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1

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

NASA Technical Reports Server (NTRS)

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

Ragon, S.; Gurdal, Z.

1993-01-01

2

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

NASA Astrophysics Data System (ADS)

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

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

2013-09-01

3

RETRACTED: Dynamic analysis of geometrically nonlinear and electrostatically actuated micro-beams  

NASA Astrophysics Data System (ADS)

This article has been retracted at the request of the Editor-in-Chief and Author. Please see Elsevier Policy on Article Withdrawal ( http://www.elsevier.com/locate/withdrawalpolicy). The authors of the article titled "Dynamic analysis of geometrically nonlinear and electrostatically actuated micro-beams", Drs. M.T. Ahmadian, H. Borhan, and E. Esmailzadeh, wish to formally retract their article from the Communications in Nonlinear Science and Numerical Simulation, Volume 14, Issue 4, 2009, 1627-1645, doi: 10.1016/j.cnsns.2008.01.006 as it contains fundamental mistakes in the content of that paper. The authors apologize for their oversight that led to this situation.

Ahmadian, M. T.; Borhan, H.; Esmailzadeh, E.

2009-04-01

4

Geometrical nonlinear analysis of thin-walled composite beams using finite element method based on first order shear deformation theory  

Microsoft Academic Search

Based on a seven-degree-of-freedom shear deformable beam model, a geometrical nonlinear analysis of thin-walled composite\\u000a beams with arbitrary lay-ups under various types of loads is presented. This model accounts for all the structural coupling\\u000a coming from both material anisotropy and geometric nonlinearity. The general nonlinear governing equations are derived and\\u000a solved by means of an incremental Newton–Raphson method. A displacement-based

Thuc Phuong Vo; Jaehong Lee

2011-01-01

5

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

PubMed

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

6

Smart damping of geometrically nonlinear vibrations of laminated composite beams using vertically reinforced 1-3 piezoelectric composites  

NASA Astrophysics Data System (ADS)

This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated composite beams using vertically reinforced 1-3 piezoelectric composite material as the material of the constraining layer of the ACLD treatment. A nonlinear finite element model has been developed for analyzing the ACLD of laminated symmetric and antisymmetric cross-ply and angle-ply composite beams integrated with such ACLD treatment. The von Kármán-type nonlinear strain-displacement relations and the first-order shear deformation theory are used for deriving this coupled electromechanical nonlinear finite element model. The Golla-Hughes-McTavish (GHM) method has been used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. The backbone curves of such a class of nonlinear systems are plotted to determine the excitation levels for causing geometrical nonlinearity. The numerical results reveal that the ACLD treatment significantly improves the damping characteristics of the cross-ply and antisymmetric angle-ply beams for suppressing the geometrically nonlinear transient vibrations of the beams.

Sarangi, S. K.; Ray, M. C.

2010-07-01

7

On the predictability of elasto-plastic and geometrically non-linear oscillations of beams under harmonic excitation  

Microsoft Academic Search

Vibrations in one plane of beams with fixed ends, vibrating in the geometrically non-linear and elasto-plastic regimes under\\u000a the influence of harmonic external forces, are studied. A p-version finite element that considers transverse and longitudinal displacements, as well as shear deformation, is employed.\\u000a The incremental theory of plasticity with isotropic hardening is followed. Numerical methods are employed to solve the

P. Ribeiro

8

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

NASA Astrophysics Data System (ADS)

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

Silwal, Baikuntha

9

Complete geometric nonlinear formulation for rigid-flexible coupling dynamics  

Microsoft Academic Search

A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall\\u000a motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were\\u000a included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated.\\u000a Numerical results show that the use of

Zhu-yong Liu; Jia-zhen Hong; Jin-yang Liu

2009-01-01

10

Geometric stiffening effect on rigid-flexible coupling dynamics of an elastic beam  

Microsoft Academic Search

In the previous work, the authors examined the effect of the geometric stiffness terms on the stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the geometrically non-linear formulations to an elastic beam with free large overall motions. The equations of motion are derived taking into account the foreshortening deformation

J. Y. Liu; J. Z. Hong

2004-01-01

11

Classical light beams and geometric phases.  

PubMed

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

Mukunda, N; Chaturvedi, S; Simon, R

2014-06-01

12

Nonlinear forced vibration analysis of clamped functionally graded beams  

Microsoft Academic Search

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

A. Shooshtari; M. Rafiee

13

Nonlinear Geometric Approach to Fault Detection and Isolation in an Aircraft Nonlinear Longitudinal Model  

Microsoft Academic Search

In this paper, aircraft actuator fault detection and isolation (FDI) is investigated and designed using a nonlinear geometric FDI approach based on a nonlinear longitudinal aircraft model. Two detection filters are designed for the throttle position and the elevator angle, respectively, which are the two main actuation signals in the longitudinal aircraft model. In nonlinear geometric FDI approach the objective

N. Meskin; T. Jiang; E. Sobhani; K. Khorasani; C. A. Rabbath

2007-01-01

14

Nonlinear behavior of geometric phases induced by photon pairs  

SciTech Connect

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

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

2011-06-15

15

Bounding solutions of geometrically nonlinear viscoelastic problems  

NASA Technical Reports Server (NTRS)

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.; Simitses, G. J.

1986-01-01

16

Bounding solutions of geometrically nonlinear viscoelastic problems  

NASA Technical Reports Server (NTRS)

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.; Simitses, G. J.

1985-01-01

17

Nonlinear and Geometric Programming - Current Status  

Microsoft Academic Search

Great strides have been made in nonlinear programming (NLP) in the last 5 years. In smooth NLP, there are now several reliable and efficient codes capable of solving large problems. Most of these implement GRG or SQP methods, and new software using interior point algorithms is under development. NLP software is now much easier to use, as it is interfaced

Leon Lasdon

2001-01-01

18

A geometric framework for nonlinear visual coding  

NASA Astrophysics Data System (ADS)

It is argued that important aspects of early and middle level visual coding may be understood as resulting from basic geometric processing of the visual input. The input is treated as a hypersurface defined by image intensity as a function of two spatial coordinates and time. Analytical results show how the Riemann curvature tensor R of this hypersurface represents speed and direction of motion. Moreover, the results can predict the selectivity of MT neurons for multiple motions and for motion in a direction along the optimal spatial orientation. Finally, a model based on integrated R components predicts global-motion percepts related to the barber-pole illusion.

Barth, Erhardt; Watson, Andrew B.

2000-08-01

19

Nonlinear geometric effects in mechanical bistable morphing structures.  

PubMed

Bistable structures associated with nonlinear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects on bistability remain elusive. We demonstrate, through both theoretical analysis and tabletop experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells. PMID:23005634

Chen, Zi; Guo, Qiaohang; Majidi, Carmel; Chen, Wenzhe; Srolovitz, David J; Haataja, Mikko P

2012-09-14

20

The Analysis of Geometrically Nonlinear Elastic-Plastic Space Frames  

Microsoft Academic Search

The establishment of the real stress-strain state of the structure is one of the most important problems for designing and undertaking the reconstruction of building constructions as well as making calculations for the purpose of optimizing cross-sections of various structural elements. This task can be achieved by analysing the structure as a geometrically nonlinear system (refusing an assumption of small

Romanas Karkauskas; Michail Popov

2011-01-01

21

Partial Stability and Geometric Problems of Nonlinear Dynamics  

Microsoft Academic Search

The key concepts of space dynamics (invariance and attractivity of nontrivial sets), stability in part of variables, and partial stability of smooth nonlinear systems are compared. Sufficient conditions for the stability and attractivity are formulated using the second Lyapunov method. Differential-geometric methods are used to derive simplified local conditions guaranteeing the partial stability of a system and attractivity of an

I. V. Miroshnik

2002-01-01

22

Nonlinear Vibrations and Frequency Response Analysis of a Cantilever Beam Under Periodically Varying Magnetic Field  

Microsoft Academic Search

In this paper, nonlinear vibration of a cantilever beam with tip mass subjected to periodically varying axial load and magnetic field has been studied. The temporal equation of motion of the system containing linear and nonlinear parametric excitation terms along with nonlinear damping, geometric and inertial types of nonlinear terms has been derived and solved using method of multiple scales.

Barun Pratiher; Santosha K. Dwivedy

2011-01-01

23

Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector  

NASA Technical Reports Server (NTRS)

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

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

2001-01-01

24

Nonlinear optical beam manipulation, beam combining, and atmospheric propagation  

Microsoft Academic Search

These proceedings collect papers on optics: Topics include: diffraction properties of laser speckle, coherent beam combination by plasma modes, nonlinear responses, deformable mirrors, imaging radiometers, electron beam propagation in inhomogeneous media, and stability of laser beams in a structured environment.

1988-01-01

25

Two-dimensional nonlinear beam shaping.  

PubMed

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

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

2012-06-01

26

Geometrically and physically nonlinear shell theory in convective description  

NASA Astrophysics Data System (ADS)

Starting from the basic equations of the 3D continuum a shell theory will be derived, considering geometrically and physically nonlinear effects, transverse shear strains and thickness stretching. Motion is described using a material description with convected coordinates. This means the independent variables are the material coordinates (theta) i of the material points P and the time t. Due to the specifics of this description the shape of the coordinate lines, the base vector system and the metric are dependent on space and time. In this case a rate formulation of the field equations proves to be useful, which leads to a nonlinear initial-boundary value problem. The nonlinearity is implied in the initial value problem whereas the boundary value problem is linear in terms of displacement rates.

Herold, M.; John, R.; Ulbricht, V.

2000-01-01

27

Free vibration of geometrically nonlinear micro-switches under electrostatic and Casimir forces  

NASA Astrophysics Data System (ADS)

This paper investigates the free vibration characteristics of micro-switches under combined electrostatic, intermolecular forces and axial residual stress, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching and the influence of Casimir force. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. The Euler-Bernoulli beam theory with von Karman type nonlinear kinematics is applied in the theoretical formulation. The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using the differential quadrature method. The natural frequencies and mode shapes of micro-switches for four different boundary conditions (i.e. clamped-clamped, clamped-simply supported, simply supported and clamped-free) are obtained. The solutions are validated through direct comparisons with experimental and other existing results reported in previous studies. A parametric study is conducted to show the significant effects of geometric nonlinearity, Casimir force, axial residual stress and material composition for the natural frequencies.

Jia, X. L.; Yang, J.; Kitipornchai, S.; Lim, C. W.

2010-11-01

28

Dynamic isolation systems using tunable nonlinear stiffness beams  

NASA Astrophysics Data System (ADS)

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

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

2013-09-01

29

Vector algorithms for geometrically nonlinear 3D finite element analysis  

NASA Technical Reports Server (NTRS)

Algorithms for geometrically nonlinear finite element analysis are presented which exploit the vector processing capability of the VPS-32, which is closely related to the CYBER 205. By manipulating vectors (which are long lists of numbers) rather than individual numbers, very high processing speeds are obtained. Long vector lengths are obtained without extensive replication or reordering by storage of intermediate results in strategic patterns at all stages of the computations. Comparisons of execution times with those from programs using either scalar or other vector programming techniques indicate that the algorithms presented are quite efficient.

Whitcomb, John D.

1989-01-01

30

Geometrically nonlinear analysis of layered composite plates and shells  

NASA Technical Reports Server (NTRS)

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

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

1983-01-01

31

Geometric Nonlinear Finite Element Analysis of Active Fibre Composite Bimorphs  

NASA Astrophysics Data System (ADS)

Active fibre composite-actuated bimorphic actuators were studied in order to measure deflection performance. The deflection of the actuators was a function of the actuating electric potential applied to the active material as well as the magnitude of the axial preload applied to the bimorphic structure. This problem required the use of geometric nonlinear modeling techniques. Geometric nonlinear finite element analysis was undertaken to determine the deflection performance of Macro Fibre Composite (MFC)- and Hollow Active Fibre (HAFC)-actuated bimorphic structures. A physical prototype MFC-actuated bimorphic structure was manufactured in order to verify the results obtained by the finite element analysis. Theses analyses determined that the bimorphic actuators were capable of significant deflection. The analyses determined that the axial preload of the bimorphic actuators significantly amplified the deflection performance of the bimorphic actuators. The deflection performance of the bimorphic actuators suggest that they could be candidates to act as actuators for the morphing wing of a micro unmanned air vehicle.

Kernaghan, Robert

32

Geometrically induced nonlinear dynamics in one-dimensional lattices  

NASA Astrophysics Data System (ADS)

We present a lattice model consisting of a single one-dimensional chain, where the masses are interconnected by linear springs and allowed to move in a horizontal direction only, as in a monorail. In the transverse direction each mass is also attached to two other linear springs, one on each side of the mass. The ends of these springs are kept at fixed positions. The nonlinearity in the model arises from the geometric constraints imposed on the motion of the masses, as well as from the configuration of the springs, where in the transverse direction the springs are either in the extended or compressed state depending on the position of the masses. Under these conditions we show that solitary waves are present in the system. In the long wavelength limit an analytic solution for these nonlinear waves is found. Numerical integrations of the equations of motion in the full system are also performed to analyze the conditions for the existence and stability of the nonlinear waves.

Hamilton, Merle D.; de Alcantara Bonfim, O. F.

2006-03-01

33

Dynamics and distributed control of geometrically nonlinear active piezothermoelastic structronic systems using the finite element technique  

NASA Astrophysics Data System (ADS)

Recent research and development of adaptive materials, smart structures and structronic systems have opened a new era to aerospace and structural engineering. Effective control of these intelligent structures and systems using piezoelectric materials can enhance operation precision, accuracy and reliability. This research is to investigate the dynamics, vibration sensing and control of the geometrically nonlinear distributed piezothermoelastic structures subjected to the combined mechanical, electrical, and thermal excitations by the finite element method. Based on the layerwise constant shear angle theory, the curved hexahedral and triangular piezothermoelastic shell elements are proposed. The generic finite element formulations for vibration sensing and control analysis of nonlinear piezothermoelastic shell structures are derived based on the total Lagrangian virtual work principle. Dynamic system equations, equations of electric potential outputs, and feedback control forces are derived and discussed. The modified Newton-Raphson method is used for efficient dynamic analysis of the nonlinear piezothermoelastic structural systems. Different control algorithms are implemented. The feedback control forces generated from the distributed actuator can effectively enhance system damping and suppress system vibration via proper feedback control techniques. Comprehensive case studies are performed to evaluate the accuracy of the newly developed piezothermoelastic shell elements and to validate the finite element code. Dynamics and vibration sensing/control of nonlinear piezothermoelastic beam and plate systems are analyzed. Distributed piezoelectric films placed on the beam and plate structures respectively serving as sensor and actuators are discussed. The effect of geometric nonlinearity is to stiffen the beam and plate structures and the control effect becomes worse when geometric nonlinearity becomes significant. It shows that negative velocity control scheme is effective to dynamically and electrically induced oscillations. However, it is not effective to the vibrations induced by the steady-state thermal field. Accordingly, one additional control voltage is required to control thermally induced offset. The non-constant curvature structures such as conical shells and toroidal shells are also investigated in linear analysis. Various actuator layouts for these shell structures are proposed and the control effectiveness of the actuators is evaluated. It is suggested that an in-depth understanding of shell dynamics and dominating modes is a must in the effective design and layout of distributed actuators to maximize the distributed control effects.

Wang, Dongwei

34

Geometrically nonlinear higher-gradient elasticity with energetic boundaries  

NASA Astrophysics Data System (ADS)

The objective of this contribution is to formulate a geometrically nonlinear theory of higher-gradient elasticity accounting for boundary (surface and curve) energies. Surfaces and curves can significantly influence the overall response of a solid body. Such influences are becoming increasingly important when modeling the response of structures at the nanoscale. The behavior of the boundaries is well described by continuum theories that endow the surface and curve with their own energetic structures. Such theories often allow the boundary energy density to depend only on the superficial boundary deformation gradient. From a physical point of view though, it seems necessary to define the boundary deformation gradient as the evaluation of the deformation gradient at the boundary rather than its projection. This controversial issue is carefully studied and several conclusions are extracted from the rigorous mathematical framework presented.

Javili, A.; dell'Isola, F.; Steinmann, P.

2013-12-01

35

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

36

Analysis of large amplitude free vibrations of unsymmetrically laminated composite beams on a nonlinear elastic foundation  

Microsoft Academic Search

The large amplitude free vibration of an unsymmetrically laminated composite beam (LCB) on a nonlinear elastic foundation\\u000a subjected to axial load has been studied. The equation of motion for the axial and transverse deformations of a geometrically\\u000a nonlinear LCB is derived. Using the Ritz method, the governing equation is reduced to a time-dependent Duffing equation with\\u000a quadratic and cubic nonlinearities.

R. A. Jafari-Talookolaei; H. Salarieh; M. H. Kargarnovin

2011-01-01

37

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

NASA Astrophysics Data System (ADS)

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

Kuether, Robert J.; Allen, Matthew S.

2014-05-01

38

Geometric arrangement of laser beams in target area  

NASA Astrophysics Data System (ADS)

A ray tracing method for design of geometrical arrangement of laser beams in target area is described in this paper. A mathematically mode for path's design are suggested to minimize the objective functions fj(Ri, Li, (alpha) i, (beta) i), which are the optical length difference between the real path length from laser amplifier to the target center and the design objective path length. And the constraint conditions for beam's path are as follows: (1) Beams illuminate the cylindrical target with the incident angles required for the physical experiments. (2) 60 beams propagate without overlapping each other, and each of them with equal optical length from the laser amplifier to the target center. (3) Bema incident to the reflection mirror Pi with the decided angle (phi) i, for example, value of (phi) i is less than or equal to 45 degrees for all paths, and etc. Mathematical methods, such as 'Depth First Search technique', or searching optimum point for objective function fj(Ri, Li, (alpha) i, (beta) i) with constraint conditions are stated. Design examples are reported, in which the 60-Gaussian beam are symmetrically distributed around the target chamber.

Tan, Jichun; Wei, XiaoFeng; Zhong, Qin; Chen, Zhe; Zhang, Xiao Min; Liu, Lirong; Shi, Ziquan

1999-07-01

39

Nonlinear behavior of double ion beam distributions  

NASA Astrophysics Data System (ADS)

We study the stability and nonlinear evolution of differential streaming between core and beam protons based on the analysis of a nonlinear kinetic dispersion relation and using hybrid simulations describing the self-consistent decay of Alfvén-cyclotron waves. The effects of ion trapping by ion acoustic waves and pitch-angle scattering induced by decay of the Alfvéen-cyclotron waves are discussed.

Muñoz, P. A.; Araneda, J. A.

