effects on the beam, much more so than fast crossings caused by synchrotron oscillations. In the design of future storage rings, sources of low-frequency tune modulation should be avoided as a way to reduce the harmful effects of high order multipolar field imperfection.

Cornacchia, M.; Evans, L.

1985-06-01

235

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

236

Finite element modeling of concrete beams prestressed with external tendons

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

Tie-jiong Lou; Yi-qiang Xiang

2006-01-01

237

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

NASA Astrophysics Data System (ADS)

The effect of phase conjugation for the second harmonic of a focused ultrasonic beam was investigated experimentally and by 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 for the second harmonic of the incident wave (2 f=6 MHz) was performed in a magnetostrictive ceramic as a result of the parametric interaction of the incident wave with the pumping magnetic field (the pumping frequency was f p=4 f=12 MHz). The axial and focal distributions of sound pressure in the incident and conjugated beams were measured using a broadband PVDF membrane hydrophone. The corresponding calculations were performed by solving numerically the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation allowing for the nonlinearity, diffraction, and thermoviscous absorption. The results of measurements agreed well with the calculations and showed that the field of a conjugate wave adequately reproduces the field of the second harmonic of the incident wave. A certain advantage of focusing with the phase conjugation for the second harmonic was demonstrated in comparison with the operation at the doubled frequency of the incident wave. The results of this study can serve as a basis for the utilization of the phase conjugation of harmonics in ultrasonic tomography and nondestructive testing.

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

2003-01-01

238

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

239

SELF-FOCUSING AND DIFFRACTION OF LIGHT IN A NONLINEAR MEDIUM

CONTENTS 1. Introduction 609 2. Geometrical Optics of a Nonlinear Medium (Equations, Focal Points, Nonlinear Aberrations, Nonstationary Processes) 617 3. Wave Optics of a Nonlinear Medium (Diffraction Corrections to the Self-focusing Length, Formation of Proper Optical Waveguide, Nonstationary Processes) 624 4. Nonlinear Optical Effects in the Field of Self-focusing Beams (Stimulated Scattering in Liquids, Experimental Data, Self-focusing and Parametric Amplification)

S A Akhmanov; Anatolii P Sukhorukov; R V Khokhlov

1968-01-01

240

NASA Astrophysics Data System (ADS)

The influence of various parameters such as tube length, change of diameter, tube shape, and tube material on the transfer function was investigated experimentally. In many cases there is a pronouncedly nonlinear behavior. A method is presented to estimate the transfer characteristics for such a nonlinear system. When unsteady pressures are measured on the end of a pressure tube instead of directly at the desired site, the pressure tube changes the unsteady signal. This characteristic is demonstrated to be frequency dependent. Pressure amplitude measurement results are used to determine real values for the transfer function. An empirical model of an estimated pressure control system is given. The possibility of approximating nonlinear pressure transfer from unsteady pressure measurement is shown.

Kienappel, K.

1982-02-01

241

NASA Astrophysics Data System (ADS)

The influence of various parameters such as tube length, change of diameter, tube shape and tube material on the transfer function was investigated experimentally. In many cases there is a pronouncedly nonlinear behavior. A method is presented to estimate the transfer characteristics for such a nonlinear system. When unsteady pressures are measured on the end of a pressure tube instead of directly at the desired site, the pressure tube changes the unsteady signal. This characteristic is demonstrated to be frequency dependent. Pressure amplitude measurement results are used to determine real values for the transfer function. An empirical model of an estimated pressure control system is given. The possibility of approximating nonlinear pressure transfer from unsteady pressure measurement is shown.

Kienappel, K.

1980-07-01

242

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

243

Nonlinear Diffraction from a Virtual Beam Solomon M. Saltiel,1,2,* Dragomir N. Neshev,1

experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic a wave vector ~k2) is observed, giving birth to the nonlinear Bragg diffraction satisfying the condition susceptibility (ð2Þ ). Interaction of the fundamental waves mediated by the nonlinear quadratic grating results

Arie, Ady

244

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

245

Purpose: To evaluate the probability of late cardiac mortality resulting from left breast irradiation planned with tangential fields and to compare this probability between the wedged beam and field-in-field (FIF) techniques and to investigate whether some geometric/dosimetric indicators can be determined to estimate the cardiac mortality probability before treatment begins. Methods and Materials: For 30 patients, differential dose-volume histograms were calculated for the wedged beam and FIF plans, and the corresponding cardiac mortality probabilities were determined using the relative seriality model. As a comparative index of the dose distribution uniformity, the planning target volume (PTV) percentages involved in 97-103% of prescribed dose were determined for the two techniques. Three geometric parameters were measured for each patient: the maximal length, indicates how much the heart contours were displaced toward the PTV, the angle subtended at the center of the computed tomography slice by the PTV contour, and the thorax width/thickness ratio. Results: Evaluating the differential dose-volume histograms showed that the gain in uniformity between the two techniques was about 1.5. With the FIF technique, the mean dose sparing for the heart, the left anterior descending coronary artery, and the lung was 15% (2.5 Gy vs. 2.2 Gy), 21% (11.3 Gy vs. 9.0 Gy), and 42% (8.0 Gy vs. 4.6 Gy) respectively, compared with the wedged beam technique. Also, the cardiac mortality probability decreased by 40% (from 0.9% to 0.5%). Three geometric parameters, the maximal length, angle subtended at the center of the computed tomography slice by the PTV contour, and thorax width/thickness ratio, were the determining factors (p = .06 for FIF, and p = .10 for wedged beam) for evaluating the cardiac mortality probability. Conclusion: The FIF technique seemed to yield a lower cardiac mortality probability than the conventional wedged beam technique. However, although our study demonstrated that FIF technique improved the dose coverage of the PTV, the restricted number of patients enrolled and the short follow-up did not allow us to evaluate and compare the breast cancer survival rates of the patients.

Pili, Giorgio; Grimaldi, Luca; Fidanza, Christian; Florio, Elena T. [Department of Medical Physics, 'A. Perrino' Hospital, Brindisi (Italy); Petruzzelli, Maria F. [Department of Radiation Oncology, 'A. Perrino' Hospital, Brindisi (Italy); D'Errico, Maria P. [Department of Laboratory Medicine, 'A. Perrino' Hospital, Brindisi (Italy); De Tommaso, Cristina; Tramacere, Francesco [Department of Radiation Oncology, 'A. Perrino' Hospital, Brindisi (Italy); Musaio, Francesca [Department of Medical Physics, 'A. Perrino' Hospital, Brindisi (Italy); Castagna, Roberta; Francavilla, Maria C. [Department of Radiation Oncology, 'A. Perrino' Hospital, Brindisi (Italy); Gianicolo, Emilio A.L. [National Research Council-Clinical Physiology Institute, Pisa-Lecce (Italy); Portaluri, Maurizio, E-mail: portaluri@hotmail.com [Department of Radiation Oncology, 'A. Perrino' Hospital, Brindisi (Italy); National Research Council-Clinical Physiology Institute, Pisa-Lecce (Italy)

2011-11-01

246

NASA Astrophysics Data System (ADS)

We propose a novel optical image hiding method based on a double-phase retrieval algorithm (DPRA) using iterative nonlinear double random phase encoding (NDRPE) in Fresnel domain under illumination of an optical vortex (OV) beam. The NDRPE-based DPRA is initially extended from the Fourier transform into the Fresnel domain, which makes the system more flexible and more compact. The proposed method has a faster convergence speed compared to its counterparts based on the linear double random phase encoding (LDRPE). A higher level of security also has been achieved by taking an OV mode as the illumination beam. Simulation results demonstrate the feasibility and security of the proposed approach.

Wang, Xiaogang; Chen, Wen; Chen, Xudong

2015-03-01

247

NASA Astrophysics Data System (ADS)

By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (V?) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.

Gao, Q. D.; Budny, R. V.

2015-03-01

248

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

249

NASA Technical Reports Server (NTRS)

Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.

Mei, Chuh; Shen, Mo-How

1987-01-01

250

NASA Astrophysics Data System (ADS)

Consideration is given to aspects of the nonlinear interaction of an electron beam with the electromagnetic field of a periodic structure both inside and outside its transmission band. A description is given of a fairly general method for the numerical analysis of the nonlinear characteristics of a multisection TWT with a slow-wave structure of coupled-resonator-chain type.

Man'kin, I. A.; Usherovich, B. L.

1991-04-01

251

A model for the nonlinear mechanism responsible for cochlear amplification.

A nonlinear model for the mechanism responsible for the amplification of the sound wave in the ear is derived using the geometric and material properties of the system. The result is a nonlinear beam equation, with the nonlinearity appearing in a coefficient of the equation. Once derived, the beam problem is analyzed for various loading conditions. Based on this analysis it is seen that the mechanism is capable of producing a spatially localized gain, as required by any amplification mechanism, but it is also capable of increasing the spatial contrast in the signal. PMID:25365605

Fessel, Kimberly; Holmes, Mark H

2014-12-01

252

-focusing. In earlier work' it was predicted that a beam of light with an asymmetric intensity profile incident upon readily from the following argument. When a beam of light with an asymmetric intensity profile, e calculate the self-bending due to a thin nonlinear film, basically concentrating on how this effect

Swartzlander Jr., Grover A.

253

According to its original Statement of Work (SOW), the overarching objective of this project is: 'To enhance substantially the understanding of the fundamental dynamics of nonequilibrium high-brightness beams with space charge.' Our work and results over the past three and half years have been both intense and fruitful. Inasmuch as this project is inextricably linked to a larger, growing research program - that of the Beam Physics and Astrophysics Group (BPAG) - the progress that it has made possible cannot easily be separated from the global picture. Thus, this summary report includes major sections on 'global' developments and on those that can be regarded as specific to this project.

C. L. Bohn (deceased), P. Piot and B. Erdelyi

2008-05-31

254

Mobius Strip underlying Nonlinear Oscillators

NASA Astrophysics Data System (ADS)

Geometrical and topolgocial aspects of phase space orbits of driven nonlinear oscillators are shown to share many features with the circuits on the mobius strips. Most important characteristic shared by nonlinear oscillators and the mobius strip is the first order geometrical phase transition characterized in terms of local variable torsion and the global variable the geometrical phase . These geometrical transitions are geometrical resonances and lead to geometrical localization that underlie not only limit cycles but also the strange attractors.

Lopaz, Edaurdo; Satija, Indubala

2004-03-01

255

New Nonlinear Evolution Equation for Steps during Molecular Beam Epitaxy on Vicinal Surfaces

A nonlinear evolution equation for a vicinal surface growing in the step flow mode is derived in the limit of weak desorption. This limit turns out to be singular, and nonlinearities of arbitrary order need to be taken into account. The meandering instability caused by step edge barriers leads to a step morphology with a fixed meander wavelength, cusp singularities,

O. Pierre-Louis; C. Misbah; Y. Saito; J. Krug; P. Politi

1998-01-01

256

NASA Astrophysics Data System (ADS)

Both linear and nonlinear interactions between oblique whistler, electrostatic, quasi-upper hybrid mode waves and an electron beam are studied by linear analyses and electromagnetic particle simulations. In addition to a background cold plasma, we assumed a hot electron beam drifting along a static magnetic field. Growth rates of the oblique whistler, oblique electrostatic, and quasi-upper hybrid instabilities were first calculated. We found that there are four kinds of unstable mode waves for parallel and oblique propagations. They are the electromagnetic whistler mode wave (WW1), the electrostatic whistler mode wave (WW2), the electrostatic mode wave (ESW), and the quasi-upper hybrid mode wave (UHW). A possible mechanism is proposed to explain the satellite observations of whistler mode chorus and accompanied electrostatic waves, whose amplitudes are sometimes modulated at the chorus frequency.

Zhang, Y. L.; Matsumoto, H.; Omura, Y.

1993-12-01

257

NASA Astrophysics Data System (ADS)

The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects could be readily achieved.

Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.

2014-05-01

258

Geometrization of quantum mechanics

Quantum mechanics is cast into a classical Hamiltonian form in terms of a symplectic structure, not on the Hilbert space of state-vectors but on the more physically relevant infinite-dimensional manifold of instantaneous pure states. This geometrical structure can accommodate generalizations of quantum mechanics, including the nonlinear relativistic models recently proposed. It is shown that any such generalization satisfying a few

T. W. B. Kibble

1979-01-01

259

NASA Astrophysics Data System (ADS)

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

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

2011-12-01

260

The PENELOPE code is used to determine direct strand break yields corresponding to photons from a (60)Co source and 28 and 30 kV x-ray beams impacting on a B-DNA geometrical model, which accounts for five organizational levels of the human genetic material. Direct single, double and total strand break probabilities are determined in a liquid water homogeneous medium with 1.06 g?cm(-3) density. The spectra produced by the x-ray beams at various depths in the phantom have been used to study the dependence of the damage yield on the depth. The relative biological effectiveness (RBE) is also estimated using the (60)Co radiation qualities as the reference. According to this work, the damage probabilities and thus the RBE are, within the uncertainties, similar for both x-ray energies and are independent of the depth into the phantom. Furthermore, the total strand break yield is invariant with respect to the energy of the incident photons. The RBE for low-energy x-ray beams determined here (1.3 ± 0.1) is lower than that reported by Kellerer, taking into account that he used a 200 kV radiation as the reference quality. However, our RBE values are consistent with those determined by Kühne et al (2005 Radiat. Res. 164 669-76), which used the same biological endpoint and reference quality as our study. Also, our RBE values are similar to those determined by Verhaegen and Reniers (2004 Radiat. Res. 162 592-9). PMID:22056816

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

2011-12-01

261

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

truncated backpropagation through time with the Node-Decoupled Extended Kalman Filter (NDEKF) algorithm governing the ball's motion (gliding and rolling) on the beam. This rules out - or at least makes it very. A shallow beam angle can allow the ball to become stuck on an undesired location, while a steep angle

Prokhorov, Danil

262

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

263

NASA Technical Reports Server (NTRS)

The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.

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

1976-01-01

264

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

265

Nonlinear Plasma Waves Excitation by Intense Ion Beams in Background Plasma

Plasma neutralization of an intense ion pulse is of interest for many applications, including plasma lenses, heavy ion fusion, cosmic ray propagation, etc. An analytical electron fluid model has been developed to describe the plasma response to a propagating ion beam. The model predicts very good charge neutralization during quasi-steady-state propagation, provided the beam pulse duration {tau}{sub b} is much longer than the electron plasma period 2{pi}/{omega}{sub p}, where {omega}{sub p} = (4{pi}e{sup 2}n{sub p}/m){sup 1/2} is the electron plasma frequency and n{sub p} is the background plasma density. In the opposite limit, the beam pulse excites large-amplitude plasma waves. If the beam density is larger than the background plasma density, the plasma waves break. Theoretical predictions are compared with the results of calculations utilizing a particle-in-cell (PIC) code. The cold electron fluid results agree well with the PIC simulations for ion beam propagation through a background plasma. The reduced fluid description derived in this paper can provide an important benchmark for numerical codes and yield scaling relations for different beam and plasma parameters. The visualization of numerical simulation data shows complex collective phenomena during beam entry and exit from the plasma.

Igor D. Kaganovich; Edward A. Startsev; Ronald C. Davidson

2004-04-15

266

Parametric down-conversion of higher-order Bessel beams in nonlinear crystals

It is revealed that orbital angular momentum can be conserved within the spontaneous parametric down-conversion of higher-order Bessel beam. A qualitative agreement of theoretical predictions with experimental results is obtained.

V. Pyragaite; A. Piskarskas; K. Regelskis; V. Smilgevicius; A. Stabinis; S. Mikalauskas

2005-01-01

267

Focal-Plane Imaging of Crossed Beams in Nonlinear Optics Experiments

NASA Technical Reports Server (NTRS)

An application of focal-plane imaging that can be used as a real time diagnostic of beam crossing in various optical techniques is reported. We discuss two specific versions and demonstrate the capability of maximizing system performance with an example in a combined dual-pump coherent anti-Stokes Raman scattering interferometric Rayleigh scattering experiment (CARS-IRS). We find that this imaging diagnostic significantly reduces beam alignment time and loss of CARS-IRS signals due to inadvertent misalignments.

Bivolaru, Daniel; Herring, G. C.

2007-01-01

268

Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams.

On the basis of recently developed Fourier continuation (FC) methods and associated efficient parallelization techniques, this text introduces numerical algorithms that, due to very low dispersive errors, can accurately and efficiently solve the types of nonlinear partial differential equation (PDE) models of nonlinear acoustics in hundred-wavelength domains as arise in the simulation of focused medical ultrasound. As demonstrated in the examples presented in this text, the FC approach can be used to produce solutions to nonlinear acoustics PDEs models with significantly reduced discretization requirements over those associated with finite-difference, finite-element and finite-volume methods, especially in cases involving waves that travel distances that are orders of magnitude longer than their respective wavelengths. In these examples, the FC methodology is shown to lead to improvements in computing times by factors of hundreds and even thousands over those required by the standard approaches. A variety of one-and two-dimensional examples presented in this text demonstrate the power and capabilities of the proposed methodology, including an example containing a number of scattering centers and nonlinear multiple-scattering events. PMID:23039433

Albin, Nathan; Bruno, Oscar P; Cheung, Theresa Y; Cleveland, Robin O

2012-10-01

269

Effects of focusing on third-order nonlinear processes in isotropic media. [laser beam interactions

NASA Technical Reports Server (NTRS)

Third-order nonlinear processes in isotropic media have been successfully used for tripling the efficiency of high-power laser radiation for the production of tunable and fixed-frequency coherent vacuum UV radiation and for up-conversion of IR radiation. The effects of focusing on two processes of this type are studied theoretically and experimentally.

Bjorklund, G. C.

1975-01-01

270

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

271

Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams

Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics through the concepts of differential geometry can help to address the non-linear phenomena in their intrinsic qualities. This results in a field of research aimed at establishing and solving dynamic models purged of any artificial nonlinearity by taking advantage of symmetry properties underlying the use of Lie groups. The geometric constructions needed for reduction are presented in the context of the "covariant" approach.

Joël Bensoam

2013-04-03

272

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

273

Nonlinear airship aeroelasticity

The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear

N. Bessert; O. Frederich

2005-01-01

274

a threshold value. Above this threshold angle, the beam simply passes through the defect. This phenomenon a soliton traveling in a specially designed lattice network or interacting with a blocker soliton [3 be reflected by bright and dark soliton blockers [17,19]. In this article, we demonstrate both theoretically

Yang, Jianke

2011-01-01

275

NASA Astrophysics Data System (ADS)

Self-focusing is a well-researched phenomenon. Nanoscale spots can be achieved through self-focusing, which is an alternative method for achieving high-density data storage, high-resolution light imaging, and maskless nanolithography. Several research groups have observed that self-focusing spots can be reduced to nanoscale levels via incident laser power manipulation. Self-focusing spots can be analyzed by solving the nonlinear Schrödinger equation and the finite difference time domain method. However, both procedures are complex and time-consuming. In the present work, a multi-layer thin-lens self-focusing model that considers diffraction effects and changes of refractive index along the radial and film thickness directions is proposed to analyze the self-focusing behavior and traveling process of light beams intuitively. The self-focusing behaviors of As2S3 are simulated, and results show that a nanoscale self-focusing spot with a radius of about 0.12 ?m can be formed at the bottom of nonlinear sample when the incident laser power exceeds 4.25 mW. Our findings are basically consistent with experimental reports and provide a good method for analyzing and understanding the self-focusing process. An appropriate application schematic design is also provided.

Wei, Jingsong; Yan, Hui

2014-08-01

276

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

277

Unconventional finite element method for nonlinear analysis of beams and plates

of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Approved by: Chair of Committee, J. N. Reddy Committee Members, Xinlin Gao Zoran Sunik Head of Department, Dennis O.... Reddy In this thesis, mixed finite element models of beams and plates bending are developed to include other variables (i.e., the membrane forces and shear forces) in addition to the bending moments and vertical deflection, and to see the effect...

Kim, Wooram

2009-05-15

278

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

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

279

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

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

280

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).

2012-09-18

281

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

282

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

283

NASA Astrophysics Data System (ADS)

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

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

2011-02-01

284

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

285

Nonlinear-optical method for combining high-power laser beams. Report for 1 April 1988-30 April 1989

The overall program goal was to investigate concepts for laser-controlled optics based on near-resonance nonlinear dispersion in gases, and to demonstrate a laser-induced grating capable of high-power laser-beam combining. The theoretical work extended the previous year's effort in giving a more detailed view of those aspects that might prevent observation of a grating, and led to optimization of experimental parameters. Modifications and improvements were made to the experimental apparatus. No grating was observed over a wide range of experimental conditions, although the apparatus was capable of such demonstration had a grating existed. The most likely cause of trouble appears to be the complexity of the SF{sub 6} medium chosen for demonstration. As an apparatus check, a medium (e.g, vanadium dioxide) can be used in which it is known that a grating can be demonstrated. Measurements were extended on the effect of noble gas admixtures into SF{sub 6} on the absorption of 16.26-micrometer radiation; helium suppresses absorption, argon and xenon enhance absorption. It would be worthwhile to continue these studies in light of information to be gained regarding the effect of collisions on absorption spectra in molecular species.

Chivian, J.S.; Glosson, C.A.; Cotten, W.D.; Cantrell, C.D.; DiMarco, S.F.

1989-04-28

286

........................................................................................ 32 6.2 Basic Idea ............................................................................................ 32 6.3 Least-squares Finite Element MODEL 1 for Euler-Bernoulli Beam Theory... to the beam axis after deformation. These assumptions neglect the Poisson?s effect and the transverse strain. These two assumptions are taken into account in Timoshenko beam theory. 11 x z, w0 x,u0z Undeformed (u ,w )0 0 (u,w) u0 -dw0 dx -dw0 dx EBT...