2014-05-01

40

Nonlinear Geometric, Material and Time Dependent Analysis of Reinforced and Prestressed Concrete Slabs and Panels.  

National Technical Information Service (NTIS)

An efficient numerical procedure for the material and geometric nonlinear analysis of reinforced and prestressed concrete slabs and panels including the time-dependent effects due to load history, temperature history, creep, shrinkage and aging of the con...

J. V. Greunen

1979-01-01

41

Iterative method for solving geometrically nonlinear inverse problems of structural element shaping under creep conditions  

NASA Astrophysics Data System (ADS)

An iterative method is proposed for solving geometrically nonlinear inverse problems of shaping structural elements under creep conditions. The method is implemented using a software package based on finite element analysis.

Bormotin, K. S.

2013-12-01

42

Nonlinear waves on charged particle beams  

NASA Astrophysics Data System (ADS)

A two dimensional particle simulation of the resistive filamentation instability on a charge and current neutralized particle beam was performed. The nonlinear development of the instability is analyzed with reference to the focusing requirements of heavy ion beams acting as drivers for pellet fusion. It is found that magnetically pinched current filaments form for all values of the dimensionless parameter. The combined area of the filaments decreases significantly as the filaments coalesce. This leads to a speculation that adequate focusing of the beam may be possible in spite of the development of this instability. Nonlinear space-charge waves in a strongly magnetized cylindrical plasma were also investigated. Soliton and periodic wave solutions were obtained. For the case of an intense unneutralized electron beam, a significant decrease in the phase velocity of the slow spce charge wave is found at large amplitudes. The importance of this result for some collective ion acceleration schemes is discussed.

Hughes, T. P.

43

Modeling of the vibrating beam accelerometer nonlinearities  

NASA Astrophysics Data System (ADS)

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

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

44

Geometric misalignment and calibration in cone-beam tomography  

SciTech Connect

We present a new high-precision method for the geometric calibration in cone-beam computed tomography. It is based on a Fourier analysis of the projection-orbit data, recorded with a flat-panel area detector, of individual point-like objects. For circular scan trajectories the complete set of misalignment parameters which determine the deviation of the detector alignment from the ideal scan geometry are obtained from explicit analytic expressions. To derive these expressions we show how to disentangle the problems of calculating misalignment parameters and point coordinates. The calculation of the coordinates of the point objects inside the scanned volume, in units of the distance from the focal spot to the center of rotation, is then possible analytically likewise. We simulate point-projection data on a misaligned detector with various amounts of randomness added to mimic measurement uncertainties. This data is then employed in our calibration to validate the method by comparing the resulting misalignment parameters and point coordinates to the known true ones. We also present our implementation and results for the geometric calibration of micro-CT systems. The effectiveness of the corresponding misalignment correction in reducing image artifacts is exemplified by reconstructed micro-CT images.

Smekal, Lorenz von; Kachelriess, Marc; Stepina, Elizaveta; Kalender, Willi A. [Institut fuer Medizinische Physik (IMP), Universitaet Erlangen-Nuernberg, Henkesstr. 91, D-91052 Erlangen (Germany)

2004-12-01

45

Nonlinear Geometric Controller for Bioprocesses: Application to the Production of Saccharomyces Cerevisiae  

Microsoft Academic Search

This work describes the simulation of a nonlinear geometric control with state estimation by extended Kalman filter (EKF) in its continuous\\/discrete form. Measurements with delays and different sampling periods are used following previous simulation studies. The biological process studied is a fed-batch reactor for baker's yeast production. The state variable estimations are applied to the nonlinear control law developed in

Mokeddem Diab; Saad Saoud Lyes; Khellaf Abdelhafid

46

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

Microsoft Academic Search

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

47

The validity of nonlinear geometric optics for weak solutions of conservation laws  

Microsoft Academic Search

The method of weakly nonlinear geometric optics is one of the main formal perturbation techniques used in analyzing nonlinear wave motion for hyperbolic systems. The tacit assumption in using such perturbation methods is that the corresponding solutions of the hyperbolic system remain smooth; since shock waves typically form in such solutions, these assumptions are rarely satisfied in practice. Nevertheless, in

Ronald J. DiPerna; Andrew Majda

1985-01-01

48

Active suppression of nonlinear composite beam vibrations by selected control algorithms  

NASA Astrophysics Data System (ADS)

This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.

Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal

2011-05-01

49

Effect of transverse shears on complex nonlinear vibrations of elastic beams  

NASA Astrophysics Data System (ADS)

Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness ? ? 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.

Krysko, V. A.; Zhigalov, M. V.; Saltykova, O. A.; Krysko, A. V.

2011-09-01

50

Beam-Plasma Interaction and Nonlinear Effects  

SciTech Connect

This paper presents a survey of perturbative nonlinear plasma theory known as the weak turbulence theory. After the basic concepts and methodology of the weak turbulence theory are outlined in sufficient detail, numerical solutions of the weak turbulence theory obtained in the context of the beam-plasma interaction are compared against particle-in-cell (PIC) numerical simulations. It is demonstrated that theory and PIC simulation are in excellent agreement.

Yoon, Peter H. [School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of); Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 (United States)

2009-11-10

51

Cross-optical-beam nonlinear photoacoustic microscopy  

NASA Astrophysics Data System (ADS)

We present a photoacoustic microscopy (PAM) technique with an optical sectioning capability. By combining crossoptical- beam illumination with nonlinear PAM, an axial resolution of 8.7 ?m was measured, demonstrating a fourfold improvement over the acoustically determined value. Compared to methods relying on high-frequency ultrasound transducers to improve the axial resolution, our approach offers a greater working distance and a higher signal-to-noise ratio.

Zhu, Liren; Gao, Liang; Li, Lei; Wang, Lidai; Ma, Teng; Zhou, Qifa; Shung, K. Kirk; Wang, Lihong V.

2014-03-01

52

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

53

Cubic nonlinearity in shear wave beams with different polarizations  

PubMed Central

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

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

2008-01-01

54

On the dynamic response of beams with multiple geometric or material discontinuities  

Microsoft Academic Search

An analytic framework is developed for determining closed form expressions for the natural frequencies, mode shapes, and frequency response function for Euler–Bernoulli beams with any number of geometric or material discontinuities. The procedure uses a convenient matrix formulation to generalize the single discontinuity beam problem to beams with multiple step changes. Specifically, the multiple discontinuity beam problem is solved by

Samuel C. Stanton; Brian P. Mann

2010-01-01

55

On the dynamic response of beams with multiple geometric or material discontinuities  

Microsoft Academic Search

An analytic framework is developed for determining closed form expressions for the natural frequencies, mode shapes, and frequency response function for Euler-Bernoulli beams with any number of geometric or material discontinuities. The procedure uses a convenient matrix formulation to generalize the single discontinuity beam problem to beams with multiple step changes. Specifically, the multiple discontinuity beam problem is solved by

Samuel C. Stanton; Brian P. Mann

2010-01-01

56

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

PubMed

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

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

2013-10-22

57

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

PubMed

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

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

2014-03-24

58

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

NASA Technical Reports Server (NTRS)

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

Rizzi, Stephen A.; Muravyov, Alexander A.

2002-01-01

59

Effect of geometric anisotropy on optical nonlinearity enhancement for periodic composites  

Microsoft Academic Search

The effect of geometric anisotropy on the optical nonlinearity enhancement for the composites with metal or semiconductor spheriodal-shaped particles periodically in an insulating host is investigated. The frequency dependences of effective nonlinear susceptibility are calculated with the Stroud-Hui relation and a series expression of space-dependent electric field in periodic composites. The results show that for both metal-insulator (MI) and semiconductor-insulator

Baifeng Yang; Chengxiang Zhang; Decheng Tian

2003-01-01

60

Beam stability & nonlinear dynamics. Formal report  

SciTech Connect

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

Parsa, Z. [ed.

1996-12-31

61

Comparison of the geometrically nonlinear and linear theories of martensitic transformation  

Microsoft Academic Search

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

K. Bhattacharya

1993-01-01

62

Nonlinear geometric feature equalizers based on minimum bit error rate criterion for EBPSK communications  

Microsoft Academic Search

A novel nonlinear geometric feature equalizer based on minimum bit error rate is proposed in this paper for the filtering of noise and interference whose frequency band overlaps with the desired signal in extended binary phase shifting keying communications. Considering that the desired signal and the interference have different stochastic characters in feature space, the proposed equalization algorithm recovers the

Renxiang Zhu; Lenan Wu

2007-01-01

63

Algebraic and geometric space time analogies in nonlinear optical pulse propagation  

Microsoft Academic Search

We extend recently developed algebraic space -time analogies for the dispersive and nonlinear propagation of optical breathers. Geometrical arguments can explain the similarity of evolutionary behavior between spatial and temporal phenomena even when strict algebraic translation of solutions may not be possible. This explanation offers a new set of tools for understanding and predicting the evolutionary structure of self-consistent Gaussian

Shayan Mookherjea; Amnon Yariv

2001-01-01

64

Nonlinear shape prior from Kernel space for geometric active contours  

NASA Astrophysics Data System (ADS)

The Geometric Active Contour (GAC) framework, which utilizes image information, has proven to be quite valuable for performing segmentation. However, the use of image information alone often leads to poor segmentation results in the presence of noise, clutter or occlusion. The introduction of shapes priors in the contour evolution proved to be an effective way to circumvent this issue. Recently, an algorithm was proposed, in which linear PCA (principal component analysis) was performed on training sets of data and the shape statistics thus obtained were used in the segmentation process. This approach was shown to convincingly capture small variations in the shape of an object. However, linear PCA assumes that the distribution underlying the variation in shapes is Gaussian. This assumption can be over-simplifying when shapes undergo complex variations. In the present work, we derive the steps for using Kernel PCA to in the GAC framework to introduce prior shape knowledge. Several experiments were performed using different training-sets of shapes. Starting with any initial contour, we show that the contour evolves to adopt a shape that is faithful to the elements of the training set. The proposed shape prior method leads to better performances than the one involving linear PCA.

Dambreville, Samuel; Rathi, Yogesh; Tannenbaum, Allen

2006-02-01

65

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

NASA Technical Reports Server (NTRS)

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

Mangalgiri, P. D.; Prabhakaran, R.

1986-01-01

66

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

National Technical Information Service (NTIS)

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 mod...

C. L. Kory

2000-01-01

67

Measurement and simulation of nonlinear beam-beam mode coupling in the Fermilab Tevatron  

Microsoft Academic Search

The Tevatron beam dynamics has been studied from the “weak-strong” representation of the beam-beam effects for various octupole field settings. A single particle is tracked using TEAPOT in the presence of the other beam. The nonlinearities introduced by the beam-beam forces introduces two unwanted effects: (1) it excites nonlinear resonances; (2) it introduces dispersion of the tunes with amplitude. The

S. Assadi; C. S. Mishra

1997-01-01

68

Nonlinear thermal stability of geometrically imperfect shape memory alloy hybrid laminated composite plates  

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

69

Nonlinear evolution of electromagnetic ion beam instabilities  

NASA Technical Reports Server (NTRS)

A comparative study of the ion/ion right-hand resonant instability and the ion/ion nonresonant instability is carried out to investigate and contrast their properties. Linear analysis demonstrates that the nonresonant instability becomes resonant if the density of the ion beam is sufficiently high. Hybrid simulations show that both the resonant and nonresonant instabilities result in the formation of nonlinear pulses, called pulsations, but with distinct features. For example, the pulsations generated by the resonant instability have a positive correlation with the ion density, while those generated by the nonresonant instability are likely to have a relatively weak negative correlation. The waves generated by the nonresonant instability are subject to a parametric decay instability and tend to form a state of condensate where the turbulence becomes nearly monochromatic.

Akimoto, K.; Winske, D.; Gary, S. P.; Thomsen, M. F.

1993-01-01

70

Magneto-thermo-elastokinetics of Geometrically Nonlinear Laminated Composite Plates. Part 1: Foundation of the Theory  

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

71

Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians  

Microsoft Academic Search

Algebraic geometrical solutions of a new shallow-water equation and Dym- type equation are studied in connection with Hamiltonian flows on nonlinear subvarieties of hyperelliptic Jacobians. These equations belong to a class of N-component integrable systems generated by Lax equations with energy- dependent Schr¨ odinger operators having poles in the spectral parameter. The classes of quasi-periodic and soliton-type solutions of these

Mark S Alber; Yuri N Fedorov

72

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

Microsoft Academic Search

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

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

1997-01-01

73

A simple finite element model for the geometrically nonlinear analysis of thin shells  

Microsoft Academic Search

A triangular flat finite element for the analysis of thin shells which undergo large displacements is proposed. It is based\\u000a upon the geometrically nonlinear theory of von Kármán for thin plates and the total Lagrangian approach. It has a total of\\u000a only twelve degrees of freedom, namely, three translations at each vertex and one rotation at each mid-side. The stiffness

E. Providas; M. A. Kattis

1999-01-01

74

A theoretical and computational setting for a geometrically nonlinear gradient damage modelling framework  

Microsoft Academic Search

The present work deals with the extension to the geometrically nonlinear case of recently proposed ideas on elastic- and\\u000a elastoplastic-damage modelling frameworks within the infinitesimal theory. The particularity of these models is that the damage\\u000a part of the modelling involves the gradient of damage quantity which, together with the equations of motion, are ensuing from\\u000a a new formulation of the

B. Nedjar

2002-01-01

75

Measurement and Simulation of Nonlinear Beam-Beam Mode Coupling in the Fermilab Tevatron.  

NASA Astrophysics Data System (ADS)

The Tevatron beam dynamics has been studies from the "Weak-Strong" representation of the beam-beam effects for various Octupole field settings. A single particle is tracked using TEAPOT in the presence of the other beam. The nonlinearities introduced by beam-beam force introduces two unwanted effects: It excites nonlinear resonances; (b) It introduces a dispersion of the tunes with amplitude. The strength of nonlinear three mode coupling satisfying the sum rules Q3=Q1+Q2 for various Octupole field settings are calculated. These higher order spectral analysis results will be presented.

Assadi, S.; Mishra, C. S.

1997-05-01

76

Nonlinear plasma and beam physics in plasma wake-fields  

SciTech Connect

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

Rosenzweig, J.B.

1990-02-12

77

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

NASA Astrophysics Data System (ADS)

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

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

2014-01-01

78

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

79

Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory.  

National Technical Information Service (NTIS)

A weak form Galerkin finite element model for the nonlinear quasi- static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory. The formulation assumes line...

G. S. Payette J. N. Reddy

2012-01-01

80

Self-accelerating optical beams in highly nonlocal nonlinear media.  

PubMed

We find self-accelerating beams in highly nonlocal nonlinear optical media, and show that their propagation dynamics is strongly affected by boundary conditions. Specifically for the thermal optical nonlinearity, the boundary conditions have a strong impact on the beam trajectory: they can increase the acceleration during propagation, or even cause beam bending in a direction opposite to the initial trajectory. Under strong self-focusing, the accelerating beam decomposes into a localized self-trapped beam propagating on an oscillatory trajectory and a second beam which accelerates in a different direction. We augment this study by investigating the effects caused by a finite aperture and by a nonlinear range of a finite extent. PMID:22109397

Bekenstein, Rivka; Segev, Mordechai

2011-11-21

81

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

82

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

PubMed Central

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

Heidari, Mohammad; Heidari, Ali; Homaei, Hadi

2014-01-01

83

Nonlinear dynamics of inhomogeneous mismatched charged particle beams  

NASA Astrophysics Data System (ADS)

This work analyzes the transversal dynamics of an inhomogeneous and mismatched charged particle beam. The beam is azimuthally symmetric, initially cold, and evolves in a linear channel permeated by an external constant magnetic field. Based on a Lagrangian approach, a low-dimensional model for the description of the beam dynamics has been obtained. The small set of nonlinear dynamical equations provided results that are in reasonable agreement with that ones observed in full self-consistent N-particle beam numerical simulations.

Nunes, R. P.; Rizzato, F. B.

2012-08-01

84

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

NASA Astrophysics Data System (ADS)

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

Liu, Chien-Sheng; Jiang, Sheng-Hong

2013-10-01

85

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

NASA Technical Reports Server (NTRS)

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

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

1991-01-01

86

Nonlinear geometric feature equalizers based on minimum bit error rate criterion for EBPSK communications  

NASA Astrophysics Data System (ADS)

A novel nonlinear geometric feature equalizer based on minimum bit error rate is proposed in this paper for the filtering of noise and interference whose frequency band overlaps with the desired signal in extended binary phase shifting keying communications. Considering that the desired signal and the interference have different stochastic characters in feature space, the proposed equalization algorithm recovers the desired signal by neural network. Simulation results show that when extended binary phase shifting keying signals are contaminated by relatively strong interference, geometric feature equalizers can provide very low bit error rate. This will provide an alternate filter used for extended binary phase shifting keying communications and also for deep-space communications etc.

Zhu, Renxiang; Wu, Lenan

2007-11-01

87

On the Nonlinear Deformation Geometry of Euler-Bernoulli Beams.  

National Technical Information Service (NTIS)

Nonlinear expressions are developed to relate the orientation of the deformed-beam cross section, torsion, local components of bending curvature, angular velocity, and virtual rotation to deformation variables. These expressions are developed in an exact ...

D. H. Hodges R. A. Ormiston D. A. Peters

1980-01-01

88

Non-linear vibration of variable speed rotating viscoelastic beams  

Microsoft Academic Search

Non-linear vibration of a variable speed rotating beam is analyzed in this paper. The coupled longitudinal and bending vibration\\u000a of a beam is studied and the governing equations of motion, using Hamilton’s principle, are derived. The solutions of the\\u000a non-linear partial differential equations of motion are discretized to the time and position functions using the Galerkin\\u000a method. The multiple scales

Davood Younesian; Ebrahim Esmailzadeh

2010-01-01

89

Derivation of linear beam equations using nonlinear continuum mechanics  

Microsoft Academic Search

Familiar linear elastic and viscoelastic beam equations (Euler-Bernoulli, Rayleigh, Kelvin-Voigt, Timoshenko, and Shear Diffusion) and boundary conditions are derived from a nonlinear theory of large motions rather than the usual variational techniques. Also included is a fairly detailed derivation of the nonlinear theory and a careful discussion of the hypotheses.

Robert C. Rogers

1993-01-01

90

Ball and Beam System - Nonlinear MPC Using Hammerstein Model  

Microsoft Academic Search

Many control methods have been applied to the ball and beam system. In this paper, simulation and on-line control results are presented. The system will be identified as a Hammerstein model. A non-minimal state space model is used to derive a nonlinear model predictive control algorithm. The results indicate that a Hammerstein model provides an accurate description of this nonlinear

Zhiyu Xi; Tim Hesketh

2007-01-01

91

Frequency conversion of Bessel light beams in nonlinear crystals  

Microsoft Academic Search

The properties of frequency conversion of Bessel light beams (BLBs) in nonlinear crystals are studied theoretically and experimentally. New possibilities and prospects of the development of methods for nonlinear optical frequency conversion using BLBs are discussed. The second harmonic generation (SHG) is studied under the conditions of critical and noncritical phase matching. The longitudinal and transverse phase matching is analysed

V N Belyi; N S Kazak; N A Khilo

2000-01-01

92

The geometrical phase transition in non-linear hydrogen bonding systems  

NASA Astrophysics Data System (ADS)

Hydrogen bonding (HB) in a system consisting of A aD d type molecules is studied by two different statistical ways that are demonstrated to be consistent with each other. The free energies of the sol and gel phases in both pregel and postgel regimes are further obtained. It is shown that the sol-gel phase transition in a non-linear HB system is a geometrical phase transition, and for describing this phase transition, the scaling laws satisfied by the moments, the radii of gyration and the gel free energy near the critical point are obtained.

Wang, Hai-Jun; Hong, Xiao-Zhong; Ba, Xin-Wu

2005-09-01

93

Dynamics of elastic nonlinear rotating composite beams with embedded actuators  

NASA Astrophysics Data System (ADS)

A comprehensive study of the nonlinear dynamics of composite beams is presented. The study consists of static and dynamic solutions with and without active elements. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Numerical solutions for the steady state and transient responses have been obtained. It is shown that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. The effect of perturbing the steady state solution has also been calculated and the results are shown to be compatible with those of the accelerating beam analysis. Next, the coupled flap-lag rigid body dynamics of a rotating articulated beam with hinge offset and subjected to aerodynamic forces is formulated. The solution to this rigid-body problem is then used, together with the finite difference method, in order to produce the nonlinear elasto-dynamic solution of an accelerating articulated beam. Next, the static and dynamic responses of nonlinear composite beams with embedded Anisotropic Piezo-composite Actuators (APA) are presented. The effect of activating actuators at various directions on the steady state force and moments generated in a rotating composite beam has been presented. With similar results for the transient response, this analysis can be used in controlling the response of adaptive rotating beams.

Ghorashi, Mehrdaad

94

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

NASA Astrophysics Data System (ADS)

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

Baskar, S.; Prasad, Phoolan

2004-08-01

95

Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations  

NASA Astrophysics Data System (ADS)

Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.

Sotoudeh, Zahra

96

Propagation of rotating parabolic cylindrical beams in nonlocal nonlinear medium  

NASA Astrophysics Data System (ADS)

I introduce a class of rotating parabolic cylindrical beams in nonlocal nonlinear media. The rotating speed keeps fixed in the case of strong nonlocality and increases with the nonlocality being weak. For the strong nonlocal case, the analytical solutions of the modified Snyder Mitchell model agree well with the numerical simulations of the nonlocal nonlinear Schrödinger equation. By simulating the propagation of the rotating parabolic cylindrical beams in liquid crystal and nonlinear thermal media numerically, I demonstrate that there exists the rotating parabolic cylindrical cosine Gaussian quasi-soliton state.

Deng, Dongmei

2012-09-01

97

Local buckling of pultruded beamsnonlinearity, anisotropy and inhomogeneity  

Microsoft Academic Search

Local buckling of pultruded fibre-reinforced plastic beams is discussed. The paper focuses on three issues related to the prediction of buckling loads both from experimental data and from analytical and numerical approaches, viz. nonlinearity, anisotropy and inhomogeneity. Experimental data obtained from full-scale buckling tests are reviewed and a method proposed for estimating the buckling stress in pultruded beams. Analytical studies

Lawrence C. Bank; Jiansheng Yin; Murali Nadipelli

1995-01-01

98

Robust nonlinear control of the ball and beam system  

Microsoft Academic Search

The robust nonlinear servomechanism theory is applied to design a tracking controller for the familiar ball and beam system. The central objective is to have the ball position asymptotically track a sinusoidal reference input in the presence of the ball mass and beam inertia, uncertainties. Simulations show that the resulting controller demonstrates excellent robust tracking property in comparison with other

Jie Huang; Ching-Fang Lin

1995-01-01

99

Using Nonlinear RF Acceleration for FEL Beam Conditioning  

SciTech Connect

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

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

2005-12-14

100

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

NASA Technical Reports Server (NTRS)

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

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

1995-01-01

101

Beam-beam interaction and pacman effects in the SSC with random nonlinear multipoles  

Microsoft Academic Search

In order to find the combined effects of beam-beam interaction (head-on and long-range) and random nonlinear multipoles in dipole magnets, transverse tunes and smears have been calculated as a function of oscillation amplitudes. Two types of particles, ''regular'' and ''pacman,'' have been investigated using a modified version of the tracking code TEAPOT. Regular particles experience beam-beam interactions in all four

G. P. Goderre; N. K. Mahale; S. Ohnuma

1989-01-01

102

Beam-beam interaction and Pacman effects in the SSC with random nonlinear multipoles  

Microsoft Academic Search

In order to find the combined effects of beam-beam interaction (head-on and long-range) and random nonlinear multipoles in dipole magnets, transverse tunes and smears have been calculated as a function of oscillation amplitudes. Two types of particles, ''regular'' and ''Pacman,'' have been investigated using a modified version of tracking code TEAPOT. Regular particles experience beam-beam interactions in all four interaction

G. P. Goderre; S. Ohnuma

1988-01-01

103

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers  

Microsoft Academic Search

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of\\u000a diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to\\u000a an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed\\u000a in the combined frequency-time domain algorithm. The diffraction is described using

V. A. Khokhlova; A. E. Ponomarev; M. A. Averkiou; L. A. Crum

2006-01-01

104

Multiscale Reduced Order Models for the Geometrically Nonlinear Response of Complex Structures  

NASA Astrophysics Data System (ADS)

The focus of this investigation includes three aspects. First, the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting "large" deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology, successfully validated in recent years on simpler panel structures, by developing a novel identification strategy of the reduced order model parameters, that enables the consideration of the large number of modes needed for complex structures, and by extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. These novel developments are successfully validated on the nonlinear static and dynamic responses of a 9-bay panel structure modeled within Nastran. In addition, a multi-scale approach based on Component Mode Synthesis methods is explored. Second, an assessment of the predictive capabilities of nonlinear reduced order models for the prediction of the large displacement and stress fields of panels that have a geometric discontinuity; a flat panel with a notch was used for this assessment. It is demonstrated that the reduced order models of both virgin and notched panels provide a close match of the displacement field obtained from full finite element analyses of the notched panel for moderately large static and dynamic responses. In regards to stresses, it is found that the notched panel reduced order model leads to a close prediction of the stress distribution obtained on the notched panel as computed by the finite element model. Two enrichment techniques, based on superposition of the notch effects on the virgin panel stress field, are proposed to permit a close prediction of the stress distribution of the notched panel from the reduced order model of the virgin one. A very good prediction of the full finite element results is achieved with both enrichments for static and dynamic responses. Finally, computational challenges associated with the solution of the reduced order model equations are discussed. Two alternatives to reduce the computational time for the solution of these problems are explored.

Perez, Ricardo Angel

105

Time domain simulation of the response of geometrically nonlinear panels subjected to random loading  

NASA Technical Reports Server (NTRS)

The response of composite panels subjected to random pressure loads large enough to cause geometrically nonlinear responses is studied. A time domain simulation is employed to solve the equations of motion. An adaptive time stepping algorithm is employed to minimize intermittent transients. A modified algorithm for the prediction of response spectral density is presented which predicts smooth spectral peaks for discrete time histories. Results are presented for a number of input pressure levels and damping coefficients. Response distributions are calculated and compared with the analytical solution of the Fokker-Planck equations. RMS response is reported as a function of input pressure level and damping coefficient. Spectral densities are calculated for a number of examples.

Moyer, E. Thomas, Jr.

1988-01-01

106

Application of triangular element invariants for geometrically nonlinear analysis of functionally graded shells  

NASA Astrophysics Data System (ADS)

This paper is an attempt to construct a computationally effective curved triangular finite element for geometrically nonlinear analysis of elastic shear deformable shells fabricated from functionally graded materials. The focus is on the concise finite-element formulation under the demand of accuracy-simplicity trade-off. To this end, a nonconventional approach based on the invariants of the natural strains of fibers parallel to the element edges is used. The approach allows one to obtain algorithmic formulas for computing the stiffness matrix, gradient, and Hessian of the total strain energy of the finite element. Transverse shear deformation effects are taken into account using the first order shear deformation theory with the shear correction factor dependent on the material property distribution across the shell thickness. The performance of the proposed finite element is demonstrated using problems of functionally graded plates and shells under mechanical and thermal loads.

Levyakov, S. V.; Kuznetsov, V. V.

2011-10-01

107

Theoretical studies on metal porphyrin halides: geometrical parameters and nonlinear optical responses.  

PubMed

The geometrical parameters and static electric properties of several metal porphyrin halides, including Fe(III) porphine chloride (FePCl), Fe(III) porphine bromide (FePBr), Fe(III) tetraphenylporphine chloride (FeTPPCl), aluminum phthalocyanine chloride (AlPcCl), gallium(III) phthalocyanine chloride (GaPcCl), and manganese(III) phthalocyanine chloride (MnPcCl), were investigated using density functional theory (DFT) methods. It was observed that FePBr and MnPcCl showed the highest total hyperpolarisabilities among the studied porphyrins. To investigate the effect of substituted phenyl groups on the nonlinear optical (NLO) responses of porphyrins, the optical properties of FeTPPCl and FePCl were compared using UBLYP/cc-pVDZ+LanL2DZ level of theory. Moreover, the polarised continuum model (PCM) was employed to study the influence of solvation on the optical properties of FePCl. PMID:19655180

Asghari-Khiavi, Mehdi; Safinejad, Feryal

2010-03-01

108

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

109

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

PubMed

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

Xu, Jingyan; Tsui, Benjamin M W

2013-09-01

110

Natural frequencies of nonlinear vibration of axially moving beams  

Microsoft Academic Search

Axially moving beam-typed structures are of technical importance and present in a wide class of engineering problem. In the\\u000a present paper, natural frequencies of nonlinear planar vibration of axially moving beams are numerically investigated via\\u000a the fast Fourier transform (FFT). The FFT is a computational tool for efficiently calculating the discrete Fourier transform\\u000a of a series of data samples by

Hu Ding; Li-Qun Chen

2011-01-01

111

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

NASA Technical Reports Server (NTRS)

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

Stoll, Frederick

1993-01-01

112

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

PubMed Central

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.

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

2013-01-01

113

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

PubMed

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

114

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

DOEpatents

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

115

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

Microsoft Academic Search

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

Satyajit Panda; M. C. Ray

2008-01-01

116

Laser acceleration and nonlinear beam dynamics. Final technical report.  

National Technical Information Service (NTIS)

This research contract covers the period April 1990, September 1991. The work to be done under the contract was theoretical research in the areas of nonlinear beam dynamics and laser acceleration. In this final report we will discuss the motivation for th...

C. Pellegrini

1991-01-01

117

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

118

Energy shedding during nonlinear self-focusing of optical beams.  

PubMed

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

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

2013-10-01

119

Nonlinear free vibration of a microscale beam based on modified couple stress theory  

NASA Astrophysics Data System (ADS)

This paper presents a nonlinear free vibration analysis of the microbeams based on the modified couple stress Euler-Bernoulli beam theory and von Kármán geometrically nonlinear theory. The governing differential equations are established in variational form from Hamilton principle, with a material length scale parameter to interpret the size effect. These partial differential equations are reduced to corresponding ordinary ones by eliminating the time variable with the Kantorovich method following an assumed harmonic time mode. The resulting equations, which form a nonlinear two-point boundary value problem in spatial variable, are then solved numerically by shooting method, and the size-dependent characteristic relations of nonlinear vibration frequency vs. central amplitude of the microbeams are obtained successfully. The comparisons with available published results show that the current approach and algorithm are of good practicability. A parametric study is conducted involving the dependency of the frequency on the length scale parameter along with Poisson ratio, which shows that the nonlinear vibration frequency predicted by the current model is higher than that by the classical one.

Wang, Yong-Gang; Lin, Wen-Hui; Liu, Ning

2013-01-01

120

Effects of Initial Geometric Imperfections On the Non-Linear Response of the Space Shuttle Superlightweight Liquid-Oxygen Tank  

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

121

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

NASA Technical Reports Server (NTRS)

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

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

1986-01-01

122

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

SciTech Connect

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

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

2012-02-01

123

Nonlinear transmission line based electron beam driver  

SciTech Connect

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

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

2012-12-15

124

Nondegenerate two-beam coupling in Kerr nonlinear photonic crystals.  

PubMed

We show that the energy-transfer efficiency by nondegenerate two-beam coupling in a one-dimensional Kerr-nonlinear superlattice can be enhanced by several orders of magnitude as compared with that in a homogeneous medium of the same nonlinearity and length. This significant enhancement utilizes the strong localized field at the band-edge state, two-frequency localized state, or defect state. Due to the intensity-induced index modulation, the bistability is observed, and because of the energy transfer between different wavelength components, the tristability behavior is induced. PMID:16241592

Xie, Ping; Zhang, Zhao-Qing

2005-09-01

125

Octopole correction of geometric aberrations for high-current heavy-ion fusion beams  

SciTech Connect

The success of heavy-ion fusion depends critically on the ability to focus heavy-ion beams to millimeter-size spots. Third-order geometric aberrations caused by fringe fields of the final focusing quadrupoles can significantly distort the focal spot size calculated by first-order theory. We present a method to calculate the locations and strengths of the octopoles that are needed to correct these aberrations. Calculation indicates that the strengths of the octopoles are substantially less than that of the final focusing quadrupoles. 9 refs., 1 fig.

Ho, D.D.M.; Haber, I.; Crandall, K.R.; Brandon, S.T.

1989-03-17

126

Spectrally variable two-beam coupling nonlinear deconvolution.  

PubMed

In previous work, we introduced a dynamic range compression-based technique for image correction using nonlinear deconvolution; the impulse response of the distortion function and the distorted image are jointly transformed to pump a clean reference beam in a photorefractive two-beam coupling arrangement. The Fourier transform of the pumped reference beam contains the deconvolved image and its conjugate. Here we extend our work to spectrally variable dynamic range compression. This approach allows the retrieval of distorted signals embedded in a very high noise environment and does not require one to work with a very high beam ratio as in our previous work. Resolution recovery of blurred noisy images is demonstrated for several different types of image blur. PMID:18059663

Haji-Saeed, Bahareh; Sengupta, Sandip K; Goodhue, William D; Khoury, Jed; Woods, Charles L; Kierstead, John

2007-12-01

127

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

NASA Astrophysics Data System (ADS)

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

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

2013-04-01

128

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

SciTech Connect

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

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

2004-03-01

129

Analysis and simulations of a nonlinear elastic dynamic beam  

NASA Astrophysics Data System (ADS)

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

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

2012-12-01

130

Optimization of Stability Constrained Geometrically Nonlinear Shallow Trusses Using an Arc Length Sparse Method with a Strain Energy Density Approach  

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

131

Manipulating nonlinear optical processes with accelerating light beams  

SciTech Connect

We show theoretically that accelerating light beams can be used to manipulate nonlinear optical processes through spatiotemporal quasi-phase-matching, allowing for unprecedented temporal and spectral shaping of the generated light. As a proof of principle, we demonstrate exquisite control over the high-order harmonic frequency conversion process, showing efficient enhancement of an extremely broad range of harmonics emitted during a selected quarter-cycle of the driving laser pulse.

Bahabad, Alon [Department of Physical Electronics, Tel-Aviv University, Tel-Aviv 69978 (Israel); JILA and Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States); Murnane, Margaret M.; Kapteyn, Henry C. [JILA and Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States)

2011-09-15

132

Active constrained layer damping of geometrically nonlinear transient vibrations of composite plates using piezoelectric fiber-reinforced composite  

Microsoft Academic Search

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated thin composite plates using piezoelectric fiber-reinforced composite (PFRC) materials. The constraining layer of the ACLD treatment is considered to be made of the PFRC materials. The Golla–Hughes–McTavish (GHM) method has been used to model the constrained viscoelastic layer of the ACLD treatment

M. C. Ray; J. Shivakumar

2009-01-01

133

Nonlinear dynamics and chaotic motions of a singularly perturbed nonlinear viscoelastic beam  

NASA Astrophysics Data System (ADS)

The dynamics of one- or two-dimensional structures such as rods, beams, plates, etc., is usually described by one- or two-dimensional nonlinear partial or integro-partial differential equations (PDE's). The equations of motion of such structural systems, with the associated boundary conditions, are amenable to numerical study and to some extent to analytical study. In practice there are many complex structural systems composed of simpler structural members or subsystems with well diverse flexibilities. A simple example is that of a frame comprised of a flexible beam mounted on two relatively stiff columns. The objective of this investigation is to relate the dynamics of a given structure to the dynamics of a simpler structure which is obtained in the limit when the much stiffer substructure of the system is assumed to be perfectly rigid. Without loss of generality, we study both analytically and numerically the dynamics of a representative complex structure, the frame. More precisely, it consists of a nonlinear viscoelastic beam hinged at its ends to two linear viscoelastic columns (supports). We view the equations of motion of the frame structure with sufficiently stiff supports as a singular perturbation of the simpler structure: the nonlinear beam pinned on rigid supports. By applying the Galerkin reduction method, we approximate the equations of motion (coupled PDEs) by a system of a finite number of coupled nonlinear oscillators interacting with a finite number of linear oscillators. Under certain conditions on system parameters, this finite system of ordinary differential equations (ODE's) constitutes the core or 'backbone' of the coupled integro-partial differential equations of motion, an infinite dimensional nonlinear dynamical system. By applying the singular perturbation methodology and the theory of invariant manifolds, we show that for sufficiently stiff linear oscillators (stiff supports) the steady state behavior including nonlinear vibrations and chaotic motions of the above finite dynamical system (full order system) is described by a system of lower dimensions. This reduced system is defined on a nonlinear invariant manifold of the full order system and it possesses symmetry properties that are exactly the same as those of the degenerate reduced system, i.e., the system obtained in the limit when the linear oscillators are assumed to be perfectly rigid.