Raut, Ameeta A.

2010-07-14

287

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?

NCTM Illuminations

2000-01-01

288

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

289

NASA Astrophysics Data System (ADS)

Acoustical imaging in complex media (e.g., biological tissue) can be affected by phase aberrations introduced in a wave during propagation. Wave phase conjugation (WPC) of ultrasound is known for its ability to compensate for phase distortions due to inhomogeneity of the propagation medium, and it can be used for improvement of acoustical imaging under these conditions. In a nonlinear medium harmonics are generated during propagation of an intense beam of ultrasound, and this principle is used in tissue harmonic imaging. The parametric method of WPC permits phase conjugation of a selected frequency component of the probe beam. In this way the peculiarities of WPC can be combined with advantages of harmonic imaging. Automated WPC-focusing of the conjugated second-harmonic component of a focused nonlinear probe beam is studied experimentally and theoretically for the case of a homogeneous medium, and experimentally for a medium with pseudo-random inhomogeneities. The generated conjugate wave can also be sufficiently intense to generate higher-order harmonics, which display enhanced focusing. Improvement of a C-scan harmonic imaging system operating in an inhomogeneous medium is provided as an example.

Krutyansky, Leonid M.; Brysev, Andrew P.; Klopotov, Roman V.; Pernod, Philippe J.; Preobrazhensky, Vladimir L.; Yan, Xiang; Hamilton, Mark F.

2003-10-01

290

.75.Lm, 42.65.Jx, 42.65.Tg The coherent transport of nonlinear waves is essential in many phenomena of nonlinear waves have been first studied in optics, where the advent of the laser as an intense coherent atom optics, including four-wave mixing of matter waves [1] and matter-wave solitons [2]. A few years

291

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

292

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

293

NSDL National Science Digital Library

We will be learning the names and properties (# of sides, vertices, parallel sides, etc.) of several different geometric shapes. By now, everybody should know how many sides a square has and be able to recognize a circle. But, do you know how many vertices a parallelogram has, or how many sides to a rhombus? After completing the following exercies, you should be able to answer those questions and many ...

Mr. Hoskins

2005-11-21

294

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

295

Coupling mechanism of granular medium and slender beams

NASA Astrophysics Data System (ADS)

We present a methodology to assess slender beams by means of highly nonlinear solitary waves. This is accomplished by understanding the coupling mechanism between highly nonlinear solitary waves propagating along a granular system and a beam in contact with the granular medium. Nonlinear solitary waves are compact non-dispersive waves that can form and travel in nonlinear systems such as one-dimensional chains of particles. In the study presented in this paper, the waves are generated by the mechanical impact of a striker and are detected by means of sensor beads located along the chain. We investigated numerically and experimentally the effect on the solitary waves of slender beams of different modulus, length, boundary condition, and axial stress. We found that the geometric and mechanical properties of the beam or thermal stress applied to the beam alter certain features of the solitary waves. In the future, these findings may be used to develop a novel sensing system for the Nondestructive Evaluation of beams.

Cai, Luyao; Rizzo, Piervincenzo; Li, Kaiyuan; Al-Nazer, Leith

2014-04-01

296

NASA Astrophysics Data System (ADS)

In standard weak interaction theory, acousto-optic Bragg analysis typically assumes that the incident light and sound beams are uniform plane waves. Acousto-optic Bragg diffraction with nonuniform profiled input beams is numerically examined under open loop via a transfer function formalism. Unexpected deviations in the first-order diffracted beam from the standard theory are observed for high Q values. These deviations are significant because the corresponding closed-loop system is sensitive to input amplitudes and initial conditions, and the overall impact on the dynamical behavior has not been studied previously in standard analyses. To explore the effect of such nonuniform output profiles on the feedback system, the numerically generated scattered output is fed back to the acoustic driver, and the resulting nonlinear dynamics are manipulated to create novel monostable, bistable, multistable, and chaotic regimes. The effects of the nonuniform input on these regimes are examined using the techniques of Lyapunov exponents and bifurcation maps. The orbital behavior is characterized with quadratic maps, which are an intuitive method of predicting the parametric behavior of the system. The latter trajectory-based approach offers yet a third arm in the process of developing a fuller understanding of the profiled output beam under feedback. The results of this work indicate that the nonlinear dynamical thresholds of the hybrid cell are significantly different for the profiled propagation problem than for the uniform case. The mono and bistable regimes do not coincide with the well-known uniform plane wave results, and the chaotic thresholds, which are critical to understanding encryption applications, are altered noticeably.

Almehmadi, F. S.; Chatterjee, M. R.

2014-04-01

297

This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be

Hussien Abd El Baky

2008-01-01

298

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

299

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

300

0 5 10 15 20?5 ?4 ?3 ?2 ?1 0 1 2 3 4 5 Applied Load, ?/pi2 Parameter c n Nayfeh and Emam (2008): Clamped?Clamped P=P2 P=P3 Stable position P=P1 Unstable position (a) 0 5 10 15 20 25 30 35 40 45?8 ?6 ?4 ?2 0 2 4 6 8... sin = 0 From the above equations, it follows that c1 sin = 0; c2 = 0; c3 = 0; c4 = 0 The solution for the rst constant implies that either c1 = 0 or (and) sin = 0. For a nontrivial solution v, we must have sin = 0 which implies n = p = n...

Mahaffey, Patrick Brian

2013-08-07

301

Nonlinear computer-generated holograms.

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering. PMID:21808390

Shapira, Asia; Juwiler, Irit; Arie, Ady

2011-08-01

302

Nonlinear computer-generated holograms

NASA Astrophysics Data System (ADS)

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite--Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.

Shapira, Asia; Juwiler, Irit; Arie, Ady

2011-08-01

303

Linearizing Intra-Train Beam-Beam Deflection Feedback

Beam-beam deflection feedback acting within the crossing time of a single bunch train may be needed to keep linear collider beams colliding at high luminosity. In a short-pulse machine such as the Next Linear Collider (NLC) this feedback must converge quickly to be useful. The non-linear nature of beam-beam deflection vs. beam-beam offset in these machines precludes obtaining both rapid convergence and a stable steady-state lock to beam offsets with a linear feedback algorithm. We show that a simply realizable programmable non-linear amplifier in the feedback loop can linearize the feedback loop, approximately compensating the beam-beam deflection non-linearity. Performance of a prototype non-linear amplifier is shown. Improvement of convergence and stability of the beam-beam feedback loop is simulated.

Smith, S.R.; /SLAC

2006-02-22

304

Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation

NASA Technical Reports Server (NTRS)

A recently developed finite-element-based equivalent linearization approach for the analysis of random vibrations of geometrically nonlinear multiple degree-of-freedom structures is validated. The validation is based on comparisons with results from a finite element based numerical simulation analysis using a numerical integration technique in physical coordinates. In particular, results for the case of a clamped-clamped beam are considered for an extensive load range to establish the limits of validity of the equivalent linearization approach.

Rizzi, Stephen A.; Muravyov, Alexander A.

2000-01-01

305

Observations from the Fast Auroral SnapshoT (FAST) satellite indicate that the parallel and perpendicular (to the Earth's magnetic field) electric field structures exhibit a spiky appearance. In this study, a magnetized plasma system consisting of protons, electrons, and a cold oxygen ion beam is considered. Both background electrons and protons are treated as hot species with Boltzmann density distributions. The

S. Moolla; R. Bharuthram; S. V. Singh; G. S. Lakhina; R. V. Reddy

2010-01-01

306

Competing nonlinearities in quadratic nonlinear waveguide arrays

between pulse peak and av- erage beam powers, and to our knowledge no experi- mental demonstration- ence of nonlinear phase cancellation [7]. Still, experi- mental results demonstrating the effect and anomalous diffraction. The competing nonlinearities are realized in an ar- ray of periodically poled

307

Transient Dynamics of PreStressed Spatially Curved Thin-Walled Beams of Open Profile

\\u000a The dynamic stability with respect to small pertubations, as well as the local damage of geometrically nonlinear elastic spatially\\u000a curved open section beams with axial precompression have been analyzed. Transient waves, which are the surfaces of strong\\u000a discontinuity and wherein the stress and strain fields experience discontinuities, are used as small pertubations, in so doing\\u000a the discontinuities are considered to

Yury A. Rossikhin; Marina V. Shitikova

308

BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint

BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented as validation.

Wang, Q.; Sprague, M.; Jonkman, J.; Johnson, N.

2015-01-01

309

The Journal of Geometric Analysis Volume 7, Number 3, 1997

by Mean Curvature,I: Convergence By Halil Mete Soner ABSTRACT. In this paper we study the asymptotic for Nonlinear Analysis. @ 1997 The Journal of Geometric Analysis ISSN 1050-6926 #12;438 Halil Mete Soner 1

Soner, Halil Mete

310

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

311

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

312

Geometric ideas are present in many areas of modern theoretical physics and they are usually associated with the presence of nonlinear phenomena. Integrable nonlinear systems play a prime role both in geometry itself and in nonlinear physics. One can mention general relativity, exact solutions of the Einstein equations, string theory, Yang-Mills theory, instantons, solitons in nonlinear optics and hydrodynamics, vortex

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

2009-01-01

313

Geometric phase of interacting qubits: Mean-field analysis

We consider a system consisting of a large number of interacting qubits and study the geometric phase of one of them. The many body interaction is analyzed within a mean-field approach when the reduced dynamics of a single qubit is described by a nonlinear Hartree equation. Generally, the geometric phase is highly sensitive to the type and the strength of interaction. However, we identify regimes where the geometric phase is almost independent of the qubit-qubit coupling.

Dajka, J.; Mierzejewski, M.; Luczka, J. [Institute of Physics, University of Silesia, 40-007 Katowice (Poland)

2009-10-15

314

NASA Astrophysics Data System (ADS)

Upstream from the supernova quasiparallel shock wave the hot component representing cosmic rays is locked at the shock front due to the scattering in the magnetic field fluctuations and is accelerated by the diffusive shock acceleration mechanism. Cosmic ray population being isotropic in the shock frame and drifting with the shock velocity relative to the interstellar plasma is shown to be unstable in respect to the non-resonant beam type electromagnetic instability similar to the fire-hose. Analysis of the dispersion relation of the instability shows that for powerlike distribution of cosmic ray particles f(?)? ?-4 resulting from the diffusive shock acceleration, the maximum growth rate of magnetic fluctuations occurs at the wavelengths comparable with the gyroradius at the upper edge of the energy spectrum. Diffusion of cosmic ray particles caused by such extremely long fluctuations of the magnetic field is calculated and is shown to be especially important for the most energetic part of cosmic rays.

Shapiro, Vitali D.; Quest, Kevin B.; Okolicsanyi, Marco

1996-11-01

315

Constrained ballistics and geometrical optics

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

316

NASA Astrophysics Data System (ADS)

A W-band traveling-wave tube (TWT) with double-groove loaded folded waveguide structure (FWSWS) has been designed and numerically modelled. The nonlinear performance of such a TWT is investigated by a particle-in-cell code MAGIC3D. Simulation results indicate this TWT produces a saturated electromagnetic power of 170.2 W at 90 GHz, corresponding to 36.9 dB gain and 69.6 mm interaction distance. A comparison between the novel folded waveguide traveling-wave tube (FWTWT) and the conventional one is also carried out to verify the effect of groove loading on the large-signal performance of TWT. Within the same working conditions, the double groove-loaded FWTWT could obtain higher saturated output power and gain in a shorter interaction length. The maximum of output power and gain of this novel TWT is 58.6% and 10% higher than those of the conventional FWTWT, while the 3-dB bandwidth of TWT is reduced to 4 GHz. With the additional advantage of ease of fabrication based on micro-electro-mechanical systems (MEMS) technologies, the double-groove loaded FWSWS is suitable for a millimeter-wave TWT with high power capacity and gain.

He, Jun; Wei, YanYu; Park, GunSik

2013-07-01

317

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.

318

On geometric factors for neutral particle analyzers

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. [University of California-Irvine, Irvine, California 92697-4575 (United States)

2014-11-15

319

Transition from linear- to nonlinear-focusing regime in filamentation

Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature. PMID:25434678

Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin

2014-01-01

320

ArithmeticGeometric Progression

VMCAI'05 The ArithmeticGeometric Progression Abstract Domain Jérôme Feret École Normale Supérieure; Overview 1. Introduction 2. Case study 3. Arithmeticgeometric progressions 4. Benchmarks 5. Conclusiongeometric progressions 4. Benchmarks 5. Conclusion Jérôme Feret, LIENS 13 January, 2005 #12; Arithmetic

Feret, Jérôme

321

NONLINEAR PROCESSES IN THE PERIODIC STRUCTURES

The three-wave interaction in an infinite periodic structure formed by two alternating semiconductor layers has been studied in the work. The nonlinearity under study is due to the nonlinearity of the free carrier current. It is shown that the phase of the nonlinear interaction matrix element depends on the physical and geometrical parameters. As the result the energy pumping from

A. A. Bulgakov; O. V. Shramkova

2007-01-01

322

Bloch-sphere representation of three-vertex geometric phases

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

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

2011-11-15

323

Topological defects, geometric phases, and the angular momentum of light

Recent reports on the intriguing features of vector vortex bearing beams are analyzed using geometric phases in optics. It is argued that the spin redirection phase induced circular birefringence is the origin of topological phase singularities arising in the inhomogeneous polarization patterns. A unified picture of recent results is presented based on this proposition. Angular momentum shift within the light beam (OAM) has exact equivalence with the angular momentum holonomy associated with the geometric phase consistent with our conjecture.

S C Tiwari

2007-04-02

324

Analysis of nonlinear self-focusing phenomenon in high-power laser system based on ray-tracing

NASA Astrophysics Data System (ADS)

In high power laser systems, nonlinear effect, one of the key factors of beam wavefront aberration and even irreversible damage to system, has always been one of the top considerations of researchers for decades. A hybrid ray-tracing method for both linear media and nonlinear media based on geometric optics is presented in this paper and realized by programming. In a simple optic system with KDP crystal, an obvious decline of beam quality is observed in high laser power density conditions and a method taking component intervals as compensation of beam quality is proved feasible. Considering the complexity of traditional modeling method based on surfaces, a modeling method based on components is established. Hopefully, the conclusions and flaws of this paper can shed light on relevant work and further research.

Wang, Weiwei; Li, Xiaotong; Cen, Zhaofeng; Zhang, Luwei

2014-11-01

325

Nonlinear springs with applications to flow regulation valves and mechanisms

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

326

Functional facets for nonlinear crystals

NASA Astrophysics Data System (ADS)

We report on a new optical device allowing to efficiently add desired functionalities to a nonlinear interaction. This is achieved by focused ion beam patterning of a nano-layer of gold sputtered at the exit facet of a nonlinear crystal. The functionality is experimentally demonstrated with three examples: spatial filtering where a fundamental beam with a poor mode quality and its' frequency-doubled beam are filtered thereby providing high mode quality beams, focusing of a generated second harmonic beam and beam shaping where a fundamental Gaussian beam is transformed into any arbitrary desired frequency-doubled beam. For the latter two examples, the functional facet also provides angular separation of the fundamental and second harmonic beams.

Shapira, Asia; Libster, Ana; Lilach, Yigal; Arie, Ady

2013-07-01

327

Beam-beam interactions in P-P colliding accelerators

Non-linear stop-bands, due to the beam-beam interaction in a P-P colliding accelerator, are computed and used to estimate the strength of the beam-beam interaction. Results for the stop-band widths due to various causes are summarized. These results are used to compare the effects of beam-beam non-linear resonances in the ISR with those in CBA (Colliding Beam Accelerator at BNL), to estimate the effect of a spectrometer magnet placed at one of the beam crossing points, and to compare the beam-beam interactions for colliding beam accelerators with different crossing angles and different ..beta..-functions at the crossing points.

Parzen, G.

1983-01-01

328

\\u000a The dynamic stability with respect to small perturbations, as well as the local damage of geometrically nonlinear elastic\\u000a spatially curved open section beams with axial precompression have been analyzed. Transient waves, which are the surfaces\\u000a of strong discontinuity and wherein the stress and strain fields experience discontinuities, are used as small perturbations,\\u000a in so doing the discontinuities are considered to

Yury A. Rossikhin; Marina V. Shitikova

329

Beam halo in high-intensity beams

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

330

Beam halo in high-intensity beams

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

331

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

332

New developments on the geometric nonholonomic integrator

NASA Astrophysics Data System (ADS)

In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911–28 Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220–9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behaviour. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behaviour of the proposed method with the example of the inhomogeneous sphere rolling without slipping on a table.

Ferraro, Sebastián; Jiménez, Fernando; Martín de Diego, David

2015-04-01

333

NASA Technical Reports Server (NTRS)

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.

Gray, Carl E., Jr.

1988-01-01

334

Geometrization of Quantum Mechanics

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

2007-03-23

335

Nonlinear dynamic modeling of micromachined microwave switches

Nonlinear dynamic lumped models of micromachined microwave switches have been formulated and successfully applied to analyses of transient characteristics and geometrical scaling. Parameter extraction through electrical measurements is summarized. The results are compared to transient quasi-2D simulations

E. K. Chan; E. C. Kan; R. W. Dutton; P. M. Pinsky

1997-01-01

336

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

337

Intrinsic Geometric Analysis of the Network Reliability and Voltage Stability

This paper presents the intrinsic geometric model for the solution of power system planning and its operation. This problem is large-scale and nonlinear, in general. Thus, we have developed the intrinsic geometric model for the network reliability and voltage stability, and examined it for the IEEE 5 bus system. The robustness of the proposed model is illustrated by introducing variations of the network parameters. Exact analytical results show the accuracy as well as the efficiency of the proposed solution technique.

N. Gupta; B. N. Tiwari; S. Bellucci

2010-11-12

338

Geometrical Aspects in Optical Wavepacket Dynamics

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

339

Geometrizing Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.

Falciano, F. T.; Novello, M.; Salim, J. M.

2010-12-01

340

NASA Astrophysics Data System (ADS)

Mathematical expressions for the acoustic scattering, instantaneous (linear), and time-averaged (nonlinear) forces resulting from the interaction of a new type of Bessel beam, termed here a first-order non-diffracting Bessel trigonometric beam (FOBTB) with a sphere, are derived. The beam is termed "trigonometric" because of the dependence of its phase on the cosine function. The FOBTB is regarded as a superposition of two equi-amplitude first-order Bessel vortex (helicoidal) beams having a unit positive and negative order (known also as topological charge), respectively. The FOBTB is non-diffracting, possesses an axial null, a geometric phase, and has an azimuthal phase that depends on cos( ?± ?0), where ?0 is an initial arbitrary phase angle. Beam rotation around its wave propagation axis can be achieved by varying ?0. The 3D directivity patterns are computed, and the resulting modifications of the scattering are illustrated for a rigid sphere centered on the beam's axis and immersed in water. Moreover, the backward and forward acoustic scattering by a sphere vanish for all frequencies. The present paper will shed light on the novel scattering properties of an acoustical FOBTB by a sphere that may be useful in particle manipulation and entrapment, non-destructive/medical imaging, and may be extended to other potentially useful applications in optics and electromagnetism.

Mitri, F. G.

2011-11-01

341

Nonlinear resonances of a single-wall carbon nanotube cantilever

NASA Astrophysics Data System (ADS)

The dynamics of an electrostatically actuated carbon nanotube (CNT) cantilever are discussed by theoretical and numerical approaches. Electrostatic and intermolecular forces between the single-walled CNT and a graphene electrode are considered. The CNT cantilever is analyzed by the Euler-Bernoulli beam theory, including its geometric and inertial nonlinearities, and a one-mode projection based on the Galerkin approximation and numerical integration. Static pull-in and pull-out behaviors are adequately represented by an asymmetric two-well potential with the total potential energy consisting of the CNT elastic energy, electrostatic energy, and the Lennard-Jones potential energy. Nonlinear dynamics of the cantilever are simulated under DC and AC voltage excitations and examined in the frequency and time domains. Under AC-only excitation, a superharmonic resonance of order 2 occurs near half of the primary frequency. Under both DC and AC loads, the cantilever exhibits linear and nonlinear primary and secondary resonances depending on the strength of the excitation voltages. In addition, the cantilever has dynamic instabilities such as periodic or chaotic tapping motions, with a variation of excitation frequency at the resonance branches. High electrostatic excitation leads to complex nonlinear responses such as softening, multiple stability changes at saddle nodes, or period-doubling bifurcation points in the primary and secondary resonance branches.

Kim, I. K.; Lee, S. I.

2015-03-01

342

Arithmetic and Geometric Sequences

NSDL National Science Digital Library

Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.

2007-12-12

343

Geometric intrinsic symmetries

The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.

Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl; Szulerecka, A.; Pedrak, A. [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)] [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)

2013-08-15

344

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.

Jimmy Raymond

345

This paper provides a novel approach for optimal route planning making efficient use of the underlying geometrical structure. It combines classical AI exploration with computa- tional geometry. Given a set of global positioning system (GPS) trajectories, the input is refined by geometric filtering and rounding algorithms. For constructing the graph and the according point localization structure, fast scan-line and divide-and-conquer

Stefan Edelkamp; Shahid Jabbar; Thomas Willhalm

2005-01-01

346

Morphing of Geometric Composites via Residual Swelling

Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth-like morphing of 2D sheets into 3D shapes by introducing a new class of geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we develop an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques.