Georgiou, Ioannis Theodorou

1993-03-01

134

Nonlinear vibration of edged cracked FGM beams using differential quadrature method  

NASA Astrophysics Data System (ADS)

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

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

2012-11-01

135

Nonlinear dynamics and chaotic motions of a singularly perturbed nonlinear viscoelastic beam  

Microsoft Academic Search

The dynamics of one- or two-dimensional structures such as rods, beams, plates, etc., is usually described by one- or two-dimensional nonlinear partial or integro-partial differential equations (PDE's). The equations of motion of such structural systems, with the associated boundary conditions, are amenable to numerical study and to some extent to analytical study. In practice there are many complex structural systems

Ioannis Theodorou Georgiou

1993-01-01

136

Snap-through and pull-in analysis of an electro-dynamically actuated curved micro-beam using a nonlinear beam model  

NASA Astrophysics Data System (ADS)

This paper presents a geometrically nonlinear micro-beam model for the electro-dynamic analysis of an initially curved micro-beam under an applied voltage, with an emphasis on its snap-through and pull-in behaviors. The governing equations of motion and the associated boundary conditions are derived in an arc coordinate system without involving any assumptions on the nonlinear deformation. Differential quadrature method (DQM) and Petzold-Gear Backward Differentiation Formulas (BDF) are employed to solve the governing equations in the space and time domains respectively to obtain the nonlinear fundamental frequency, snap-through voltage, pull-in voltage and the corresponding mode shapes of a micro-beam clamped at both ends. The present analysis is validated through a direct comparison with the published experimental and numerical results. A parametric study is conducted to investigate the influences of the initial gap, base length, arc rise, and initial curved configuration on the snap-through and pull-in behaviors of the micro-beam.

Hu, Y. J.; Yang, J.; Kitipornchai, S.

2013-07-01

137

NONLINEAR EVOLUTION OF BEAM-PLASMA INSTABILITY IN INHOMOGENEOUS MEDIUM  

SciTech Connect

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

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

2011-01-20

138

Networked nonlinear model predictive control of the ball and beam system  

Microsoft Academic Search

Aiming at ball and beam system-a typical nonlinear control plant, establish its affine nonlinear model, based on the nonlinear model predictive control method, some amelioration is made, combined with the networked predictive control scheme, a networked nonlinear model predictive control method is introduced, which can compensate the network induced time delay and the packet loss, and used in the implementation

Dong Zhe; Zheng Geng; Liu Guoping

2008-01-01

139

Nonlinear modes of parametric vibrations and their applications to beams dynamics  

NASA Astrophysics Data System (ADS)

An iterative loop combining nonlinear modes and the Rauscher method is suggested for analyzing finite degree-of-freedom nonlinear mechanical systems with parametric excitation. This method is applied to an analysis of the parametric vibration of beams.

Avramov, K. V.

2009-05-01

140

Nonlinear Finite Element Analysis of FRP Strengthened Reinforced Concrete Beams  

NASA Astrophysics Data System (ADS)

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

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

2012-12-01

141

Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates  

NASA Astrophysics Data System (ADS)

The nonlinear free vibration of carbon nanotubes/fiber/polymer composite (CNTFPC) multi-scale plates with surface-bonded piezoelectric actuators is studied in this paper. The governing equations of the piezoelectric nanotubes/fiber/polymer multiscale laminated composite plates are derived based on first-order shear deformation plate theory (FSDT) and von Kármán geometrical nonlinearity. Halpin–Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. A perturbation scheme of multiple time scales is employed to determine the nonlinear vibration response and the nonlinear natural frequencies of the plates with immovable simply supported boundary conditions. The effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) on the linear and nonlinear natural frequencies of the piezoelectric nanotubes/fiber/polymer multiscale composite plate are investigated through a detailed parametric study.

Rafiee, M.; Liu, X. F.; He, X. Q.; Kitipornchai, S.

2014-07-01

142

Conduction in random networks on super-normal conductors: geometrical interpretation and enhancement of nonlinearity  

Microsoft Academic Search

Critical behaviour of conduction in random networks of super-normal conductors near the percolation threshold is investigated from a geometrical point of view. A fractal dimensionality dCA describing a contact area between typical size clusters is introduced and evaluated explicitly. Non-analytic power law behaviour (divergence) of the conductivity and dielectric constant is given a purely geometrical interpretation in terms of dCA.

T. Ohtsuki; T. Keyes

1984-01-01

143

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

PubMed

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

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

2013-01-28

144

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

SciTech Connect

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

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

2011-09-01

145

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

146

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

PubMed

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

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

2008-07-21

147

Effects of nonlinear left-hand circularly polarized waves supported by a proton beam on linear beam-plasma instabilities  

SciTech Connect

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

148

A geometric approach to problems of synchronization of linear and nonlinear oscillations  

Microsoft Academic Search

Conceptually different problems of oscillation synchronization for multivariable Lagrangian systems are analyzed from the geometric standpoint and synchronous behavior is associated with the system evolution along attracting sets. The approach proposed implies the use of coordinate transformation techniques, dynamic properties of orbital motion and task-oriented decoupling. To achieve local stability of the attractors and a desired mode of system averaged

Iliya MIROSHNIK; Sergey KOROLEV

1997-01-01

149

Computation of on-axis Gaussian beam scattering by nonuniform glass microbeads using a geometrical-optics approach  

NASA Astrophysics Data System (ADS)

Within the framework of geometrical optics, we obtain the on-axis Gaussian beam scattering of nonuniform glass microbeads. The phase shift due to the optical path is deduced and the scattering angles of the p ray are given. On the basis of this work, the scattering intensity distribution is calculated and compared with that obtained by the generalized Lorenz-Mie theory. As indicated by the comparison, the surface wave effect of this gradient index (GRIN) microbead is smaller than that of a homogeneous microbead. The calculation time of the geometrical-optics approximation (GOA) is much less than that of generalized Lorenz-Mie theory (GLMT).

Li, Xiangzhen; Han, Xiang'e.

2009-10-01

150

A method to analyze the cord geometrical uncertainties during head and neck radiation therapy using cone beam CT.  

PubMed

We developed a method to analyze quantitatively the residual cord geometrical uncertainties after image registration during head and neck radiation therapy by using sequential cone beam CT (CBCT). The geometrical centroid line of cervical spinal canal was computed to serve as a cord surrogate. We found that the cord motions were non-uniform from C1 to C6, and that the patterns of motion were variable across patients. This method has potential applications in monitoring cord setup accuracy and in designing treatment margins. PMID:18950886

Zeng, Grace G; Breen, Stephen L; Bayley, Andrew; White, Elizabeth; Keller, Harald; Dawson, Laura; Jaffray, David A

2009-02-01

151

Filamentation instability of laser beams in nonlocal nonlinear media  

NASA Astrophysics Data System (ADS)

The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.

Wen, Shuang-chun; Fan, Dian-yuan

2001-11-01

152

Nonlinear theory of beam bunching and bunch break-off due to cavity damping.  

National Technical Information Service (NTIS)

A nonlinear theory of beam bunching and deceleration in a coasting beam-cavity system is presented. The theory is based on a single-wave model of the cavity. Numerical simulations show that different nonlinear bunch behavior can develop, depending on the ...

P. H. Stoltz J. R. Cary

1998-01-01

153

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

154

Active control of geometrically nonlinear vibrations of functionally graded laminated composite plates using piezoelectric fiber reinforced composites  

NASA Astrophysics Data System (ADS)

This paper deals with the geometrically nonlinear dynamic analysis of functionally graded (FG) laminated composite plates integrated with a patch of active constrained layer damping (ACLD) treatment. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber reinforced composite (PFRC) material. Each layer of the substrate FG laminated composite plate is made of fiber-reinforced composite material in which the fibers are longitudinally aligned in the plane parallel to the top or bottom surface of the layer and the layer is assumed to be graded in the thickness direction by way of varying the fiber orientation angle across its thickness according to a power-law. The novelty of the present work is that, unlike the traditional laminated composite plates, the FG laminated composite plates are constructed in such a way that the continuous variation of material properties and stresses across the thickness of the plates is achieved. The constrained viscoelastic layer of the ACLD treatment is modeled using the Golla-Hughes-McTavish (GHM) method. Based on the first-order shear deformation (FSDT) theory, a finite element model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG laminated composite plates. Both symmetric and asymmetric FG laminated composite plates are considered as the substrate plates for presenting the numerical results. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the PFRC material for active control of geometrically nonlinear forced vibrations of FG laminated composite plates. The effect of piezoelectric fiber orientation in the active constraining PFRC layer on the damping characteristics of the overall FG plates is also investigated.

Panda, Satyajit; Ray, M. C.

2009-08-01

155

Boundary layers and non-linear vibrations in an axially moving beam  

Microsoft Academic Search

The non-linear oscillations of a one-dimensional axially moving beam with vanishing flexural stiffness and weak non-linearities are analysed. The solution of the initial-boundary value problem for the partial differential equation that describes the motion of the beam when two parameters related to the flexural stiffness and the non-linear terms vanish is expanded into a perturbative double series. Two singular perturbation

Francesco Pellicano; Francesco Zirilli

1998-01-01

156

Hamiltonian chaos in a nonlinear polarized optical beam  

SciTech Connect

This lecture concerns the applications of ideas about temporal complexity in Hamiltonian systems to the dynamics of an optical laser beam with arbitrary polarization propagating as a traveling wave in a medium with cubically nonlinear polarizability. We use methods from the theory of Hamiltonian systems with symmetry to study the geometry of phase space for this optical problem, transforming from C{sup 2} to S{sup 3} {times} S{sup 1}, first, and then to S{sup 2} {times} (J, {theta}), where (J, {theta}) is a symplectic action-angle pair. The bifurcations of the phase portraits of the Hamiltonian motion on S{sub 2} are classified and displayed graphically. These bifurcations take place when either J (the beam intensity), or the optical parameters of the medium are varied. After this bifurcation analysis has shown the existence of various saddle connections on S{sup 2}, the Melnikov method is used to demonstrate analytically that the traveling-wave dynamics of a polarized optical laser pulse develops chaotic behavior in the form of Smale horseshoes when propagating through spatially periodic perturbations in the optical parameters of the medium. 20 refs., 7 figs.

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

1989-01-01

157

Effect of focusing field nonlinearities in MBE-4 on transverse beam dynamics  

SciTech Connect

A particle simulation code was used to study the effect on transverse beam dynamics of nonlinearities of the focusing field in a linear accelerator transporting a multiple beam array. Nonlinear field strengths for various multiple-beam design geometries were calculated by relaxation codes for use in the simulation calculation. Nonlinearities due to asymmetry of the electrode array with respect to a single beam were found to be negligible. Electrode end effect nonlinearities led to emittance growth for off-axis beams, though for the geometry of MBE-4, this was negligible. For misaligned beams, a dodecapole field caused significant emittance growth. This was not seen in single particle tracking calculations. Fields due to induced charge on the electrodes can reduce this effect, or the dodecapole field can be eliminated by proper choice of the electrode radius.

Celata, C.M.; Brady, V.O.; Laslett, L.J.; Smith, L.; Haber, I.

1985-05-01

158

Quasiperiodic forced vibrations of a beam interacting with a nonlinear spring  

Microsoft Academic Search

Summary  A simply supported beam with fixed ends and an attached strongly nonlinear spring is considered. As the forced bending vibrations\\u000a of the beam have moderate amplitudes, the stretching force is a nonlinear function of the deflection. The vibrations are presented\\u000a as a series with respect to the modes of the beam without attachment. Applying the Bubnov-Galerkin procedure, an infinite\\u000a system

K. V. Avramov; O. V. Gendelman

2007-01-01

159

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

SciTech Connect

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

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

2001-11-08

160

Theoretical studies on metal porphyrin halides: geometrical parameters and nonlinear optical responses  

Microsoft Academic Search

The geometrical parameters and static electric properties of several metal porphyrin halides, including Fe(III) porphine chloride\\u000a (FePCl), Fe(III) porphine bromide (FePBr), Fe(III) tetraphenylporphine chloride (FeTPPCl), aluminum phthalocyanine chloride\\u000a (AlPcCl), gallium(III) phthalocyanine chloride (GaPcCl), and manganese(III) phthalocyanine chloride (MnPcCl), were investigated\\u000a using density functional theory (DFT) methods. It was observed that FePBr and MnPcCl showed the highest total hyperpolarisabilities\\u000a among the

Mehdi Asghari-Khiavi; Feryal Safinejad

2010-01-01

161

Effects of magnetic non-linearities on a stored proton beam and their implications for superconducting storage rings  

SciTech Connect

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

162

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

SciTech Connect

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

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

2013-07-15

163

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

NASA Astrophysics Data System (ADS)

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

Ragon, Scott Alan, II

164

A geometrically nonlinear theory of shear deformable laminated composite plates and its use in the postbuckling analysis  

NASA Technical Reports Server (NTRS)

This paper is devoted to the formulation of a higher-order, geometrically nonlinear theory of anisotropic symmetrically-laminated composite plates and to the analysis, in this context, of their postbuckling behavior. Special attention is given to the postbuckling analysis of plates made of transversely isotropic layers for which case, the influence played by the degree of transversal-isotropy of the layers as well as by the goemetrical parameters of the panel is investigated. Finally, the results obtained within the present higher-order theory are compared with their first order transverse shear deformation as well as with their classical (Kirchhoff) counterparts and a number of conclusions concerning their range of applicability and the influence of various parameters are presented.

Librescu, L.; Stein, M.

1988-01-01

165

Multiple-mode large deflection random response of beams with nonlinear damping subjected to acoustic excitation  

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

166

A nonlinear-optical method for combining high power laser beams in gases or plasmas  

Microsoft Academic Search

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.

Jay S. Chivian; C. D. Cantrell III; C. A. Glosson; W. D. Cotten; S. F. Dimarco

1988-01-01

167

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

NASA Astrophysics Data System (ADS)

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

McMahon, Matthew David

168

Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections  

Microsoft Academic Search

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

169

On the Use of Equivalent Linearization for High-Cycle Fatigue Analysis of Geometrically Nonlinear Structures  

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

170

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18  

NASA Technical Reports Server (NTRS)

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Buttrill, Carey S.

1989-01-01

171

Geometrically nonlinear analysis of laminated composite thin shells using a modified first-order shear deformable element-based Lagrangian shell element  

Microsoft Academic Search

The formulation of a nonlinear composite 9-node modified first-order shear deformable element-based Lagrangian shell element is presented for the solution of geometrically nonlinear analysis of laminated composite thin plates and shells. The application limit of modified shear deformation theory is presented for the correct analysis of composite laminates. However, it is evident that it results in a parabolic distribution of

Sung-Cheon Han; Ala Tabiei; Weon-Tae Park

2008-01-01

172

A quasi-discrete Hankel transform for nonlinear beam propagation  

NASA Astrophysics Data System (ADS)

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

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

2009-09-01

173

Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium  

SciTech Connect

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

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

2010-05-15

174

Geometric existence theory for the control-affine nonlinear optimal regulator  

NASA Astrophysics Data System (ADS)

For infinite horizon nonlinear optimal control problems in which the control term enters linearly in the dynamics and quadratically in the cost, well-known conditions on the linearised problem guarantee existence of a smooth globally optimal feedback solution on a certain region of state space containing the equilibrium point. The method of proof is to demonstrate existence of a stable Lagrangian manifold M and then construct the solution from M in the region where M has a well-defined projection onto state space. We show that the same conditions also guarantee existence of a nonsmooth viscosity solution and globally optimal set-valued feedback on a much larger region. The method of proof is to extend the construction of a solution from M into the region where M no-longer has a well-defined projection onto state space.

McCaffrey, D.; Banks, S. P.

2005-05-01

175

Nonlinear-Optical Method for Combining High Power Laser Beams in Gases or Plasmas.  

National Technical Information Service (NTIS)

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 cohe...

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

1988-01-01

176

Nonlinear interactions in the planar dynamics of cable-stayed beam  

Microsoft Academic Search

An analytical model is proposed to study the nonlinear interactions between beam and cable dynamics in stayed-systems. The integro-differential problem, describing the in-plane motion of a simple cable-stayed beam, presents quadratic and cubic nonlinearities both in the cable equation and at the boundary conditions. Mainly studied are the effects of quadratic interactions, appearing at relatively low oscillation amplitude. To this

Vincenzo Gattulli; Marco Lepidi

2003-01-01

177

Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams  

Microsoft Academic Search

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate\\u000a analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The\\u000a transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential\\u000a equation. The material time derivative is used in the viscoelastic

Hu Ding; Li-Qun Chen

2011-01-01

178

On the accuracy of the harmonic balance method concerning vibrations of beams with nonlinear supports  

Microsoft Academic Search

A homogeneous beam supported by a nonlinear cubic rotational spring and excited by a prescribed harmonic translational motion was analysed by the harmonic balance method. Harmonic and sub-harmonic solutions were determined as functions of frequency, excitation amplitude and material damping. The results were verified against numerical time integrations of the governing nonlinear differential equations. The numerical method was based on

P. Gudmundson

1989-01-01

179

Nonlinear dynamics of a three-beam structure with attached mass and three-mode interactions  

Microsoft Academic Search

Nonlinear dynamics of elastic structures with two-mode interactions have been extensively studied in the literature. In this\\u000a work, nonlinear forced response of elastic structures with essential inertial nonlinearities undergoing three-mode interactions\\u000a is studied. More specifically, a three-beam structural system with attached mass is considered, and its multidegree-of-freedom\\u000a discretized model for the structure undergoing planar motions is carefully studied. Linear modal

Fengxia Wang; Anil K. Bajaj

2010-01-01

180

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

NASA Astrophysics Data System (ADS)

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

Zhou, Guoquan

2014-11-01

181

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

PubMed Central

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

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

2013-01-01

182

Comparison of convergent beam electron diffraction and geometric phase analysis for strain measurement in a strained silicon device.  

PubMed

Convergent beam electron diffraction and geometric phase analysis were used to measure strain in the gate channel of a p-type strained silicon metal-oxide-semiconductor field-effect transistor. These measurements were made on exactly the same transmission electron microscopy specimen allowing for direct comparison of the relative advantages of each technique. The trends in the strain values show good agreement in both the [110] and [001] directions, but the absolute strain values are offset from each other. This difference in the absolute strain measured using the two techniques is attributed to the way the reference strain is defined for each. PMID:21118218

Diercks, D; Lian, G; Chung, J; Kaufman, M

2011-02-01

183

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

NASA Astrophysics Data System (ADS)

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

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

2013-10-01

184

Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes  

NASA Astrophysics Data System (ADS)

Nonlinear phenomena in a driven plasma diode are studied using a fluid code and the particle-in-cell simulation code xpdp1. When a uniform electron beam is injected to a bounded diode filled with uniform ion background, the beam is destabilized by the Pierce instability and a perturbation grows to exhibit nonlinear oscillations including chaos. Two standard routes to chaos, period doubling and quasiperiodicity, are observed. Mode lockings of various winding numbers are observed in an ac driven system. A new diagnostic quantity is used to parametrize various nonlinear oscillations.

Hur, Min Sup; Lee, Hae June; Lee, Jae Koo

1998-07-01

185

Infinite-Dimensional Control of Nonlinear Beam Vibrations by Piezoelectric Actuator and Sensor Layers  

Microsoft Academic Search

An infinite-dimensional approach for the active vibration control of a multilayered straight composite piezoelectric beam is presented. In order to control the excited beam vibrations, distributed piezoelectric actuator and sensor layers are spatially shaped to achieve a sensor\\/actuator collocation which fits the control problem. In the sense of von Kármán a nonlinear formulation for the axial strain is used and

A. Kugi; K. Schlacher; H. Irschik

1999-01-01

186

A Nonlinear, Elastic Beam-Column Element (Ett Olinjaert Elastiskt Balkpelarelement).  

National Technical Information Service (NTIS)

In this report, bending axially-loaded, freely-suspended beam elements is dealt with. Briefly, the fundamental presuppositions of the presentation are as follows: The technical beam theory is used with a nonlinear, analytical and clear-cut connection betw...

L. Agardh

1976-01-01

187

Effect of Geometric Azimuthal Asymmetries of PPM Stack on Electron Beam Characteristics  

NASA Technical Reports Server (NTRS)

A three-dimensional (3D) beam optics model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA. The model includes an electron beam with initial transverse velocity distribution focused by a periodic permanent magnet (PPM) stack. All components of the model are simulated in three dimensions allowing several azimuthally asymmetric traveling wave tube (TWT) characteristics to be investigated for the first time. These include C-magnets, shunts, and magnet misalignment and their effects on electron beam behavior. The development of the model is presented and 3D TWT electron beam characteristics are compared in the absence of and under the influence of the azimuthally asymmetric characteristics described.

Kory, Carol L.; Heinen, Vernon (Technical Monitor)

2000-01-01

188

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

NASA Astrophysics Data System (ADS)

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

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

2013-12-01

189

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

PubMed

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

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

2013-12-01

190

Nonlinear FEM Analysis of RC Beam-Column Joint Upgraded by Planar Joint Expansion  

Microsoft Academic Search

This paper presents a nonlinear finite element analysis of substandard reinforced concrete beam-column connections retrofitted by joint planar expansion. The method is based on a two-dimensional expansion of beam- column joint using cast in-situ concrete and dowel bars. The method is economical and architecturally acceptable. The test of three half-scale beam-column specimens under quasi-static cyclic loading was conducted. One was

P. Chaimahawan; A. Pimanmas

191

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

SciTech Connect

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

Jacobs, Kurt; Dowling, Jonathan P. [Quantum Science and Technologies Group, Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, 202 Nicholson Hall, Tower Drive, Baton Rouge, Louisiana 70803 (United States)

2006-12-15

192

Nonlinear dynamics of diocotron instability  

SciTech Connect

The nonlinear dynamics of the diocotron instability of an electron beam in a waveguide is investigated by numerical simulations. A study is made of how the structures arising in the beam depend on the geometric parameters of the problem. It is shown that the energy source for such azimuthal structures is the initial (stored in the formation of the beam) electrostatic energy of the unneutralized beam charge.

Kartashov, I. N.; Kuzelev, M. V. [Moscow State University (Russian Federation)

2010-06-15

193

Nonlinear dynamics of diocotron instability  

NASA Astrophysics Data System (ADS)

The nonlinear dynamics of the diocotron instability of an electron beam in a waveguide is investigated by numerical simulations. A study is made of how the structures arising in the beam depend on the geometric parameters of the problem. It is shown that the energy source for such azimuthal structures is the initial (stored in the formation of the beam) electrostatic energy of the unneutralized beam charge.

Kartashov, I. N.; Kuzelev, M. V.

2010-06-01

194

Effect of geometric azimuthal asymmetries of PPM stack on electron beam characteristics [TWTs  

Microsoft Academic Search

A three-dimensional (3-D) beam optics model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA. The model includes an electron beam with initial transverse velocity distribution focused by a periodic permanent magnet (PPM) stack. All components of the model are simulated in three dimensions, allowing several azimuthally asymmetric traveling wave tube (TWT) characteristics to be investigated for the first

Carol L. Kory

2001-01-01

195

The Discrete Geometric Conservation Law and the Nonlinear Stability of ALE Schemes for the Solution of Flow Problems on Moving Grids  

NASA Astrophysics Data System (ADS)

Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.

Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline

2001-12-01

196

Nonlinear thermocurrent beam instability of a weakly ionized plasma  

SciTech Connect

The boundaries of the thermocurrent instability in the linear theory and its maximum development increment are determined. It is shown that the group velocity in this instability depends on the wave vector giving rise to the modulational instability. Then the theory of the thermocurrent instability is considered in the nonlinear regime. In the nonlinear regime, the one-dimensional theory of the thermocurrent instability shows that the instability is caused by negative diffusion in a dense quasineutral plasma under the condition of nonresonant Cerenkov radiation. In this case, plasma diffuses from the rarefied region to the dense region until density falls down so that the quasineutrality condition would be violated and thus diffusion again would become positive. In conclusion, a longitudinal periodic nonlinear structure with a specific parameter is formed in the plasma.

Hatami, M. M.; Niknam, A. R. [Laser-Plasma Research Institute of Shahid Beheshti University, Evin, 1983963113 Tehran (Iran, Islamic Republic of); Shokri, B. [Physics Department and Laser-Plasma Research Institute of Shahid Beheshti University, 19839 Tehran (Iran, Islamic Republic of); Rukhadze, A. A. [General Physics Institute, Vavilova St., 38-117942 Moscow (Russian Federation)

2008-02-15

197

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

PubMed

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

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

2012-09-24

198

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

NASA Astrophysics Data System (ADS)

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

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2012-10-01

199

Nonlinear Longitudinal Space Charge Oscillations in Relativistic Electron Beams  

SciTech Connect

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

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

2011-05-06

200

Analysis of stable self-trapping of laser beams in cubic-quintic nonlinear media  

NASA Astrophysics Data System (ADS)

A numerical and analytical analysis of two-dimensional laser beam propagation in cubic-quintic nonlinear optical media demonstrates the existence of stable stationary radially symmetric modes. By means of a variational method, involving super-Gaussian trial functions and Ritz optimization, approximate stationary solutions are obtained, showing very good agreement with numerical results, even in the strongly non-linear, almost saturated, regime. The stability of the stationary modes are verified by analytical analysis and by direct numerical simulations.

Dimitrevski, Kristian; Reimhult, Erik; Svensson, Erik; Öhgren, Anders; Anderson, Dan; Berntson, Anders; Lisak, Mitek; Quiroga-Teixeiro, Manuel L.

1998-11-01

201

Bistable and negative lateral shifts of the reflected light beam from Kretschmann configuration with nonlinear left-handed metamaterials  

NASA Astrophysics Data System (ADS)

We study the bistable and negative lateral shifts of the reflected light beam from Kretschmann configuration containing left-handed metamaterials with self-focusing and self-defocusing Kerr-type nonlinearity. It is shown that the lateral shifts can be large and negative when the thickness of the middle metal film is smaller than the critical value. Taking the nonlinear effect into account, there exists a hysteretic response between the beam shift and the intensity of the incident light beam. These results suggest that the bistable and negative beam shifts can be modulated by nonlinear coefficients and intensity of incident beam, which might be used in integrated photonics and optical switches.

Chen, X.; Wei, R.-R.; Shen, M.; Zhang, Z.-F.; Li, C.-F.

2010-10-01

202

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

NASA Astrophysics Data System (ADS)

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

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

2006-08-01

203

Nonlinear Models of Reinforced and Post-tensioned Concrete Beams  

Microsoft Academic Search

Commercial finite element software generally includes dedicated numerical models for the nonlinear response of concrete under loading. These models usually include a smeared crack analogy to account for the relatively poor tensile strength of concrete, a plasticity algorithm to facilitate concrete crushing in compression regions and a method of specifying the amount, the distribution and the orientation of any internal

P. Fanning

2001-01-01

204

Nonlinear response of a beam under distributed moving contact load  

Microsoft Academic Search

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

B. Kang; C. A. Tan

2006-01-01

205

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

206

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

SciTech Connect

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

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

2009-05-01

207

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

Microsoft Academic Search

Breast cancer is the second leading cause of cancer death in women in the United States. Currently, X-ray mammography is the method of choice for screening and diagnosing breast cancer. However, this 2D projective modality is far from perfect; with up to 17% breast cancer going unidentified. Over past several years, there has been an increasing interest in cone-beam CT

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

2006-01-01

208

Time-delay control for non-linear dynamic cantilever beam  

Microsoft Academic Search

Based on spring time-delay feedback controller, the excited cantilever beam modeled as an inextensible Euler-Bernoulli beam is investigated for the primary resonance. The spring controller is designed to control the dynamic behavior of the nonlinear dynamic system. The method of multiple scales is utilized directly to obtain the linear equations. The effect of the feedback gain and time-delay on the

Canchang Liu; Chuanbo Ren

2010-01-01

209

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

NASA Astrophysics Data System (ADS)

A nonlinear ?f particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R. C. Davidson, and W. W. Lee, Phys. Rev. ST Accel. Beams 3, 084401 (2000); 3, 109901 (2000)], the nonlinear ?f method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high intensity charged particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek et al., in Proceedings of the Particle Accelerator Conference, Chicago, 2001 (IEEE, Piscataway, NJ, 2001), Vol. 1, p. 688] at the Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very-high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles.

Qin, Hong

2003-05-01

210

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

Microsoft Academic Search

Two prototype nonlinear multipole magnets have been designed for use in the 800-MeV beam test of the APT beam-expansion concept at LANSCE. The iron-dominated magnets each consist of three independent coils, two for producing a predominately octupole field with a tunable duodecapole component, and one for canceling the residual quadrupole field. Two such magnets, one for shaping each transverse plane,

D. B. Barlow; R. E. Shafer; R. P. Martinez; P. L. Walstrom; S. Kahn; A. Jain; P. Wanderer

1997-01-01

211

Magnetic Design and Measurement of Nonlinear Octupole Magnets for the APT Beam Expander System  

Microsoft Academic Search

Two prototype nonlinear multipole magnets have been designed for use in the 800-MeV beam test of the APT beam-expansion concept at LANSCE. The iron-dominated magnets each consist of three independent coils, two for producing a predominantly octupole field with a tunable duodecapole component, and one for canceling the residual quadrupole field. Two such magnets, one for shaping each transverse plane,

D. B. Barlow; R. E. Shafer; R. P. Martinez; P. L. Walstrom; S. A. Kahn; A. K. Jain; P. J. Wanderer

1997-01-01

212

Effect of non-linearities on beam dynamics in the SNS accumulator ring  

Microsoft Academic Search

Uncontrolled beam losses lead to excessive radio- activation in high-intensity proton rings. Designing a suc- cessful high-intensity ring therefore requires a good under- standing of the sources of such beam losses. This paper presents, for the Spallation Neutron Source (SNS) accumu- lator ring, dynamic aperture studies in which we explore the effect of non-linearities arising from kinematic terms and various

A. V. Fedotov; D. T. Abell; Y. Y. Lee; N. Malitsky; Y. Papaphilippou; J. Wei

2000-01-01

213

Interactions between self-channeled optical beams in soft-matter systems with artificial nonlinearities.  

PubMed

We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions. PMID:24104820

Fardad, Shima; Mills, Matthew S; Zhang, Peng; Man, Weining; Chen, Zhigang; Christodoulides, D N

2013-09-15

214

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

NASA Astrophysics Data System (ADS)

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

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

2013-10-01

215

Global nonlinear control of the ball and beam system  

Microsoft Academic Search

In this paper, we study the regulation problem for the ball and beam system. Since the system does not have well defined relative degree, exact input-output linearization method may fail. The approximate linearization approach can only be used in a limited region. By representing the system as a fuzzy dynamic model, we give a global control law which is the

Yi Guo; David J. Hill; Zhong-Ping Jiang

1996-01-01

216

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

NASA Astrophysics Data System (ADS)

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

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

1997-05-01

217

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

NASA Astrophysics Data System (ADS)

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

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

2000-10-01

218

NON-LINEAR BEAM OSCILLATIONS EXCITED BY LATERAL FORCE AT COMBINATION RESONANCE  

Microsoft Academic Search

Non-linear oscillations of a beam subjected to a periodic force at a combination resonance are considered. Using the Galerkin method, a partial differential equation of oscillations is reduced to a system of ordinary differential equations with a small parameter. A system of three autonomous differential equations is derived, the multiple scales method being used. Qualitative properties of trajectories are analyzed.

K. V. Avramov

2002-01-01

219

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

NASA Astrophysics Data System (ADS)

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

Stickney, James; Zozulya, Alex

2003-07-01

220

Application of Chebyshev Formalism to Identify Nonlinear Magnetic Field Components in Beam Transport Systems  

SciTech Connect

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

221

On the delamination detection in composite beams with active piezoelectric sensors using non-linear ultrasonics  

Microsoft Academic Search

This paper investigates the potential of a novel SHM method for the detection of delamination cracks in composites which exploits the nonlinear ultrasonic response with in-situ d31 piezoceramic actuators and sensors. Composite beam specimens with artificially created delamination cracks are tested, entailing two piezoceramic actuator patches, the first to generate a low frequency, high power modal excitation and the second

Nikolaos A. Chrysochoidis; Antigoni K. Barouni; Dimitris A. Saravanos

2009-01-01

222

Nonlinear Finite Element Analysis of Fibrous Reinforced Concrete Beam-Column Joints  

Microsoft Academic Search

In this paper, the finite element method is used to study the nonlinear behaviour of beam-column fibrous reinforced concrete joints under short-term monotonic loading. Concrete is represented by eight nodded isoparametric elements and the reinforcement was represented by axial two noded bar elements embedded in the concrete elements. Strain hardening approach, has been employed to model the compressive behavior of

S. A. Al-Ta; N. S. Al-Saffar

2008-01-01

223

Nonlinear analysis of beam–column joints using softened truss model  

Microsoft Academic Search

The aim of this study is to expand the application of the nonlinear softened truss model for membrane elements on beam–column joints. The softened truss model employs three equations for equilibrium, three for compatibility and four equations for the constitutive laws of materials. The constitutive equations for both the concrete and steel are based on the actually observed stress–strain relationships.

P. G. Bakir; H. M. Boduroglu

2006-01-01

224

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

National Technical Information Service (NTIS)

In this paper, a 3-D nonlinear perturbative particle simulation code (BEST) (H. Qin, R.C. Davidson and W.W. Lee, Physical Review Special Topics on Accelerators and Beams 3 (2000) 084401) is used to systematically study the stability properties of intense ...

E. A. Startsev R. C. Davidson H. Qin

2002-01-01

225

On the nonlinear deformation geometry of Euler-Bernoulli beams. [rotary wings  

NASA Technical Reports Server (NTRS)

Nonlinear expressions are developed to relate the orientation of the deformed beam cross section, torsion, local components of bending curvature, angular velocity, and virtual rotation to deformation variables. The deformed beam kinematic quantities are proven to be equivalent to those derived from various rotation sequences by identifying appropriate changes of variable based on fundamental uniqueness properties of the deformed beam geometry. The torsion variable used is shown to be mathematically analogous to an axial deflection variable commonly used in the literature. Rigorous applicability of Hamilton's principle to systems described by a class of quasi-coordinates that includes these variables is formally established.

Hodges, D. H.; Ormiston, R. A.; Peters, D. A.

1980-01-01

226

Variational approach to nonparaxial self-focusing of high-power laser beams in nonlinear media  

NASA Astrophysics Data System (ADS)

We apply the variational approach to solve the nonparaxial nonlinear Schrodinger equation to disclose the nonparaxial propagation properties of a Gaussian beam. A system of differential equations for the evolution of the parameters of Gaussian beam is obtained. The obtained analytical results clearly show the nonparaxial propagation process of periodic focusing-defocusing. This process is significantly influenced by the initial power and chirp of the beam. A positive chirp retards the first self-focus, while a negative chirp brings forward the first self-focus. Both positive and negative chirps increase the subsequent focusing-defocusing cycles.

Jin, Jing; Wen, Shuangchun; Cai, Wangyang; Fu, Xiquan; Fan, Dianyuan

2005-01-01

227

Nonlinear-resonance line shapes: Dependence on the transverse intensity distribution of a light beam  

SciTech Connect

We analyze the line shape and width of atomic coherent-population-trapping (CPT) resonances excited by laser beams with different transverse intensity profiles. A dramatic difference in the resonance line shape is found when comparing a beam with a 'steplike' profile to a beam with a Gaussian profile. In particular, for nonuniform profiles, a non-Lorentzian functional form is given that is more appropriate for describing the nonlinear resonance line shape than is a conventional Lorentzian. Our analysis is supported by measurements of CPT line shapes in a thermal vapor of {sup 85}Rb.

Taichenachev, A.V.; Yudin, V.I. [Novosibirsk State University, Pirogova 2, Novosibirsk 630090 (Russian Federation); Time and Frequency Division, NIST Boulder, 325 South Broadway, Boulder, Colorado 80305 (United States); Institute of Laser Physics, SD RAS, Lavretyev pr. 13/3, Novosibirsk 630090 (Russian Federation); Tumaikin, A.M. [Novosibirsk State University, Pirogova 2, Novosibirsk 630090 (Russian Federation); Institute of Laser Physics, SD RAS, Lavretyev pr. 13/3, Novosibirsk 630090 (Russian Federation); Staehler, M. [Time and Frequency Division, NIST Boulder, 325 South Broadway, Boulder, Colorado 80305 (United States); Institut fuer Angewandte Physik, Universitaet Bonn, Wegelerstrasse 8, D-53115 Bonn (Germany); Wynands, R. [Institut fuer Angewandte Physik, Universitaet Bonn, Wegelerstrasse 8, D-53115 Bonn (Germany); Departement de Physique, Universite de Fribourg, Chemin du Musee 3, 1700 Fribourg (Switzerland); Kitching, J. [Time and Frequency Division, NIST Boulder, 325 South Broadway, Boulder, Colorado 80305 (United States); Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States); Hollberg, L. [Time and Frequency Division, NIST Boulder, 325 South Broadway, Boulder, Colorado 80305 (United States)

2004-02-01

228

Nonlinear theory of the plasma wave excitation in a bounded beam-plasma system  

NASA Astrophysics Data System (ADS)

The nonlinear evolution of a relatively weak monoenergetic electron beam in a homogeneous plasma enclosed by a metallic wall for an excited quasi-potential wave is investigated for both the magnetic field-free case and for a magnetized electron beam. A new, efficient theoretical method for calculating the self-consistently changing form of the perpendicular wave potential profile is reported. The theoretical method, which is based on a Green's function technique, can be easily extended to three-dimensional systems or to beam-plasma systems with other boundary conditions. The main features of the saturation process of the basic unstable wave types are discussed.