Matteo Pezzulla; Steven A. Shillig; Paola Nardinocchi; Douglas P. Holmes

2015-04-12

347

Hierarchies of Geometric Entanglement

We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of generalized geometric measures provides a quantification and 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 to the study of entanglement in different classes of $N$-qubit pure states. These classes include $W$ and $GHZ$ states, and their symmetric superpositions; symmetric multi-magnon states; cluster states; and, finally, asymmetric generalized $W$-like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that 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 of Wei and Goldbart that $W$ states possess a larger global entanglement than $GHZ$ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.

M. Blasone; F. Dell'Anno; S. De Siena; F. Illuminati

2008-05-28

348

NASA Astrophysics Data System (ADS)

The size-dependent nonlinear free vibration and instability of fluid-conveying single-walled boron nitride nanotubes (SWBNNTs) embedded in thermal environment are studied in this paper. The fluid-conveying SWBNNT is modeled as a Timoshenko beam by which the effects of transverse shear deformation and rotary inertia is taken into consideration. The modified strain gradient theory is used to capture the size effect. To consider the nonlinear effect, the geometric nonlinearity, based on von Kármán's assumption is introduced to develop the nonlinear governing equations of motion. By employing Hamilton's principle, the governing equations and associated boundary conditions are derived. Thereafter, a numerical solution procedure based on the generalized differential quadrature (GDQ) is introduced, according to which the nonlinear governing equations and the corresponding boundary conditions are discretized via the operational matrix of differentiation. The discretized equations are then solved analytically through the harmonic balance approach. Effects of different parameters including material length scale parameter, spring and damping constants of surrounding viscoelastic medium, and flow velocity on the nonlinear free vibration and instability of SWBNNTs are examined.

Ansari, R.; Norouzzadeh, A.; Gholami, R.; Faghih Shojaei, M.; Hosseinzadeh, M.

2014-07-01

349

Exact linearization of nonlinear differential algebraic systems

Describes an approach of exact linearization for single input nonlinear differential algebraic systems in general. The nonlinear differential algebraic control system being considered is not in state variable form. Some new definitions of M derivative and M bracket that are similar to the definitions of classic differential geometric theory and some related revised results are given. The definitions of M

Jie Wang; Chen Chen

2001-01-01

350

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

351

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.

Ferdinand Anayo Oguama

2003-01-01

352

Inflation from geometrical tachyons

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

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

2005-10-15

353

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

354

Geometrical output coupling method of harmonics in enhancement cavities

Geometrical access to an enhancement cavity is presented, that could be used for output coupling of harmonics. No dispersion or nonlinearity for the fundamental radiation is introduced. Small diffraction losses allow for a finesse >3000. OCIS codes: (070.5753) resonators; (140.7240) UV, EUV, and X-ray lasers

Johannes Weitenberg; Peter Rusbuldt; Ioachim Pupeza; Hans-Dieter Hoffmann; Reinhart Poprawe

2011-01-01

355

Geometric shape of invariant manifolds for a class of stochastic partial differential equations

Geometric shape of invariant manifolds for a class of stochastic partial differential equations dynamical behaviors for nonlinear stochas- tic partial differential equations. However, the geometric shape of invariant man- ifolds for a class of stochastic partial differential equations with multiplicative white

356

Complex geometric optics for symmetric hyperbolic systems I: linear theory

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

357

NASA Technical Reports Server (NTRS)

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.

Simitses, George J.; Carlson, Robert L.; Riff, Richard

1991-01-01

358

Some sound is absorbed Multiply bands by some absorption coefficient A[2] Coefficient is basedGeometric Sound Propagation Micah Taylor #12;Sound propagation Given a sound source in a scene arrive at the listener #12;Sound propagation Sound travels slow 344 m/s Specular reflections Perfect

North Carolina at Chapel Hill, University of

359

NASA Technical Reports Server (NTRS)

This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.

Ives, David

1995-01-01

360

ERIC Educational Resources Information Center

Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…

Burgess, Claudia R.

2014-01-01

361

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

362

LABORATORY I: GEOMETRIC OPTICS

Lab I - 1 LABORATORY I: GEOMETRIC OPTICS In this lab, you will solve several problems related to the formation of optical images. Most of us have a great deal of experience with the formation of optical images this laboratory, you should be able to: Â· Describe features of real optical systems in terms of ray diagrams

Minnesota, University of

363

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

364

Geometric Modelling Dagstuhl 2002

, simulation, and medical imaging, and it attracts researchers with backgrounds in computer science as well, Houston Editorial Geometric Modeling is the branch of Computer Science concerned with the efficient to the following diverse topics: Â· curve and surface modeling Â· non-manifold modeling in CAD Â· multiresolution

Hahmann, Stefanie

365

A new technique to compute invariant curves based on the method of formal series of Dubois-Violette has been developed. The solution of the Hamilton-Jacobi equation is represented as a ratio of two series in the perturbation parameter (and the nonlinear action invariant), rather than a conventional power series proposed by canonical perturbation theory. It is well behaved even for large values of the perturbation parameter not very close to strong resonances.

Tzenov, S.I. [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, boul. Tzarigradsko shosse 72, 1784 Sofia (Bulgaria)

1995-09-01

366

Metal nanoclusters of Ag, Au and Cu have been produced by ion implantation into x- and z-cut lithium niobate. MeV Ag implantation followed by heat treatment simultaneously produced a waveguide and Ag clusters with a high nonlinear index. Co-implantation of O with Ag at 500{degree} enhanced the ability of the clusters to withstand heat treatment. {copyright} {ital 1999 American Institute of Physics.}

Williams, E.K.; Ila, D. [Center for Irradiation of Materials, PO Box 1447 Alabama AM University, Normal, Alabama 35762 (United States); Sarkisov, S. [Department of Natural and Physical Sciences, Alabama AM University, Normal, Alabama 35762 (United States); Hensley, D.K. [Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)

1999-06-01

367

Metal nanoclusters of Ag, Au and Cu have been produced by ion implantation into x- and z-cut lithium niobate. MeV Ag implantation followed by heat treatment simultaneously produced a waveguide and Ag clusters with a high nonlinear index. Co-implantation of O with Ag at 500[degree] enhanced the ability of the clusters to withstand heat treatment. [copyright] [ital 1999 American Institute of Physics.

Williams, E.K.; Ila, D. (Center for Irradiation of Materials, PO Box 1447 Alabama AM University, Normal, Alabama 35762 (United States)); Sarkisov, S. (Department of Natural and Physical Sciences, Alabama AM University, Normal, Alabama 35762 (United States)); Hensley, D.K. (Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States))

1999-06-01

368

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

369

The fracture patterns of active elements of pulsed green lasers with transverse electron-beam pumping, based on ZnSe-containing quantum-size structures, have been investigated. The fracture in the form of thin (˜1 mum) and long (to 100-150 mum) filaments can be explained by the self-focusing of the intrinsic laser radiation in the semiconductor structure.

M. M. Zverev; V. O. Val'Dner; N. A. Gamov; R. V. Esin; S. I. Gronin; E. V. Zhdanova; S. V. Ivanov; P. S. Kop'ev; D. V. Peregoudov; I. V. Sedova; S. V. Sorokin; V. B. Studionov

2011-01-01

370

Geometrical aspects of quantum spaces

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

371

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

372

The hysteretic behavior of cantilever I-beam subjected to cyclic lateral loads is investigated in this paper. Finite Element Method (FEM) considering the geometrical and material non-linearities is utilized in this study. Special attention is paid to the effects of local buckling occurring in the flanges and the web, and the material work-hardening properties on the performance of I-beam in view of a seismic design considerations. The behavior of I-beam subjected to cyclic lateral loads is closely examined with respect to the ductility, strength and absorbed energy. From this study, it is found that smaller slenderness ratios of the flange and web are recommended for improving the ductility, strength and absorbed energy. Also, the material having lower yield-to-tensile strength improves the ductility of I-beam under cyclic lateral loads as well as monotonically increasing load.

Shaker, R.E.; Murakawa, Hidekazu; Ueda, Yukio [Osaka Univ. (Japan)

1993-12-31

373

Second-harmonic generation of limited diffraction beams

NASA Astrophysics Data System (ADS)

This paper presents an analytical result concerning second-harmonic generation of a general limited diffraction beam in nonlinear media. The result is based on quasilinear solutions of the Khokhlov-Zabolotskaya-Kuznetsov nonlinear wave equation. It is shown that second-harmonic generation by the nonlinear interaction of two arbitrary Bessel beams gives a nearly radially limited diffraction beam. For an arbitrary limited diffraction beam from the linear superposition of basis mode Bessel beams, results also indicate that the second-harmonic beam remains an almost radially or transversely limited diffraction beam.

Ding, Desheng; Huang, Jin H.

2007-12-01

374

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

375

Nonlinear vibrational microscopy

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

376

Confined energy distribution for charged particle beams

A charged particle beam is formed to a relatively larger area beam which is well-contained and has a beam area which relatively uniformly deposits energy over a beam target. Linear optics receive an accelerator beam and output a first beam with a first waist defined by a relatively small size in a first dimension normal to a second dimension. Nonlinear optics, such as an octupole magnet, are located about the first waist and output a second beam having a phase-space distribution which folds the beam edges along the second dimension toward the beam core to develop a well-contained beam and a relatively uniform particle intensity across the beam core. The beam may then be expanded along the second dimension to form the uniform ribbon beam at a selected distance from the nonlinear optics. Alternately, the beam may be passed through a second set of nonlinear optics to fold the beam edges in the first dimension. The beam may then be uniformly expanded along the first and second dimensions to form a well-contained, two-dimensional beam for illuminating a two-dimensional target with a relatively uniform energy deposition.

Jason, Andrew J. (Los Alamos, NM); Blind, Barbara (Los Alamos, NM)

1990-01-01

377

The classical geometrization electromagnetism

Following the line of the history, if by one side the electromagnetic theory was consolidated on the 19th century, the emergence of the special and the general relativity theories on the 20th century opened possibilities of further developments, with the search for the unification of the gravitation and the electromagnetism on a single unified theory. Some attempts to the geometrization of the electromagnetism emerged in this context, where these first models resided strictly on a classical basis. Posteriorly, they were followed by more complete and embracing quantum field theories. The present work reconsiders the classical viewpoint, with the purpose of showing that in a first order of approximation the electromagnetism constitutes a geometric structure aside other phenomena as gravitation. Even though being limited, the model is consistent and offers the possibility of an experimental test of validity.

C. A. Duarte

2015-02-11

378

MESHLESS GEOMETRIC SUBDIVISION Carsten Moenning

MESHLESS GEOMETRIC SUBDIVISION By Carsten Moenning Facundo MÂ´emoli Guillermo Sapiro Nira DynÂ0436 Phone: 612/624-6066 Fax: 612/626-7370 URL: http://www.ima.umn.edu #12;Meshless Geometric Subdivision by introducing the notion of meshless, or point cloud, geometric subdivision. Our meshless subdivision approach

Minnesota, University of

379

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.