Kruscha, K. J. G.

229

Cerenkov interaction of a tubular electron beam with a dielectric waveguide. II - Nonlinear theory  

NASA Astrophysics Data System (ADS)

A nonlinear theory for the stationary generation of electromagnetic waves in a dielectric waveguide by a tubular relativistic electron beam is presented which allows for the space charge. Calculations are carried out for specific waveguide geometries, and determinations are made of the generation efficiency and optimal waveguide length as a function of the beam current and radius. It is shown that the highest efficiency is achieved in the case where the space charge field has a noticeable effect on the beam-wave interaction.

Karbushev, N. I.; Shlapakovskii, A. S.

1990-01-01

230

Nonlinear dissipation of circularly polarized Alfven waves due to the beam-induced obliquely propagating waves  

SciTech Connect

In the present study, the dissipation processes of circularly polarized Alfven waves in solar wind plasmas including beam components are numerically discussed by using a 2-D hybrid simulation code. Numerical results suggest that the parent Alfven waves are rapidly dissipated due to the presence of the beam-induced obliquely propagating waves, such as kinetic Alfven waves. The nonlinear wave-wave coupling is directly evaluated by using the induction equation for the parent wave. It is also observed both in the 1-D and 2-D simulations that the presence of large amplitude Alfven waves strongly suppresses the beam instabilities.

Nariyuki, Y. [Faculty of Human Development, University of Toyama, 3190, Toyama City, Toyama 930-8555 (Japan); Hada, T. [Department of Earth System Science and Technology, Kyushu University, 6-1, Kasuga City, Fukuoka 816-8580 (Japan); Tsubouchi, K. [Department of Earth and Planetary Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033 (Japan)

2012-08-15

231

Thermodynamic bounds on nonlinear electrostatic perturbations in intense charged particle beams  

SciTech Connect

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

Logan, Nikolas C.; Davidson, Ronald C. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)

2012-07-15

232

Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams  

SciTech Connect

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

Nikolas C. Logan and Ronald C. Davidson

2012-07-18

233

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

234

Geometric Mechanics  

NASA Astrophysics Data System (ADS)

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

Talman, Richard

1999-10-01

235

Nonlinear Charge and Current Neutralization of an Ion Beam Pulse in a Pre-formed Plasma  

SciTech Connect

The propagation of a high-current finite-length ion beam in a cold pre-formed plasma is investigated. The outcome of the calculation is the quantitative prediction of the degree of charge and current neutralization of the ion beam pulse by the background plasma. The electric magnetic fields generated by the ion beam are studied analytically for the nonlinear case where the plasma density is comparable in size with the beam density. Particle-in-cell simulations and fluid calculations of current and charge neutralization have been performed for parameters relevant to heavy ion fusion assuming long, dense beams with el >> V(subscript b)/omega(subscript b), where V(subscript b) is the beam velocity and omega subscript b is the electron plasma frequency evaluated with the ion beam density. An important conclusion is that for long, nonrelativistic ion beams, charge neutralization is, for all practical purposes, complete even for very tenuous background plasmas. As a result, the self-magnetic force dominates the electric force and the beam ions are always pinched during beam propagation in a background plasma.

Igor D. Kaganovich; Gennady Shvets; Edward Startsev; Ronald C. Davidson

2001-01-30

236

Nonlinear dynamics of diocotron instability  

Microsoft Academic Search

The nonlinear dynamics of the diocotron instability of an electron beam in a waveguide is investigated by numerical simulations.\\u000a A study is made of how the structures arising in the beam depend on the geometric parameters of the problem. It is shown that\\u000a the energy source for such azimuthal structures is the initial (stored in the formation of the beam)

I. N. Kartashov; M. V. Kuzelev

2010-01-01

237

Sensitivity of a Three-Mirror Cavity to Thermal and Nonlinear Lensing: Gaussian-Beam Analysis  

NASA Astrophysics Data System (ADS)

We consider a compact three-mirror cavity consisting of a flat output coupler, a curved folding mirror, and an active medium with one facet cut at the Brewster angle and the other facet coated for unit reflectivity. We examine the sensitivity to thermal lensing and to self-focusing in the active medium of the Gaussian beam that is circulating in that cavity. We use a simple thin-lens model; the astigmatism of the beam that is circulating in the cavity and the nonlinear coupling between the field distributions along the two orthogonal axes are taken into account. We find configurations in which beam ellipticity is compensated for at either end of the cavity in the presence of thermal lensing. We have derived an analytical criterion that predicts the sensitivity of the beam size to nonlinear lensing. The ability of the cavity to favor self-mode locking is found to be sensitive to the strength of thermal lensing. In the absence of thermal lensing, cavities operated as telescopic systems ( C 0 ) or self-imaging systems ( B 0 ) are most appropriate for achieving self-mode locking, with nonlinear mode selection accomplished through saturation of the spatially varying laser gain. We identify conditions for which self-mode locking can be produced by variable-reflectivity output couplers with either maximum or minimum reflectivity at the center of the coupler. We use our model to estimate the nonlinear gain produced in laser cavities equipped with such output couplers. We identify a cavity configuration for which nonlinear lensing can simultaneously produce mode locking and correction of beam ellipticity at the output coupler.

Anctil, Geneviève; McCarthy, Nathalie; Piché, Michel

2000-12-01

238

Soliton pair generation in the interactions of Airy and nonlinear accelerating beams.  

PubMed

We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear (NL) accelerating beams in Kerr and saturable NL media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and, after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not. PMID:24322080

Zhang, Yiqi; Beli?, Milivoj; Wu, Zhenkun; Zheng, Huaibin; Lu, Keqing; Li, Yuanyuan; Zhang, Yanpeng

2013-11-15

239

Understanding the nonlinear beam dynamics of the Advanced Light Source  

SciTech Connect

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

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

1996-09-18

240

Comparisons of typical nonlinear states in single- and dual-beam optically injected semiconductor lasers  

NASA Astrophysics Data System (ADS)

The characteristics of the typical nonlinear states in an optically injected laser system with single- and dual-beam injection are analyzed and compared numerically. Both single- and dual-beam optical injection systems can generate periodic oscillations and chaos states but with different characteristics. By observing the evolution process of periodic oscillations, it is found that dual-beam injection induced periodic oscillations have multiple time series patterns including continuous periodic signals with single peak (CPS) and continuous periodic signals with subharmonic (CPSSH), while for single-beam injection with either of the dual-beam injection parameters generated periodic oscillations, the extremum numbers of the time series equal to the frequency period numbers of the optical spectrum. In addition, the great advantages of bandwidth enhancement effect for chaos oscillations are obtained by using dual-beam injection. Furthermore, extensive numerical simulations reveal that dual-beam injection system undergoes period-doubling routes to chaos, which is identical to that in single-beam injection system. Finally, the characteristics of newly clustered NDFWM dynamics in dual-beam injection system are analyzed.

Qi, Xiaoqiong; Xie, Liang; Liu, Yuping

2013-11-01

241

Differential Polarization Nonlinear Optical Microscopy with Adaptive Optics Controlled Multiplexed Beams  

PubMed Central

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

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

2013-01-01

242

Nonlinear polarization rotation and orthogonal polarization generation experienced in a single-beam configuration  

NASA Astrophysics Data System (ADS)

Nonlinear polarization rotation and generation of a polarization component orthogonal to the input beam were observed along fourfold axes of YVO4 and BaF2 crystals. We demonstrate experimentally that in both crystals the angle of rotation is proportional, at low intensities, to the square of the product of the input intensity and the crystal length and is the result of simultaneous action of two third-order processes. This type of nonlinear polarization rotation is driven by the real part of the cubic susceptibility. The recorded energy exchange between the two orthogonal components can exceed 10%. It is to our knowledge the highest energy-conversion efficiency achieved in a single beam nonresonant ?(3) interaction. A simple theoretical model is elaborated to describe the dependence of nonlinear polarization rotation and orthogonal polarization generation on the intensity of the input beam at both low- and high-intensity levels. It reveals the potential contributions from the real and the imaginary parts of the susceptibility tensor. Moreover, this kind of measurement is designed to permit the determination of the magnitude and the sign of the anisotropy of the real part of third-order nonlinearity in crystals with cubic or tetragonal symmetry on the basis of polarization-rotation measurements. The ?xxxx(3) component of the third-order susceptibility tensor and its anisotropy sign and amplitude value for BaF2 and YVO4 crystals are estimated and discussed.

Minkovski, N.; Petrov, G. I.; Saltiel, S. M.; Albert, O.; Etchepare, J.

2004-09-01

243

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual  

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

244

A geometric nonlinear degenerated shell element using a mixed formulation with independently assumed strain fields. Final Report; Ph.D. Thesis, 1989  

NASA Technical Reports Server (NTRS)

A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.

Graf, Wiley E.

1991-01-01

245

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

NASA Astrophysics Data System (ADS)

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

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

2013-01-01

246

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

NASA Technical Reports Server (NTRS)

The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam velocity distributions in great detail. The effects of both proton and oxygen ring-beams are considered. The study of instabilities excited by a proton ring-beam is relevant to the region upstream of the Earth's bow shock, whereas the oxygen ring-beam corresponds to cometary ions picked up by the solar wind. Linear theory has shown that for a ring-beam, four instabilities are found, one on the nonresonant mode, one on the Alfven mode, and two along the magnetosonic/whistler branch. The relative growth rate of these instabilities is a sensitive function of parameters. Although one of the magnetosonic instabilities has maximum growth along the magnetic field, the other has maximum growth in oblique directions. We have studied the competition of these instabilities in the nonlinear regime using 2-D simulations. As in the linear limit, the nonlinear results are a function of beam density and distribution function. By performing the simulations as both initial value and driven systems, we have found that the outcome of the simulations can vary, suggesting that the latter type simulations is needed to address the observations. A general conclusion of the simulation results is that field-aligned beams do not result in the formation of shocklets, whereas ring-beam distributions can.

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

1995-01-01

247

Formation and nonlinear dynamics of the squeezed state of a helical electron beam with additional deceleration  

SciTech Connect

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., E-mail: evgeniy.n.egorov@gmail.com; Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E. [Chernyshevsky Saratov State University (Russian Federation)] [Chernyshevsky Saratov State University (Russian Federation)

2013-11-15

248

Formation and nonlinear dynamics of the squeezed state of a helical electron beam with additional deceleration  

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

249

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

Microsoft Academic Search

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

E. J. Sapountzakis; J. A. Dourakopoulos

2009-01-01

250

Nonlinear finite element analysis of steel fiber reinforced concrete deep beams  

Microsoft Academic Search

By the nonlinear finite element analysis (FEA) method, the mechanical properties of the steel fiber reinforced concrete (SFRC)\\u000a deep beams were discussed in terms of the crack load and ultimate bearing capacity. In the simulation process, the ANSYS parametric\\u000a design language (APDL) was used to set up the finite element model; the model of bond stress-slip relationship between steel\\u000a bar

Lihua Xu; Yin Chi; Jie Su; Dongtao Xia

2008-01-01

251

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

Microsoft Academic Search

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

Luis G. Maqueda; Ahmed A. Shabana

2007-01-01

252

Singleparticle and collective effects of cubic nonlinearity in the beam dynamics of proton synchrotrons  

Microsoft Academic Search

This thesis describes some new studies of the effects of cubic nonlinearities arising from image-charge forces and octupole magnets on the transverse beam dynamics of proton synchrotrons and storage rings, and also a study of the damping of coherent oscillations using a feed-back damper. In the latter case, various corrective algorithms were modeled using linear one-turn maps. Kicks of fixed

Hy J. Tran

1998-01-01

253

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

Microsoft Academic Search

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

John Hauser; Shankar Sastry; P. Kokotovic

1992-01-01

254

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

Microsoft Academic Search

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

Django Manglunki; M. MARTINI

1997-01-01

255

Quasi-periodic solutions of a quasi-periodically forced nonlinear beam equation  

NASA Astrophysics Data System (ADS)

In this paper, one quasi-periodically forced nonlinear beam equation utt+uxxxx+?u+?g(?t,x)u3=0,?>0,x?[0,?] with hinged boundary conditions is considered. Here ? is a small positive parameter, g( ?t, x) is real analytic in all variables and quasi-periodic in t with a frequency vector ? = ( ?1, ?2, … , ?m). It is proved that the above equation admits small-amplitude quasi-periodic solutions.

Wang, Yi

2012-06-01

256

Frequency analysis of finite beams on nonlinear Kelvin-Voight foundation under moving loads  

NASA Astrophysics Data System (ADS)

The vibration of an Euler-Bernoulli beam, resting on a nonlinear Kelvin-Voight viscoelastic foundation, traversed by a moving load is studied in the frequency domain. The objective is to obtain the frequency responses of the beam and the effects of different parameters on the system response. The parameters include the magnitude and speed of the moving load and the foundation nonlinearity and its damping coefficient. The solution is obtained by using the Galerkin method in conjunction with the multiple scales method (MSM). The governing nonlinear partial differential equations of motion are discretized into sets of nonlinear ordinary differential equations. Subsequently, the solution is calculated for different harmonics by using the MSM as one of the powerful perturbation techniques. The steady-state responses of the main harmonic as well as its two super-harmonics are then obtained. As a case study, a conventional railway track is dynamically simulated and the jump phenomenon in the response is observed for three harmonics. Moreover, a thorough stability analysis of the system is carried out.

Ansari, M.; Esmailzadeh, E.; Younesian, D.

2011-03-01

257

Vibration reduction of beams under successive traveling loads by means of linear and nonlinear dynamic absorbers  

NASA Astrophysics Data System (ADS)

The goal of the present work is to assess the performances of dynamic vibration absorbers (DVA) in suppressing the vibrations of a simply supported beam subjected to an infinite sequence of regularly spaced concentrated moving loads. In particular, several types of DVA are considered: linear, cubic, higher odd-order monomials and piecewise linear stiffness; linear, cubic and linear-quadratic viscous damping. The purpose is to clarify if nonlinear DVAs show improvements with respect to the classical linear devices. The dynamic scenario is deeply investigated in a wide range of operating conditions, spanning the parameter space of the DVA (damping, stiffness). Nonlinear stiffness can lead to complex dynamics such as quasi-periodic, chaotic and sub-harmonic responses; moreover, acting on the stiffness nonlinearity no improvement is found with respect to the linear DVA. A nonlinear non-symmetric dissipation in the DVA leads to a great reduction of the beam response, the reduction is larger with respect to the linear DVA.

Samani, Farhad S.; Pellicano, Francesco

2012-05-01

258

Nonlinear Free Vibration of Simply Supported Beams Considering the Effects of Shear Deformation and Rotary Inertia, a Homotopy Perturbation Approach  

NASA Astrophysics Data System (ADS)

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 a nonlinear ordinary differential equation. HPM is then used to find analytic expressions for nonlinear natural frequencies of the pre-stretched beam. A parametric study has also been applied in order to investigate the effects of design parameters such as applied axial load and slenderness ratio. Comparison between presented results and numerical results which are in full agreement shows that HPM can significantly improve the accuracy of previously reported results in the literature.

Mojahedi, Mahdi; Moeenfard, Hamid; Ahmadian, Mohammad Taghi

259

Nonlinear theory of beam-wave interaction in the pasotron with a phase-mixed electron beam  

SciTech Connect

The nonlinear theory describing the interaction processes in traveling-wave-amplifier (TWT) and backward-wave-oscillator (BWO) configurations of pasotrons is developed. It is shown that space charge forces in electron bunches formed in the process of beam-wave interaction in the pasotron play a role completely different from that in linear-beam devices with a strong magnetic focusing of electron beams. While in the latter devices the space charge forces limit the device efficiency due to saturation of the axial bunching, in the pasotron they do not destroy electron bunches but cause the radial expansion of them, which may increase device efficiency. The role of these forces is compared with the ion focusing and the radial electric field of the wave, and it is shown that, under certain conditions, it may dominate. The efficiency of the pasotron-TWT with a phase-mixed beam well focused at the entrance may exceed 50%. In the pasotron-BWO, the efficiency is lower (up to 26% in the case studied), but it can grow as the equivalent of the Pierce gain parameter increases.

Bliokh, Yu.P.; Nusinovich, G.S. [Technion, Haifa, 32000 (Israel); Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland, 20742-3511 (United States)

2006-02-15

260

Far field intensity distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media.  

PubMed

In this work we present a simple model that can be used to calculate the far field intensity distributions when a Gaussian beam cross a thin sample of nonlinear media but the response can be nonlocal. PMID:20941108

Ramirez, E V Garcia; Carrasco, M L Arroyo; Otero, M M Mendez; Cerda, S Chavez; Castillo, M D Iturbe

2010-10-11

261

Fused biconical tapered technique based light beam coupling between a single mode fiber and a high nonlinearly photonic crystal fiber  

Microsoft Academic Search

Light beam coupling between a single-mode fiber and a highly nonlinear photonic crystal fiber based on fused biconical tapered technique is experimentally demonstrated. As a result, more than 90% coupling ratio are achieved.

Jianguo Liu; Tee-Hiang Cheng; Yong-kee Yeo; Yixin Wang; Zhaowen Xu; Dawei Wang

2009-01-01

262

Frequency-domain subspace identification for nonlinear mechanical systems  

NASA Astrophysics Data System (ADS)

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

Noël, J. P.; Kerschen, G.