Illuminations National Council of Teachers of Mathematics

2010-05-26

380

Geometric Solids and Their Properties

NSDL National Science Digital Library

Explore geometric solids and their properties with these interactive tools, beginning with an introduction to the faces of basic polyhedra; counting the number of faces, edges, and corners (vertices) in various solids; discovering Euler's Formula; constructing physical models of geometric solids; and identifying which geometric solids can be made from given nets.

Illuminations; National Council of Teachers of Mathematics (NCTM)

2000-01-01

381

Compatible Geometric Matchings

This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also non-crossing. Our first result states that for any two perfect matchings M and M0 of the same set of n points, for some k 2 O(logn), there is a sequence of perfect matchings M =

Oswin Aichholzer; Sergey Bereg; Adrian Dumitrescu; Alfredo García; Clemens Huemer; Ferran Hurtado; Mikio Kano; Alberto Márquez; David Rappaport; Shakhar Smorodinsky; Diane L. Souvaine; Jorge Urrutia; David R. Wood

2008-01-01

382

Geometrical theory of diffraction

Geometrical theory of diffraction (GTD) is an alternative model of diffraction propounded first by Thomas Young in 1802. GTD\\u000a has a long history of nearly 150 years over which many eminent people enriched this model which has now become an accepted\\u000a tool in the calculation of diffraction patterns. In the conventional Helmholtz-Kirchhoff theory the diffracted field is obtained\\u000a by computing

P B Sunil Kumar; G S Ranganath

1991-01-01

383

Random Geometric Identification

The practical problem can be described in the following way. Physical objects (credit cards, important documents) should be\\u000a identified using geometric labels. An optical device reads the label and a simple computation checks whether the label belongs\\u000a to the given object or not. This could be done by ”asking” an authority which stores certain data (e.g. the reading of the

Gyula O. H. Katona

2008-01-01

384

Acoustic nonlinearity in fluorinert FC-43

Fluorinert FC-43 nonlinearity was investigated using two approaches: (i) a finite amplitude method with harmonic production; and (ii) a nonlinear frequency mixing in the fluid with consequent beam profile measurement of the difference frequency. The finite amplitude method provides information on the coefficient of nonlinearity, {beta}, through the amplitudes of the fundamental and the second harmonic, at a certain transmitter-receiver distance. A calibrated hydrophone was used as a receiver, in order to obtain direct pressure measurements of the acoustic waves in the fluid. The role of transmitter-receiver distance in {beta} determination is investigated. In the second approach, a single transducer is used to provide two high-frequency beams. The collinear high-frequency beams mix nonlinearly in the fluid resulting in a difference frequency beam and higher order harmonics of the primaries. The difference frequency beam profite is investigated at lengths beyond the mixing distance. The experimental data are compured with the KZK theory.

Pantea, Cristian [Los Alamos National Laboratory; Sinha, Dipen N [Los Alamos National Laboratory; Osterhoudt, Curtis F [Los Alamos National Laboratory; Mombourquette, Paul C [Los Alamos National Laboratory

2009-01-01

385

Simulation of Geometrical Longitudinal Impedance of the TCDS diluter

The results of wake-field simulations to estimate the geometrical longitudinal impedance of the TCDS are presented. This impedance is related to the shape and not to the ohmic losses of the surface. In particular, the contribution from the end transitions of the beam absorber blocks is calculated. Moreover, power loss due to the presence of trapped modes in the transitions is estimated.

Grudiev, A

2006-01-01

386

Geometrical Wake of a Smooth Flat Collimator

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

387

Geometric phase in Bohmian mechanics

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

388

Nonlinearity and self-interaction in physical field theories with singularities

We investigate rigorous mathematical modeling of nonlinear problems in physical field theories involving differential geometric objects with singularities. We intend to develop a framework allowing for an unrestricted application of a large class of nonlinear operations to geometric objects, in particular tensor fields representing physical quantities arising in classical electrodynamics and general relativity. A convenient setting for this kind of

G. Hörmann; M. Kunzinger

1998-01-01

389

Nonlinear left-handed metamaterials

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

2004-10-27

390

Representing geometrical knowledge.

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

391

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

392

Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups and automata lead to simplifications of the graphs on which the corresponding finite semigroups act. We show in particular that every finite semigroup can be finitely expanded so that the expansion acts on a labeled directed graph which resembles the right Cayley graph of a free Burnside semigroup in many respects.

McCammond, Jon; Steinberg, Benjamin

2011-01-01

393

Observation of the geometric spin Hall effect of light.

The spin Hall effect of light (SHEL) is the photonic analogue of the spin Hall effect occurring for charge carriers in solid-state systems. This intriguing phenomenon manifests itself when a light beam refracts at an air-glass interface (conventional SHEL) or when it is projected onto an oblique plane, the latter effect being known as the geometric SHEL. It amounts to a polarization-dependent displacement perpendicular to the plane of incidence. In this work, we experimentally investigate the geometric SHEL for a light beam transmitted across an oblique polarizer. We find that the spatial intensity distribution of the transmitted beam depends on the incident state of polarization and its centroid undergoes a positional displacement exceeding one wavelength. This novel phenomenon is virtually independent from the material properties of the polarizer and, thus, reveals universal features of spin-orbit coupling. PMID:24702371

Korger, Jan; Aiello, Andrea; Chille, Vanessa; Banzer, Peter; Wittmann, Christoffer; Lindlein, Norbert; Marquardt, Christoph; Leuchs, Gerd

2014-03-21

394

Indentation resistance of sandwich beams

High-order sandwich beam theory is used to model the local deformation under the central indentor for sandwich beams loaded under three-point bending. `High-order' refers to the non-linear variations of in-plane and vertical displacements through the height of the core which the model incorporates. The analysis is elastic, which is appropriate to describe the beam response up to peak load for

A. Petras; M. P. F. Sutcliffe

1999-01-01

395

Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

Bloembergen, Nicolaas

1996-01-01

396

Ion-beam Plasma Neutralization Interaction Images

Neutralization of the ion beam charge and current is an important scientific issue for many practical applications. The process of ion beam charge and current neutralization is complex because the excitation of nonlinear plasma waves may occur. Computer simulation images of plasma neutralization of the ion beam pulse are presented.

Igor D. Kaganovich; Edward Startsev; S. Klasky; Ronald C. Davidson

2002-04-09

397

Geometric and topological approaches to significance testing in wavelet analysis

NASA Astrophysics Data System (ADS)

Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, i.e., contiguous regions of significant wavelet power coefficients with respect to some noise model. This geometric significance test was found to produce results similar to an existing areawise significance test while being more computationally flexible and efficient. The geometric significance test can be readily applied to pointwise significance patches at various pointwise significance levels in wavelet power and coherence spectra. The geometric test determined that features in wavelet power of the North Atlantic Oscillation (NAO) are indistinguishable from a red-noise background, suggesting that the NAO is a stochastic, unpredictable process, which could render difficult the future projections of the NAO under a changing global system. The geometric test did, however, identify features in the wavelet power spectrum of an El Niño index (Niño 3.4) as distinguishable from a red-noise background. A topological analysis of pointwise significance patches determined that holes, deficits in pointwise significance embedded in significance patches, are capable of identifying important structures, some of which are undetected by the geometric and areawise tests. The application of the topological methods to ideal time series and to the time series of the Niño 3.4 and NAO indices showed that the areawise and geometric tests perform similarly in ideal and geophysical settings, while the topological methods showed that the Niño 3.4 time series contains numerous phase-coherent oscillations that could be interacting nonlinearly.

Schulte, J. A.; Duffy, C.; Najjar, R. G.

2015-03-01

398

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

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

399

Manifestation of the geometric phase in neutron spin-echo experiments

We show how the geometric (Berry's) phase becomes manifest on adiabatic rotation of the polarization vector in the magnetic field configuration in the arms in a neutron spin echo (NSE) experiment. When the neutron beam used is monochromatic, a geometric phase collected in one spin-echo arm can be exactly compensated in the other arm either by an opposite geometrical rotation or by adding/subtracting a dynamic (Larmor) phase. This is not possible in a white beam, because, contrary to the dynamic phase, the geometric phase is independent of wavelength. Therefore, the NSE pattern can be disturbed. We demonstrate that adiabatic resonant spin flippers inherently produce a geometric phase which can influence the performance of NSE setups based on such flippers. This effect can be avoided by a proper mutual symmetry of the gradient fields in these flippers.

Kraan, W. H.; Rekveldt, M. T. [Department R3, Faculty of Applied Sciences, Delft University of Technology, 2629 JB Delft (Netherlands); Grigoriev, S. V. [Department R3, Faculty of Applied Sciences, Delft University of Technology, 2629 JB Delft (Netherlands); Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300 (Russian Federation)

2010-07-15

400

Nonlinear dynamics experiments

The goal of nonlinear dynamics experiments is to improve the understanding of single particle effects that increase the particle amplitude and lead to loss. Particle motion in storage rings is nearly conservative and for transverse dynamics the Hamiltonian in action angle variables (I{sub x},I{sub y},{phi}{sub x},{phi}{sub y}) near an isolated resonance k{nu}{sub x} + l{nu}{sub y} {approx} p is H = I{sub x}{nu}{sub x0} + I{sub y}{nu}{sub y0} + g(I{sub x}, I{sub y}) + h(I{sub x}, I{sub y})cos(k{phi}{sub x} + l{phi}{sub y} - p{theta}), (1) where k, l, p are integers, {theta} = 2{pi}s/L is the azimuth, and s and L are the path length and circumference respectively. The amplitude dependent tunes are given by {nu}{sub x,y}(I{sub x},I{sub y}) = {nu}{sub x0,y0} + {partial_derivative}g(I{sub x},I{sub y})/{partial_derivative}I{sub x,y} (2) and h(I{sub x},I{sub y}) is the resonance driving term (RDT). If the motion is governed by multiple resonances, h(I{sub x},I{sub y}) has to be replace by a series of terms. The particle motion is completely determined by the terms g and h, which can be calculated from higher order multipoles (Sec. ??), or obtained from simulations. Deviations from pure Hamiltonian motion occur due to synchrotron radiation damping (Sec. ??) in lepton or very high energy hadron rings, parameter variations, and diffusion processes such as residual gas and intrabeam scattering. The time scale of the non-Hamiltonian process determines the applicability of the Hamiltonian analysis. Transverse nonlinearities are introduced through sextupoles or higher order multipoles and magnetic field errors in dipoles and quadrupoles. Sextupoles can already drive all resonances. The beam-beam interaction and space charge also introduce nonlinear fields. Intentionally introduced nonlinearities are used to extract beam on a resonance or through capture in stable islands. Localization and minimization of nonlinearities in a ring is a general strategy to decrease emittance growth and increase the beam lifetime. The minimization of nonlinear effects can be done locally or globally. Except for resonant extraction, amplitude increase and particle loss is the result of chaotic particle motion. Large chaotic regions allow particles to increase their amplitudes, and ensures their ultimate loss. However, chaotic particles can, on average, still survive the time period of interest, i.e. the storage time. Nonlinear dynamics experiments aim to determine either the detuning and driving terms g and h directly, or their effect on other quantities. Nonlinear phenomena observed in experiments include phase space deformations and resonant islands in Poincare surfaces of section, nonlinear phase advances, amplitude detuning g, decoherence (Sec. ??), resonance driving terms h, smear, halo formation, echoes (Sec. ??), the tune response matrix, dynamic aperture (Sec. ??), emittance growth, and particle loss. Nonlinear experiments can also be done in the longitudinal plane.

Fischer, W.

2011-01-01

401

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

402

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

403

Chiral symmetry breaking as a geometrical process

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

404

Nonlinear analysis of smart composite plate and shell structures

and used to study vibration/deflection suppression characteristics of plate and shell structures. The von K??rm??n type geometric nonlinearity is included in the formulation. Third-order shear deformation theory based on Donnell and Sanders nonlinear shell...

Lee, Seung Joon

2005-08-29

405

Error detection and control for nonlinear shell analysis

NASA Technical Reports Server (NTRS)

A problem-adaptive solution procedure for improving the reliability of finite element solutions to geometrically nonlinear shell-type problem is presented. The strategy incorporates automatic error detection and control and includes an iterative procedure which utilizes the solution at the same load step on a more refined model. Representative nonlinear shell problem are solved.

Mccleary, Susan L.; Knight, Norman F., Jr.

1990-01-01

406

Nonlinear Wave Mixing at Hybrid Frequencies in an Inhomogeneous Plasma

The nonlinear coupling of waves near the hybrid resonances for a magnetized inhomogeneous plasma is investigated. In this case, the geometric optics approximation is no longer valid and the full wave equations must be used. In contrast to the homogeneous plasma treatment no synchronism relation for the propagation vectors occurs and nonlinear processes are possible which are absent in the

I. Fidone; G. Granata; J. Teichmann

1971-01-01

407

AIAA-99-1470 NONLINEAR AEROELASTICITY AND FLIGHT

.2 ONERA stall model was used for aerodynamic loads. Tang and Dowell have studied the flutter and forced response of a flexible rotor blade.3 In this study, geometrical structural nonlinearity and free-play struc- tural nonlinearity is taken into consideration. Again, high-angle-of-attack unsteady aerodynamics

Patil, Mayuresh

408

Circle actions in geometric quantisation

NASA Astrophysics Data System (ADS)

The aim of this article is to present unifying proofs for results in geometric quantisation with real polarisations by exploring the existence of symplectic circle actions. It provides an extension of Rawnsley's results on the Kostant complex, and gives a partial result for the focus-focus contribution to geometric quantisation; as well as, an alternative proof for theorems of ?niatycki and Hamilton.

Solha, Romero

2015-01-01

409

Computational Topology for Geometric Design

"mi03 2005/ page i i i i i i i i Computational Topology for Geometric Design and Molecular Design Edward L. F. Moore , Thomas J. Peters Abstract The nascent field of computational topology holds great. Commercial CAGD packages depend upon complementary geometric and topological algorithms. The emergence of geo

Peters, Thomas J.

410

Solitary waves in particle beams

Since space charge waves on a particle beam exhibit both dispersive and nonlinear character, solitary waves or solitons are possible. Dispersive, nonlinear wave propagation in high current beams is found to be similar to ion-acoustic waves in plasmas with an analogy between Debye screening and beam pipe shielding. Exact longitudinal solitary wave propagation is found for potentials associated with certain transverse distributions which fill the beam pipe. For weak dispersion, the waves satisfy the Korteweg-deVries (KdV) equation, but for strong dispersion they exhibit breaking. More physically realizable distributions which do not fill the beam pipe are investigated and shown to also satisfy a KdV equation for weak dispersion if averaging over rapid transverse motion is physically justified. Scaling laws are presented to explore likely parameter regimes where these phenomena may be observed experimentally.

Bisognano, J.J. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

1996-07-01

411

Auto calibration of a cone-beam-CT

Purpose: This paper introduces a novel autocalibration method for cone-beam-CTs (CBCT) or flat-panel CTs, assuming a perfect rotation. The method is based on ellipse-fitting. Autocalibration refers to accurate recovery of the geometric alignment of a CBCT device from projection images alone, without any manual measurements. Methods: The authors use test objects containing small arbitrarily positioned radio-opaque markers. No information regarding the relative positions of the markers is used. In practice, the authors use three to eight metal ball bearings (diameter of 1 mm), e.g., positioned roughly in a vertical line such that their projection image curves on the detector preferably form large ellipses over the circular orbit. From this ellipse-to-curve mapping and also from its inversion the authors derive an explicit formula. Nonlinear optimization based on this mapping enables them to determine the six relevant parameters of the system up to the device rotation angle, which is sufficient to define the geometry of a CBCT-machine assuming a perfect rotational movement. These parameters also include out-of-plane rotations. The authors evaluate their method by simulation based on data used in two similar approaches [L. Smekal, M. Kachelriess, S. E, and K. Wa, 'Geometric misalignment and calibration in cone-beam tomography,' Med. Phys. 31(12), 3242-3266 (2004); K. Yang, A. L. C. Kwan, D. F. Miller, and J. M. Boone, 'A geometric calibration method for cone beam CT systems,' Med. Phys. 33(6), 1695-1706 (2006)]. This allows a direct comparison of accuracy. Furthermore, the authors present real-world 3D reconstructions of a dry human spine segment and an electronic device. The reconstructions were computed from projections taken with a commercial dental CBCT device having two different focus-to-detector distances that were both calibrated with their method. The authors compare their reconstruction with a reconstruction computed by the manufacturer of the CBCT device to demonstrate the achievable spatial resolution of their calibration procedure. Results: Compared to the results published in the most closely related work [K. Yang, A. L. C. Kwan, D. F. Miller, and J. M. Boone, 'A geometric calibration method for cone beam CT systems,' Med. Phys. 33(6), 1695-1706 (2006)], the simulation proved the greater accuracy of their method, as well as a lower standard deviation of roughly 1 order of magnitude. When compared to another similar approach [L. Smekal, M. Kachelriess, S. E, and K. Wa, 'Geometric misalignment and calibration in cone-beam tomography,' Med. Phys. 31(12), 3242-3266 (2004)], their results were roughly of the same order of accuracy. Their analysis revealed that the method is capable of sufficiently calibrating out-of-plane angles in cases of larger cone angles when neglecting these angles negatively affects the reconstruction. Fine details in the 3D reconstruction of the spine segment and an electronic device indicate a high geometric calibration accuracy and the capability to produce state-of-the-art reconstructions. Conclusions: The method introduced here makes no requirements on the accuracy of the test object. In contrast to many previous autocalibration methods their approach also includes out-of-plane rotations of the detector. Although assuming a perfect rotation, the method seems to be sufficiently accurate for a commercial CBCT scanner. For devices which require higher dimensional geometry models, the method could be used as a initial calibration procedure.

Gross, Daniel; Heil, Ulrich; Schulze, Ralf; Schoemer, Elmar; Schwanecke, Ulrich [Department of Design, Computer Science and Media, RheinMain University of Applied Sciences, 65195 Wiesbaden, Germany and Institute of Computer Science, Johannes Gutenberg University Mainz, 55128 Mainz (Germany); Department of Oral Surgery (and Oral Radiology), University Medical Center of the Johannes Gutenberg University Mainz, 55131 Mainz (Germany); Institute of Computer Science, Johannes Gutenberg University Mainz, 55128 Mainz (Germany); Department of Design, Computer Science and Media, RheinMain University of Applied Sciences, 65195 Wiesbaden (Germany)

2012-10-15

412

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

413

Optimization of biotechnological systems through geometric programming

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

414

Free-space propagation of second harmonic beams carrying optical vortices

A vorticity of free propagating SH beam produced in nonlinear crystal by combined beam composed of two coaxial Laguerre–Gaussian vortex beams is analyzed. It is revealed that the vortical structures of SH beam in the near and far fields are different when two vortex beams are carrying vortices with topological charges of different signs. The diffraction of SH beam under

S. Orlov; K. Regelskis; V Smilgevi?ius; A. Stabinis

2003-01-01

415

An algorithm for the topology optimization of geometrically nonlinear structures

and Senne [6], Sigmund [7], Kikuchi et al. [8], Nishiwaki et al. [9]) and the Sequential Quadratic those written by Jog [12], Buhl, Pedersen and Sigmund [13], Bruns and Tortorelli [14], Gea and Luo [15], Bruns, Sigmund and Tortorelli [16], Ohsaki and Nishiwaki [17], Luo and Tong [18], Lazarov, Schevenels

Gomes, Francisco A. M.

416

Diffractive Nonlinear Geometrical Optics for Variational Wave Equations

, and INFN-Gruppo c. Cosenza AND John K. Hunter University of California at Davis Abstract We derive Wiley Periodicals, Inc. #12;2 G. AL`i AND J. K. HUNTER The Einstein equations may be derived from the Hunter-Saxton equation (2.12), (1.1) av + 1 2 a2 + Na = 1 2 a2 - a2 , where the angular brackets

Hunter, John K.

417

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

418

A Geometric Approach to Nonlinear Fault Detection and Isolation

-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

419

Regular and chaotic oscillations of a Timoshenko beam subjected to mechanical and thermal loadings

NASA Astrophysics Data System (ADS)

Dynamics of a Timoshenko beam under an influence of mechanical and thermal loadings is analysed in this paper. Nonlinear geometrical terms and a nonuniform heat distribution are taken into account in the considered model. The mathematical model is represented by a set of partial differential equations (PDEs) which takes into account thermal and mechanical loadings. The problem is simplified to two PDEs and then reduced to ordinary differential equations (ODEs) by means of the Galerkin method taking into account three modes of a linear Timoshenko beam. Correctness of the analytical model is verified by a finite element method. Then, the nonlinear model is studied numerically by a continuation method or by a direct numerical integration of ODEs. An effect of the temperature distribution on the resonance near the first natural frequency and on stability of the solutions is presented. The increase of mechanical loading results in hardening of the resonance curve. Thermal loading may stabilise the beam dynamics when the temperature is decreased. The elevated temperature may transit dynamics from regular to chaotic oscillations.

Warminska, Anna; Manoach, Emil; Warminski, Jerzy; Samborski, Sylwester

2014-08-01

420

November 2007, Orsay Geometrical Frustration 1/21 GeometricalGeometrical FrustrationFrustration

3d N=4 U ~ -7 e U ~ -9 e N=5 #12;November 2007, Orsay Geometrical Frustration 9/21 PackingPacking Triangles : non frustrated case Pentagons : frustrated case Geometrical Frustration ! Possible extension tetrahedra - Local icosahedral coordination - Dense sphere packing Coxeter helices Symmetry group of order

Paris-Sud 11, UniversitÃ© de

421

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

Sinitsyn, Nikolai [Los Alamos National Laboratory

2008-01-01

422

Compatible Geometric Matchings

This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are \\emph{compatible} if they have the same vertex set and their union is also non-crossing. Our first result states that for any two perfect matchings $M$ and $M'$ of the same set of $n$ points, for some $k\\in\\Oh{\\log n}$, there is a sequence of perfect matchings $M=M_0,M_1,...,M_k=M'$, such that each $M_i$ is compatible with $M_{i+1}$. This improves the previous best bound of $k\\leq n-2$. We then study the conjecture: \\emph{every perfect matching with an even number of edges has an edge-disjoint compatible perfect matching}. We introduce a sequence of stronger conjectures that imply this conjecture, and prove the strongest of these conjectures in the case of perfect matchings that consist of vertical and horizontal segments. Finally, we prove that every perfect matching with $n$ edges has an edge-disjoint compatible matching with approximately $3n/4$ edges.