2013-11-01

263

The oscillatory behavior, static and dynamic analyses of a micro/nano gyroscope considering geometric nonlinearities and intermolecular forces  

NASA Astrophysics Data System (ADS)

The nonlinear dynamic and static deflection of a micro/nano gyroscope under DC voltages and base rotation are investigated. The gyroscope undertakes two coupled bending motions along the drive and sense directions and subjected to electrostatic actuations and intermolecular forces. The nonlinear governing equations of motion for the system with the effect of electrostatic force, intermolecular tractions and base rotation are derived using extended Hamilton principle. Under constant voltage, the gyroscope finds the preformed shape. First, the deflection of the micro/nano gyroscope under electrostatic forces is obtained by static and dynamic analyses. Furthermore, the static and dynamic instability of the system are investigated. Afterward the oscillatory behavior of the pre-deformed micro/nano gyroscope around equilibrium is studied. The effects of intermolecular and nonlinear parameters on the static and dynamic deflection, natural frequencies and instability of the micro/nano gyroscope are studied. The presented model can be used to exactly determine static and the dynamic behavior of vibratory micro/nano gyroscopes.

Mojahedi, M.; Ahmadian, M. T.; Firoozbakhsh, K.

2013-12-01

264

Electromagnetic Radiation and Nonlinear Energy Flow in a Beam Plasma System.  

NASA Astrophysics Data System (ADS)

The mechanism by which unstable electron plasma waves are converted into the observed electromagnetic waves is investigated. Electromagnetic radiation is generated upon injection of an energetic electron beam into a uniform quiescent magnetoplasma. The emission is observed to peak near the plasma frequency ((omega)(,em) > (omega)(,p) >> (omega)(,c)) is observed to result from the scattering of intense electrostatic plasma waves off self-consistently produced ion acoustic waves. The frequency and wave vector matching conditions are experimentally verified ((omega)(,e) = (omega)(,i) + (omega)(,em), k(,e) = k(,i) + k(,em), k(,e) = k(,i)). The emission is found to be localized, polarized and negligible in intensity at (omega)(,em) = 2(omega)(,p). The space-time growth properties of the three wave interaction are presented. We have also observed the nonlinear damping of the electron plasma waves and the subsequent production of an energetic electron tail on the background plasma. The two dimensional character of an axisymmetric beam plasma system are investigated. The two dimensional cross-correlation function and the (omega)-k properties of the electron plasma waves are investigated. The high energy beam electrons are diagnosed using a novel directional energy analyzer, which is capable of resolving the true three dimensional distribution function. The beam electrons are observed to diffuse in both parallel and perpendicular velocity as the unstable plasma waves gain energy. The background electrons are diagnosed with respect to both energy and direction. The nonlinear damping is seen as an anomalous ac resistivity produced by large amplitude density fluctuations ((delta)n(,i)/n(,i) (TURNEQ) 5%) in the electron beam region.

Whelan, David Arthur

1983-12-01

265

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

SciTech Connect

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

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

2013-12-15

266

Second order nonlinear optical properties of zinc oxide films deposited by low temperature dual ion beam sputtering  

SciTech Connect

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

267

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

NASA Astrophysics Data System (ADS)

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

Sepehri Javan, N.; Adli, F.

2013-10-01

268

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

269

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

270

Research on non-linear structural behaviors of prestressed concrete beams made of high strength and steel fiber reinforced concretes  

Microsoft Academic Search

The flexural behaviors of fully and partially prestressed concrete beams made of high strength and steel fiber reinforced concretes are studied by experiment and non-linear finite element method. Three levels of partial prestress ratio (PPR) are considered, and for each PPR, a pair of two-span continuous beams with box-section are designed. In each pair of the test beams, one is

Haibo Liu; Tianyu Xiang; Renda Zhao

2009-01-01

271

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

NASA Astrophysics Data System (ADS)

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.

2010-12-01

272

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

SciTech Connect

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

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

2010-12-15

273

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

Microsoft Academic Search

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

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

1988-01-01

274

Justification of a nonlinear Schrödinger model for laser beams in photopolymers  

NASA Astrophysics Data System (ADS)

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

Pelinovsky, Dmitry; Ponomarev, Dmitry

2014-06-01

275

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

276

Thermomechanical nonlinear vibration analysis of a spring-mass-beam system  

Microsoft Academic Search

Thermo-mechanical vibrations of a simply supported spring-mass-beam system are investigated analytically in this paper. Taking\\u000a into account the thermal effects, the nonlinear equations of motion and internal\\/external boundary conditions are derived\\u000a through Hamilton’s principle and constitutive relations. Under quasi-static assumptions, the equations governing the longitudinal\\u000a motion are transformed into functions of transverse displacements, which results in three integro-partial differential equations

Mergen H. Ghayesh; Siavash Kazemirad; Mohammad A. Darabi; Pamela Woo

277

Propagation of Gaussian beam in self-defocusing photovoltaic photorefractive nonlinear crystal of LiNbO3:Fe  

NASA Astrophysics Data System (ADS)

We investigate experimentally the propagation of Gaussian beam in self-defocusing photovoltaic photorefractive nonlinear crystal of iron-doped lithium niobate. In steady-state, the propagating beam in the low-refractive-index optical channel written by the beam itself is affected mostly by linear diffraction and anisotropic divergence of the saturated negative lenslike effect. And the latter affects the incident beam with convergent wavefront much more than that with divergent wavefront. In the case of the incident beam with the convergent wavefront, the angular width of the spatial spectrum of the output beam decreases along with the size of the output beam. We believe that the phase-type spatial filtering of the funnel-type low-refractive-index optical channel written by the propagating beam itself causes the results.

Wang, Dayun; Liu, Simin; Liu, Zhaohong; Guo, Ru; Huang, Chunfu; Zhu, Nan; Song, Tao; Zhao, Peide; Zhang, Yong

2008-12-01

278

Model for nonlinear evolution of localized ion ring beam in magnetoplasma  

SciTech Connect

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

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

2012-06-15

279

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

280

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

281

Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging  

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

282

Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging.  

PubMed

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. PMID:15704404

Yang, Xinmai; Cleveland, Robin O

2005-01-01

283

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

PubMed

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

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

2013-11-01

284

Nonlinear optical beam manipulation and high energy beam propagation through the atmosphere; Proceedings of the Meeting, Los Angeles, CA, Jan. 18-20, 1989  

SciTech Connect

Various papers on nonlinear optical beam manipulation and high-energy beam propagation through the atmosphere are presented. Individual topics addressed include: suppression of Raman amplification using large Stokes seeds, review of multiple-short-pulse SBS experiments and theory, laser-induced gratings for beam manipulation in a gas, considerations for computing realistic atmospheric distortion parameter profiles, effect of turbulent diffusion on laser propagation, use of multiple photon processes in krypton for laser guiding of electron beams, effect of ionization on intense electron beam propagation in low-pressure media, lidar measurements of the troposphere and middle atmosphere, seasonal and diurnal changes in cloud obscuration to visible and IR energy transmission, new cloud composite climatologies using meteorological satellite imagery, effect of neutral atmospheric structure on beam propagation, small-scale electron density fluctuations in a disturbed ionospheric environment, and SDIO radio frequency communications in a structured environment.

Fisher, R.A.; Wilson, L.E.

1989-01-01

285

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

SciTech Connect

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

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

2013-06-15

286

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

NASA Astrophysics Data System (ADS)

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

Sepehri Javan, N.; Adli, F.

2013-06-01

287

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

PubMed

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

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

2006-06-01

288

Out-of-resonance vibration modulation of ultrasound with a nonlinear oscillator for microcrack detection in a cantilever beam  

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

289

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

SciTech Connect

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 2-4 MW continuous-wave (CW) at 170 GHz to meet the demand of very high radio frequency CW power 1-2 MW 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 [Research Institute of High Energy Electronics, University of Science and Technology of China, Chengdu, Sichuan, 610054 (China)

2007-10-15

290

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

NASA Astrophysics Data System (ADS)

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

Hora, Heinrich; Handel, Peter H.

2013-05-01

291

The Effect of Non-Linear Inertia on the Steady State Response of a Beam System Subjected to Combined Excitations  

NASA Astrophysics Data System (ADS)

In this paper a weakly non-linear beam system subjected simultaneously to parametric and harmonic excitations is studied. There are many types of resonant phenomena under these loading conditions. The weakly non-linear differential equation is derived by use of the averaging method and the method of multiple scales. Even for the first approximate solutions, it is found that different results arise due to the existence of a non-linear inertia factor of the governing equation. The transient amplitudes obtained by these two methods are compared with those obtained by the Runge-Kutta method. Steady state responses are also shown for the various cases of resonances.

Fung, R.-F.

1997-06-01

292

Femtosecond single-beam direct laser poling of stable and efficient second-order nonlinear optical properties in glass  

NASA Astrophysics Data System (ADS)

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 ?eff(2) ˜ 0.6 pm V-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.; Petit, Y.; Royon, A.; Dussauze, M.; Rodriguez, V.; Cardinal, T.; Canioni, L.

2014-03-01

293

SELF-FOCUSING AND DIFFRACTION OF LIGHT IN A NONLINEAR MEDIUM  

Microsoft Academic Search

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

294

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

NASA Astrophysics Data System (ADS)

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

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

2004-03-01

295

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

296

Influence of thermal nonlinearity on the spatial coherence of a laser beam in a randomly inhomogeneous medium  

Microsoft Academic Search

The paper deals with the problem of the combined effect of thermal nonlinearity and random inhomogeneities of the medium on the spatial coherence of a light beam. It is shown that the presence of a defocusing thermal lens leads to an increase in the spatial radius of the coherence field.

M. S. Belenkii; A. A. Zemlianov

1979-01-01

297

Effects of magnetic non-linearities on a stored proton beam and their implications for superconducting storage rings  

SciTech Connect

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

298

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

299

Breathing and beating dynamics of Gaussian beam in planar graded-index absorbing nonlinear waveguides  

NASA Astrophysics Data System (ADS)

The spatial dynamics of laser beams in absorbing planar waveguides with a parabolic index profile in a saturable or cubic-quintic medium are calculated using the "collective variable approach" technique. In the absence of losses, we construct diagrams which define regions of self-focusing and self-diffractive beam propagation for both types of media. It is found that propagating pulses exhibit an oscillatory pattern, similar to breathing behavior in homogeneous media. If the incident pulse spatial profile and the center of the index profile are not aligned, the pulse oscillates around the index origin with a "beat" frequency that depends on the graded index. Both the breathing and the beat frequencies are also calculated for other graded-index profiles, such as those with additional higher-power terms, and are found to be extremely sensitive to the index profile. In media with linear and nonlinear absorption, we demonstrate the difference between the breathing behavior in graded-index and homogeneous waveguides.

Ianetz, D.; Kaganovskii, Yu.; Wilson-Gordon, A. D.

2012-08-01

300

Nonlinear properties of the Kapchinskij-Vladimirskij equilibrium and envelope equation for an intense charged-particle beam in a periodic focusing field  

NASA Astrophysics Data System (ADS)

The nonlinear properties of the Kapchinskij-Vladimirskij (KV) equilibrium and envelope equation are examined for an intense charged-particle beam propagating through an applied periodic solenoidal focusing magnetic field, including the effects of the self-electric and self-magnetic fields associated with the beam space charge and current. It is found that the beam emittance is proportional to the maximum canonical angular momentum achieved by the particles within the KV distribution. The Poincaré mapping technique is used to determine systematically the axial dependence of the radius of the matched (equilibrium) beam and to study nonlinear behavior in the nonequilibrium beam envelope oscillations. It is shown that the nonequilibrium beam envelope oscillations exhibit nonlinear resonances and chaotic behavior for periodic focusing magnetic fields and sufficiently high beam densities. Certain correlations are found between the nonlinear resonances and well-known instabilities for the KV equilibrium. It is also shown, in agreement with previous studies, that there exists a uniquely matched beam in the parameter regime of practical interest, i.e., ?0<90°, where ?0 is the vacuum phase advance over one axial period of the focusing field. The nonlinear resonances and chaotic behavior in the nonequilibrium beam envelope oscillations may play an important role in mismatched or multiple beam transport, including emittance growth and beam halo formation and evolution.

Chen, Chiping; Davidson, Ronald C.

1994-06-01

301

Evaluation of the geometric, scatter, and septal penetration components in fan-beam collimators using Monte Carlo simulation  

Microsoft Academic Search

The quantitative analysis of single-photon emission computed tomography data requires an accurate determination of the collimator point spread function (PSF). The aim of this paper is to characterize fan-beam collimators' PSFs by using Monte Carlo simulation. Given a particular collimator configuration, a detailed hexagonal hole array was generated and information describing its geometry was stored in a lookup table. When

A. Cot; J. Sempau; D. Pareto; S. Bullich; J. Pavia; F. Calvino; D. Ros

2002-01-01

302

Spectral element methods for nonlinear spatio-temporal dynamics of an Euler-Bernoulli beam  

NASA Astrophysics Data System (ADS)

Spectral element methods are high order accurate methods which have been successfully utilized for solving ordinary and partial differential equations. In this paper the space-time spectral element (STSE) method is employed to solve a simply supported modified Euler-Bernoulli nonlinear beam undergoing forced lateral vibrations. This system was chosen for analysis due to the availability of a reference solution of the form of a forced Duffing's equation. Two formulations were examined: i) a generalized Galerkin method with Hermitian polynomials as interpolants both in spatial and temporal discretization (HHSE), ii) a mixed discontinuous Galerkin formulation with Hermitian cubic polynomials as interpolants for spatial discretization and Lagrangian spectral polynomials as interpolants for temporal discretization (HLSE). The first method revealed severe stability problems while the second method exhibited unconditional stability and was selected for detailed analysis. The spatial h-convergence rate of the HLSE method is of order ?= p s+1 (where p s is the spatial polynomial order). Temporal p-convergence of the HLSE method is exponential and the h-convergence rate based on the end points (the points corresponding to the final time of each element) is of order 2 p T-1 ???2 p T+1 (where p T is the temporal polynomial order). Due to the high accuracy of the HLSE method, good results were achieved for the cases considered using a relatively large spatial grid size (4 elements for first mode solutions) and a large integration time step (1/4 of the system period for first mode solutions, with p T=3). All the first mode solution features were detected including the onset of the first period doubling bifurcation, the onset of chaos and the return to periodic motion. Two examples of second mode excitation produced homogeneous second mode and coupled first and second mode periodic solutions. Consequently, the STSE method is shown to be an accurate numerical method for simulation of nonlinear spatio-temporal dynamical systems exhibiting chaotic response.

Bar-Yoseph, P. Z.; Fisher, D.; Gottlieb, O.

1996-11-01

303

Dependence of beating dynamics on the ellipticity of a Gaussian beam in graded-index absorbing nonlinear fibers  

NASA Astrophysics Data System (ADS)

Using the collective variable approach technique, we analyze propagation of elliptical Gaussian beams in nonlinear waveguides with a parabolic graded-index (GRIN) profile. We considered both saturable and cubic-quintic models to describe the nonlinearity, taking into account both linear and nonlinear absorption. For lossless media, we construct diagrams, which define regions of self-focusing and self-diffractive beam propagation for both models in GRIN waveguides and compare them with those for nongraded waveguides. The widths of the propagating elliptic beam exhibit an oscillatory pattern, similar to the “breathing” and “beating” behavior found in nongraded media. Two types of beating oscillations are observed in both models. We calculate the dependence of Lbeat/Lbr, the ratio of the “beating” to “breathing” oscillation periods, on the beam ellipticity ? and the GRIN index g. We find that there is a remarkable difference in this dependence between saturable and cubic-quintic media: in the saturable model, Lbeat/Lbr is a monotonic function of ?, whereas in the cubic-quintic model, it is characterized by singularities, which correspond to transitions between the types of beat oscillations. For lossy media, we discuss the difference between the breathing behavior in nongraded and GRIN waveguides.

Ianetz, D.; Kaganovskii, Yu.; Wilson-Gordon, A. D.

2013-04-01

304

Nonlinear Diffraction.  

National Technical Information Service (NTIS)

The equations governing the geometrical approximation for nonlinear wave propagation that were derived in a previous paper of this series are used here to construct a special solution that describes diffraction at an edge. The effect described is a purely...

F. E. Bisshopp

1969-01-01

305

Geometric Additions +Logarithms = Geometric Multiplication  

NSDL National Science Digital Library

Mathematicians often argue that anything which can be represented numerically or algebraically can also be represented geometrically. This is perhaps true even to the extent that simple numeric calculations can be demonstrated geometrically. This example illustrates one such geometric process of addition. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

306

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

NASA Technical Reports Server (NTRS)

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

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

1984-01-01

307

Geometric Solids  

NSDL National Science Digital Library

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

Lessonplans, Utah

2012-09-18

308

Ion-beam sputtered (IBS) thin-film interference filters for nonlinear optical imaging  

NASA Astrophysics Data System (ADS)

Nonlinear optical (NLO) microscopy is emerging as a powerful technique for the study of biological samples. By combining several different imaging modalities such as multiphoton (MP) fluorescence, second-harmonic and thirdharmonic generation (SHG and THG), and coherent Raman scattering techniques such as coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS), it is possible to combine the best practices of label and label-free imaging into a single platform capable of imaging structures within single cells and elucidating the health of biological tissue samples, even at the submicron level. Single-substrate, ion-beam-sputtered (IBS) thinfilm interference filters are a key enabling technology in laser-based optical microscopy and play a critical role in multimodal NLO imaging. In microscopy applications, optical filters are used to select and discriminate exactly which wavelengths of light are to be transmitted, reflected and suppressed. In this paper we discuss various important characteristics of hard-coated thin-film interference filters, such as high light throughput, steep edges, and high out-of-band blocking, all of which require careful consideration when designing and manufacturing optical filters for NLO imaging applications. To understand the true performance of hard-coated IBS filters, a simple CARS imaging experiment was performed. We found a 2.6 times increase in signal enhancement and 70% improvement in image contrast when compared to a commercially available filter commonly used in CARS microscopy applications.

Anderson, Neil; Prabhat, Prashant; Erdogan, Turan

2012-02-01

309

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

PubMed

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

310

Generation of low-frequency electrostatic and electromagnetic waves as nonlinear consequences of beam-plasma interactions  

SciTech Connect

Nonlinear evolution of the electron two-stream instability in a current-carrying plasma is examined by using a two-dimensional electromagnetic particle-in-cell simulation. Formation of electron phase-space holes is observed as an early nonlinear consequence of electron-beam-plasma interactions. Lower-hybrid waves, electrostatic, and electromagnetic whistler mode waves are also excited by different mechanisms during the ensuing nonlinear wave-particle interactions. It is shown by the present computer simulation with a large simulation domain and a long simulation time that these low-frequency waves can disturb the electrostatic equilibrium of electron phase-space holes, suggesting that the lifetime of electron phase-space holes sometimes becomes shorter in a current-carrying plasma.

Umeda, Takayuki [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8601 (Japan)

2008-06-15

311

Nanosecond nonlinear ?erenkov conical beams generation by intracavity sum frequency mixing in KTiOAsO4 crystal.  