Aichholzer, Oswin; Dumitrescu, Adrian; García, Alfredo; Huemer, Clemens; Hurtado, Ferran; Kano, Mikio; Márquez, Alberto; Smorodinsky, Shakhar; Souvaine, Diane; Urrutia, Jorge; Wood, David R

2007-01-01

423

[Geometrical property of navigation].

There is a tendency that a blind or a blind-folded subject fails to return to a starting point within the range of errors when he or she walks to a place, next turns to right or left, and then comes back to the starting point. We studied this tendency from a non-Euclidean geometrical point of view. In Experiment 1, total of 28 blind-folded subjects walked to construct a square, a regular triangle and a circle. The result showed that the location of the final reaching point was on the fronto-right side of the starting point in the square and triangle conditions and went over the starting point in the circle condition. In Experiment 2, 15 subjects judged visual properties (angles and distances) of a triangle and constructed the triangle by walking. The walking loci were compared with the visual properties. It was found that the walking loci were curved, differing from the visual properties. These results implied that the walking loci agree with the nature of elliptic geometry. PMID:14584253

Watanabe, Toshio

2003-08-01

424

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

425

Ring for test of nonlinear integrable optics

Nonlinear optics is a promising idea potentially opening the path towards achieving super high beam intensities in circular accelerators. Creation of a tune spread reaching 50% of the betatron tune would provide strong Landau damping and make the beam immune to instabilities. Recent theoretical work has identified a possible way to implement stable nonlinear optics by incorporating nonlinear focusing elements into a specially designed machine lattice. In this report we propose the design of a test accelerator for a proof-of-principle experiment. We discuss possible studies at the machine, requirements on the optics stability and sensitivity to imperfections.

Valishev, A.; Nagaitsev, S.; Kashikhin, V.; /Fermilab; Danilov, V.; /SNS Project, Oak Ridge

2011-03-01

426

This paper presents the development and applications of the finite element software, NASAB, which can be used for linear, geometrically nonlinear, and materially nonlinear analyses of structure and nonlinear aerostatic stability analysis of cable-supported bridges. The software program consists of two main parts: a programming part and a computational part. The windows programming part written in FORTRAN90 was designed mainly

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

2003-01-01

427

Controlling Second Harmonic Efficiency of Laser Beam Interactions

NASA Technical Reports Server (NTRS)

A method is provided for controlling second harmonic efficiency of laser beam interactions. A laser system generates two laser beams (e.g., a laser beam with two polarizations) for incidence on a nonlinear crystal having a preferred direction of propagation. Prior to incidence on the crystal, the beams are optically processed based on the crystal's beam separation characteristics to thereby control a position in the crystal along the preferred direction of propagation at which the beams interact.

Barnes, Norman P. (Inventor); Walsh, Brian M. (Inventor); Reichle, Donald J. (Inventor)

2011-01-01

428

Repeating Decimals and Geometric Series

NSDL National Science Digital Library

This activity begins by reviewing conversions between fractions and decimals with an emphasis on repeating decimals. The formula for the partial sum of a geometric series is bypassed and students are directed to use find partial sums by using the “multiply, subtract, and solve” technique which mimics the derivation of the formula for the partial sum of a geometric series. This sets the stage for students to quickly find the fraction representation of a repeating decimal number. This activity would be well-suited as a prelude to introducing infinite and partial sums of geometric sequences.

2011-01-01

429

Optical traps with geometric aberrations

We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems.

Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G

2006-05-20

430

Optical traps with geometric aberrations.

We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems. PMID:16708086

Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G

2006-05-20

431

Antenna with Dielectric Having Geometric Patterns

NASA Technical Reports Server (NTRS)

An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.

Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)

2013-01-01

432

Numerical Simulation of Beam-Beam Effects in the Proposed Electron-Ion Colider at Jefferson Lab

One key limiting factor to a collider luminosity is beam-beam interactions which usually can cause serious emittance growth of colliding beams and fast reduction of luminosity. Such nonlinear collective beam effect can be a very serious design challenge when the machine parameters are pushed into a new regime. In this paper, we present simulation studies of the beam-beam effect for a medium energy ring-ring electron-ion collider based on CEBAF.

Balsa Terzic, Yuhong Zhang

2010-05-01

433

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

434

NASA Astrophysics Data System (ADS)

Numerical results on the response of a flexible rotor supported by nonlinear active magnetic bearings are presented. Nonlinearity arising from the magnetic actuator forces that are nonlinear functions of the coil current and the air gap between the rotor and the stator, and from the geometric coupling of the magnetic actuators is incorporated into the mathematical model of the flexible rotor - active magnetic bearing system. For relatively large values of the geometric coupling parameter, the response of the rotor with the variation of the speed parameter within the range 0.05 lesseqgtr ? lesseqgtr 5.0 displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of periods -2, -3, -6, -9, and -17, quasi-periodicity and chaos. Numerical results also reveal the occurrence of bi-stable operation within certain ranges of the speed parameter where multiple attractors may co-exist at the same speed parameter value depending on the operating speed of the rotor.

Inayat-Hussain, J. I.

2008-02-01

435

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

436

Property Testing with Geometric Queries

This paper investigates geometric problems in the context of property testing algorithms. Property testing is an emerging area in computer science in which one is aiming at verifying whether a given object has a predetermined property or is \\

Artur Czumaj; Christian Sohler

2001-01-01

437

The promise of geometric morphometrics

Nontraditional or geometric morphomet- ric methods have found wide application in the biological sciences, especially in anthropology, a field with a strong history of measurement of biological form. Controversy has arisen over which method is the \\

Joan T. Richtsmeier; Valerie Burke Deleon; Subhash R. Lele

2002-01-01

438

Geometrical optics in general relativity

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

439

Hidden symmetry and nonlinear paraxial atom optics

A hidden symmetry of the nonlinear wave equation is exploited to analyze the propagation of paraxial and uniform atom-laser beams in time-independent and quadratic transverse potentials with cylindrical symmetry. The quality factor and the paraxial ABCD formalism are generalized to account exactly for mean-field interaction effects in such beams. Using an approach based on moments, these theoretical tools provide a simple yet exact picture of the interacting beam profile evolution. Guided atom laser experiments are discussed. This treatment addresses simultaneously optical and atomic beams in a unified manner, exploiting the formal analogy between nonlinear optics, nonlinear paraxial atom optics, and the physics of two-dimensional Bose-Einstein condensates.

Impens, Francois [SYRTE, Observatoire de Paris, CNRS, 61 Avenue de l'Observatoire, 75014 Paris (France) and Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, RJ (Brazil)

2009-12-15

440

Algorithms of NCG geometrical module

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., E-mail: prianik@adis.vver.kiae.ru [National Research Centre Kurchatov Institute (Russian Federation)

2012-12-15

441

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

442

Geometric phases in astigmatic optical modes of arbitrary order

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

443

NASA Astrophysics Data System (ADS)

It was in the early 1960s, immediately after the development of the ruby and the helium-neon lasers that the first observations were made of optical harmonics, two-photon absorption, stimulated Raman and Brillouin scattering, and self-trapping and focusing of laser beams. This was an exciting period for nonlinear optics, and Charles Townes and his students and collaborators were major players in the exploration of this field of research. The author briefly reviews some aspects of this group's contributions.

Stoicheff, B. P.

444

Nonlinear optical protection against frequency agile lasers

An eye-protection or equipment-filter device for protection from laser energy is disclosed. The device may be in the form of a telescope, binoculars, goggles, constructed as part of equipment such as image intensifiers or range designators. Optical elements focus the waist of the beam within a nonlinear frequency-doubling crystal or nonlinear optical element or fiber. The nonlinear elements produce a harmonic outside the visible spectrum in the case of crystals, or absorb the laser energy in the case of nonlinear fibers. Embodiments include protectors for the human eye as well as filters for sensitive machinery such as TV cameras, FLIR systems or other imaging equipment.

McDowell, V.P.

1988-08-04

445

Evolution of an Airy beam in a saturated medium

NASA Astrophysics Data System (ADS)

The nonlinear dynamics of an Airy beam in a saturated medium is presented. An analytical expression for the evolution of the Airy beam width in the root-mean-square sense is derived. The novel features of the collapsing beams of an Airy beam in a saturated medium are demonstrated by numerical calculation. These collapsing beams shift laterally and are the main property of the Airy beam. However, the collapsing beam in the major lobe of an Airy beam tends to shift in the opposite direction for conservation of the beam centroid. The location and evolution of the collapsing beams depend strongly on the initial powers. The peak intensities of the collapsing beams oscillate at almost the same intensity in the saturated medium, regardless of their initial powers. These results are useful for manipulating nonlinear wave collapse and multi-filamentation.

Chen, Rui-Pin; Chew, Khian-Hooi; Zhao, Ting-Yu; Li, Pei-Gang; Li, Chao-Rong

2014-11-01

446

Nonlinear Magnetohydrodynamics

Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas.The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are

V. Shafranov

1998-01-01

447

Noncollinear interaction of optical vortices in Kerr nonlinear medium

The noncollinear interaction of singular light beams (degenerate four-wave mixing) in Kerr nonlinear medium is analyzed. It is demonstrated that vorticity of diffracted beams significantly depends on the topological charges of pump beams. The results of an experimental observation of the phenomenon are presented.

V. Pyragaite; K. Regelskis; V. Smilgevicius; A. Stabinis

2001-01-01

448

Multiscale geometric modeling of macromolecules I: Cartesian representation

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

449

Multiscale geometric modeling of macromolecules I: Cartesian representation

NASA Astrophysics Data System (ADS)

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.

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

2014-01-01

450

Multiscale geometric modeling of macromolecules I: Cartesian representation

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.

Xia, Kelin [Department of Mathematics, Michigan State University, MI 48824 (United States)] [Department of Mathematics, Michigan State University, MI 48824 (United States); Feng, Xin [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States)] [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Chen, Zhan [Department of Mathematics, Michigan State University, MI 48824 (United States)] [Department of Mathematics, Michigan State University, MI 48824 (United States); Tong, Yiying [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States)] [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Mathematics, Michigan State University, MI 48824 (United States) [Department of Mathematics, Michigan State University, MI 48824 (United States); Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824 (United States)

2014-01-15