PubMed

Nanosecond ?erenkov-type conical beam at 628 nm is obtained by intracavity sum frequency mixing (SFM) of 1064 and 1534 nm in KTiOAsO(4) (KTA) crystal. The 1534 nm signal generated by the KTA optical parametric oscillation (OPO), respectively, interacts with the orthogonally polarized 1064 nm radiations by the nonlinear ?erenkov SFM, emitting two red rings with cone angles of 11.4° and 16.0°, respectively. Multidomain structure observed in the KTA crystal can account for the corresponding phenomenon. The KTA crystal simultaneously serves as OPO medium and ?erenkov radiation emitter in this experiment, indicating that it is a promising multifunctional nonlinear crystal material. Furthermore, the naturally grown crystal combined with intracavity ?erenkov-type configuration will provide a simple and compact approach, opening a door for the wide application of nonlinear ?erenkov radiation sources due to its cost-effectiveness. PMID:23455141

Huang, Haitao; Shen, Deyuan; He, Jingliang; Chen, Hao; Wang, Yong

2013-02-15

312

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

NASA Technical Reports Server (NTRS)

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

Moyer, E. T., Jr.

1984-01-01

313

Higher-order contribution to obliquely nonlinear electron-acoustic waves with electron beam in a magnetized plasma  

SciTech Connect

Propagation of electron-acoustic waves in a strongly magnetized four-component plasma consisting of cold and hot electrons, a warm electron beam, and stationary ions is investigated. The present model considered weakly dispersive and strongly magnetized plasma in the limit of long wavelengths. The introduction of an electron beam allows the existence of electron-acoustic solitons with velocity related to the beam velocity. With increasing the beam velocity and the beam temperature, both the soliton amplitude and the width increase. Applying a reductive perturbation theory, a nonlinear Zakharov-Kuznetsov (ZK) equation for the first-order perturbed potential and a linear inhomogeneous Zakharov-Kuznetsov (ZK-type) equation for the second-order perturbed potential are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. These solutions admit either compressive or rarefactive soliton type depending on the electron-beam parameters. Moreover, the dependence of the solution on the beam parameters, obliqueness on the magnetic field, and the magnetic field itself is also investigated. The application of the present investigation to the broadband electrostatic noise in the dayside auroral zone of the Earth's magnetosphere is considered.

El-Labany, S.K.; El-Taibany, W.F.; El-Abbasy, O.M. [Department of Physics, Faculty of Science-Damietta, Mansoura University, Damietta El-Gedida, P.O. 34517 (Egypt)

2005-09-15

314

Non-linear dynamics of flexible multibody systems  

Microsoft Academic Search

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

Adnan Ibrahimbegovic; Robert L. Taylor; H. Lim

2003-01-01

315

Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method  

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

316

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

NASA Astrophysics Data System (ADS)

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

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

1998-12-01

317

A graphical method for determining the in-plane rotation angle in geometric calibration of circular cone-beam CT systems.  

PubMed

It is well known that seven parameters completely describe a circular cone-beam geometry in either flat-panel X-ray computed tomography (CT) or single pinhole SPECT imaging. This paper considers the problem of determining one of the seven parameters only, the detector in-plane rotation or twist angle ?. We describe a graphical procedure that can determine ? independently of all other six parameters from a geometric calibration scan of point objects. Our method is exact in the ideal noise-free case and is general in that the other two out-of-plane detector rotation angles ? and ? can be nonzero. The calibration scan typically needs at least two point objects and an even number of projection views over a full 360° data acquisition. Under certain conditions, projection data truncation or a short scan acquisition of 180° + fan angle can be accommodated without affecting the accuracy of the calibration result. The graphical method is equally applicable to rotational multipinhole SPECT geometry. In this case, the final result is averaged from the individual estimates considering each pinhole separately. We use computer simulations and a multipinhole SPECT experiment to demonstrate the accuracy and precision of the proposed method. PMID:22231693

Xu, Jingyan; Tsui, Benjamin M W

2012-03-01

318

Large Amplitude Free and Forced Oscillations of Functionally Graded Beams  

Microsoft Academic Search

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

Mohammad Rafiee; Hamed Kalhori

2012-01-01

319

Strong nonlinear focusing of light in nonlinearly controlled electromagnetic active metamaterial field concentrators  

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

320

Nonlinear Propagation of a Mixture of TEM00 and TEM01 Modes of a Laser Beam in a Cubic Quintic Medium  

Microsoft Academic Search

We have presented an investigation on the characteristics of a laser beam, which is a mixture of two degenerate modes (TEM00 and TEM01), that is propagating through cubic quintic nonlinear media. Employing WKBJ method and paraxial ray approximation we have derived a pair of dynamical equations for the beam widths of the mixture of two modes. These equations are identical

S. Konar; Soumendu Jana

2005-01-01

321

Nonlinear vibrations and buckling of a flexible rotating beam: A prescribed torque approach  

Microsoft Academic Search

This work is concerned with theoretical and numerical analyses of the nonlinear transverse free vibrations of a flexible rotating arm attached with a setting angle to a rigid hub. The system is assumed to be subjected to an external torque and a rotation dissipation load which collectively referred to as perturbations. A set of two strongly coupled second-order ordinary nonlinear

F. S. M. Jarrar; M. N. Hamdan

2007-01-01

322

A state observer for nonlinear systems and its application to ball and beam system  

Microsoft Academic Search

In this paper, we present a state observer for single-input\\/single-output nonlinear systems which fail to have well defined relative degree. It is shown that there exists a local state observer for a nonlinear system if it has robust relative degree n. The proposed observer utilizes the coordinate change which transforms a system into an approximate normal form. The proposed method

Nam H. Jo; Jin H. Seo

2000-01-01

323

Influence of non-linear index on coherent passive beam combining of fiber lasers  

Microsoft Academic Search

Coherent laser beam combining is potentially attractive way to increase the output beam brightness beyond the limits imposed on single-mode lasers by technological problems. Passive phase locking does not need complex external management. A specific feature of fiber amplifiers and lasers is that they possess optical path differences of many wavelengths magnitude. Cold-cavity theory of coherent laser beam combining predicts

A. P. Napartovich; N. N. Elkin; D. V. Vysotsky

2011-01-01

324

Nonlinear - Spectroscopic Studies of Highly Excited States of Molecules in Supersonic Beams.  

NASA Astrophysics Data System (ADS)

This thesis describes nonlinear optical spectroscopic experiments on molecules and molecular clusters in supersonic beams. First, the absorption spectrum of water dimers in the O-H stretching region ({~}3400 -3800 cm^{-1}) was obtained with a resolution of {~ }2 cm^{-1}, by monitoring vibrational predissociation. The O-H stretching frequencies of the dimer were found to be shifted by hydrogen bonding, with respect to those of the monomer. In a similar, lower-resolution experiment, {rm (H _2O)_{19}} clusters were studied. The effect of the cluster temperature on the absorption spectrum was discussed. A tunable, narrowband ({~ }1.5 cm^{-1} resolution) XUV source in the 904-1024 A region has been developed using frequency tripling in a pulsed jet of gas. Rotationally resolved photoionization spectra of H_2 O and D_2O were then obtained with this source. XUV-UV and XUV-visible double-resonance experiments on H_2 are described. The former probed the ion-pair production in the (H^ {+} + H^{-}) continuum, and detected previously-unobserved Rydberg series which converge to high vibrational levels (v^ {+} ~ 10) of H _sp{2}{+}. The latter probed the region slightly below the ionization potential and detected electronic states with medium principal quantum number (n ~ 5). Predissociation properties of these levels were found to vary greatly with the symmetries of their electronic configurations. Two infrared-ultraviolet double resonance experiments on benzene were performed. In both, vibrational state selection of the benzene molecules was accomplished using resonantly-enhanced two-photon ionization (R2PI). In the first, the overtones of C-H stretches in electronic-ground -state benzene and the benzene dimer were studied with a resolution of {~}1 cm ^{-1}. The spectra showed newly-resolved vibrational features with bandwidths less than a few cm^{-1}. The dimer's C-H stretching fundamental spectrum showed combination bands with van der Waals intermolecular vibrations, and widths of rotational bands support the argument that the dimer is T-shaped. In the second experiment, hitherto unknown frequencies of C-H stretching and bending modes in benzene's first excited singlet state were determined. A reassignment of the benzene UV spectrum is suggested, with the result that the C-H stretches of different symmetry in the excited electronic state all have their frequencies increased by {~}20 cm^ {-1} from the ground electronic state. (Abstract shortened with permission of author.).

Page, Ralph Henry

1987-09-01

325

A result on quasi-periodic solutions of a nonlinear beam equation with a quasi-periodic forcing term  

NASA Astrophysics Data System (ADS)

In this paper, a quasi-periodically forced nonlinear beam equation {u_{tt}+u_{xxxx}+? u+\\varepsilon?(t)h(u)=0} with hinged boundary conditions is considered, where ? > 0, {\\varepsilon} is a small positive parameter, {?} is a real analytic quasi-periodic function in t with a frequency vector ? = ( ? 1, ? 2 . . . , ? m ), and the nonlinearity h is a real analytic odd function of the form {h(u)=?_1u+?_{2bar{r}+1}u^{2bar{r}+1}+sum_{k? bar{r}+1}?_{2k+1}u^{2k+1},?_1,?_{2bar{r}+1} neq0, bar{r} in {mathbb {N}}.} The above equation admits a quasi-periodic solution.

Wang, Yi; Si, Jianguo

2012-02-01

326

Nonlinear Dynamics of High-Brightness Electron Beams and Beam-Plasma Interactions: Theories, Simulations, and Experiments  

SciTech Connect

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

327

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

Microsoft Academic Search

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

J. Sussmann; Guoqing Tang

1991-01-01

328

Geometric Approach  

Microsoft Academic Search

An automatic cortical gray matter segmentation from a three-dimensional brain images (MR or CT) is a well known problem in medical image processing. In this paper we first formulate it as a geometric variational problem for propagation of two coupled bounding surfaces. An efficient numerical scheme is then used to implement the geodesic active surface model. Exper- imental results of

Roman Goldenberg; Ron Kimmel; Ehud Rivlin; Michael Rudzsky

329

Nonlinear Curvature Expressions for Combined Flapwise Bending, Chordwise Bending, Torsion and Extension of Twisted Rotor Blades  

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

330

Physical origin of observed nonlinearities in Poly (1-naphthyl methacrylate): Using a single transistor—transistor logic modulated laser beam  

NASA Astrophysics Data System (ADS)

A thermal lens technique is adopted using a single modulated continuous wave (cw) 532-nm laser beam to evaluate the nonlinear refractive index n2, and the thermo-optic coefficient dn/dT, in polymer Poly (1-naphthyl methacrylate) (P-1-NM) dissolved in chloroform, tetrahydrofuran (THF), and dimethyl sulfoxide (DMSO) solvents. The results are compared with Z-scan and diffraction ring techniques. The comparison reveals the effectiveness and the simplicity of the TTL modulation technique. The physical origin is discussed for the obtained results.

Qusay, M. A. Hassan; Hussain, A. Badran; Alaa, Y. AL-Ahmad; Chassib, A. Emshary

2013-11-01

331

Finding a near integrable nonlinear lattice using a convenient time averaging scheme and control of beam halo formation through nonlinear transport.  

NASA Astrophysics Data System (ADS)

A condition for improved dynamic aperture of nonlinear, alternating gradient transport systems has been derived using Lie-transform perturbation theory. The Lie transformation method exploits the property of canonical invariance of Poisson brackets thereby making the formulation less tedious especially when the form of the Hamiltonian is complex. Using this method, we have shown that one can transform to a time averaged reference frame where the focusing is azimuthally symmetric under certain conditions. These conditions are met when sextupoles or octupoles are inserted exactly between the alternate gradient quadrapoles and themselves alternate in sign. This symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame leading to reduced chaos and improved confinement when compared to a system that is not close to integrability. Our numerical calculations show that this is indeed the case. The effects of space charge shall also be discussed. We propose the use of nonlinear focusing to mitigate beam halo formation. Various simulation results shall also be presented to demonstrate this.

Sonnad, Kiran G.; Cary, John R.

2002-11-01

332

DURIP-94 Gigawatt The Beam System for Linear and Nonlinear Fir Spectroscopy.  

National Technical Information Service (NTIS)

Under the support from AFOSR-DRRIP, Ultrafast Optoelectronics Lab. Rensselaer Polytechnic Institute has installed a new laser system (Spectra-Physics Ti:sapphire laser and Optical parametric oscillator) for linear and nonlinear terahertz spectroscopy. Bas...

X. C. Zhang

1996-01-01

333

Measurement of optical nonlinear susceptibility of CdS single crystal using a single beam  

Microsoft Academic Search

We report a measurement of optical nonlinear susceptibility of CdS using Z-scan method. The input laser light irradiating on the CdS single crystal had a wavelength of 514.5 nm and a flux density of 16 kW\\/cm(sup 2). We estimate a nonlinear susceptibility of chi(sup (3)) = 3.5 x 10(sup - 9) (esu) being in agreement with an anharmonic oscillator model

Zhengang Li; Guangnan Xiong; Zhihong Zhao; Xiwu Fan

1994-01-01

334

Nonlinear airship aeroelasticity  

Microsoft Academic Search

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

335

Geometric Models  

NSDL National Science Digital Library

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

Siegrist, Kyle

2009-02-23

336

Neurocontroller alternatives for “fuzzy” ball-and-beam systems with nonuniform nonlinear friction  

Microsoft Academic Search

The ball-and-beam problem is a benchmark for testing control algorithms. Zadeh proposed (1994) a twist to the problem, which, he suggested, would require a fuzzy logic controller. This experiment uses a beam, partially covered with a sticky substance, increasing the difficulty of predicting the ball's motion. We complicated this problem even more by not using any information concerning the ball's

Paul H. Eaton; Danil V. Prokhorov; Donald C. Wunsch II

2000-01-01

337

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

SciTech Connect

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

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

2005-03-01

338

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

NASA Astrophysics Data System (ADS)

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

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

2014-06-01

339

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

NASA Astrophysics Data System (ADS)

Gold nanocluster thin films (˜ 200 nm thickness) consisting of metal clusters ˜ 5 nm in size embedded in a matrix of Nb 2O 5 were deposited by ion beam-assisted deposition (IBAD) by coevaporation of Au and Nb with O 2+ ion bombardment. The microstructure and optical characteristics of these films were examined as-deposited and after annealing at 600°C. Annealing crystallized the amorphous oxide matrix and ripened the nanoclusters. A strong linear absorption at the wavelength of the surface plasmon resonance for Au developed as a result of annealing. The linear optical behavior was modeled using Mie scattering theory. Good agreement was found between the nanocluster sizes predicted by the theory and the particle sizes observed experimentally using transmission electron microscopy (TEM). The nonlinear optical (NLO) properties of the nanocluster films were probed experimentally using degenerate four wave mixing and nonlinear transmission. The wavelength was near the peak of the surface plasmon resonance as measured by VIS/UV spectroscopy. Values of | ?xxxx(3)| were 7.3 × 10 -8 and 3.0 × 10 -10 esu for annealed and unannealed samples, respe The dominant mechanism for the nonlinear response was change in dielectric constant due to the generation of a distribution of hot, photoexcited electrons.

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

1997-05-01

340

Nonlinear Plasma Waves Excitation by Intense Ion Beams in Background Plasma  

SciTech Connect

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

341

Study on asymptotic analytical solutions using HAM for strongly nonlinear vibrations of a restrained cantilever beam with an intermediate lumped mass  

Microsoft Academic Search

Presented herein is to establish the asymptotic analytical solutions for the fifth-order Duffing type temporal problem having\\u000a strongly inertial and static nonlinearities. Such a problem corresponds to the strongly nonlinear vibrations of an elastically\\u000a restrained beam with a lumped mass. Taking into consideration of the inextensibility condition and using an assumed single\\u000a mode Lagrangian method, the single-degree-of-freedom ordinary differential equation

Y. H. Qian; S. K. Lai; W. Zhang; Y. Xiang

342

Neurocontroller alternatives for (quote)fuzzy(quote) ball-and-beam systems with nonuniform nonlinear friction  

Microsoft Academic Search

The ball-and-beam problem is a benchmark for testing control algorithms. In the WorldCongress On Neural Networks, 1994, Prof. Lotfi Zadeh proposed a twist to the problem, which,he suggested, would require a fuzzy logic controller. This experiment uses a beam, partiallycovered with a sticky substance, increasing the difficulty of predicting the ball's motion. Wecomplicated this problem even more by not using

P. h. Eaton; D. v. Prokhorov; D. c. Wunsch

2000-01-01

343

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

344

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

Microsoft Academic Search

The authors present an approach for the approximate input-output linearization of nonlinear systems, particularly those for which relative degree is not well defined. They show 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

J. Hauser; S. Sastry; P. Kokotovic

1989-01-01

345

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

NASA Astrophysics Data System (ADS)

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

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

346

A self-consistent nonlinear theory of a premodulated electron beam propagating through a helix-loaded waveguide  

SciTech Connect

A self-consistent nonlinear theory of a relativistic electron beam propagating through a waveguide loaded with a sheath helix is developed by making use of Maxwell equations. A closed integrodifferential equation is obtained for the normalized beam current described in terms of the normalized time {theta} and propagation distance {zeta}. An analytical investigation of the partial integrodifferential equation of the current modulation is carried out by Fourier decomposing the current modulation with harmonic number scr(l). The mode strength c{sub scr(l)}({zeta}) is obtained in terms of the spatial oscillation frequency {eta}{sub scr(l)} and growth rate {xi}{sub scr(l)} of the mode amplitude, which are, in turn, determined in terms of the electrostatic and helix effects. The spatial oscillation frequency increases as the electrostatic effect (g{sub scr(l)}) increases. On the other hand, the growth rate increases with the strength of the helix effect. It is found that the mode strength c{sub scr(l)} is oscillatory and that it grows during propagation when the spatial frequency {eta}{sub scr(l)} (the electrostatic effect) is considerably larger than the growth rate {xi}{sub scr(l)} (the helix effect). Otherwise, the exponential growth dominates. Investigation of the helix mode must include the electrostatic effect for an intense beam.

Uhm, H.S. [Carderock Division, Naval Surface Warfare Center, 9500 MacArthur Boulevard, West Bethesda, Maryland 20817-5700 (United States)] [Carderock Division, Naval Surface Warfare Center, 9500 MacArthur Boulevard, West Bethesda, Maryland 20817-5700 (United States)

1997-10-01

347

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

348

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

NASA Astrophysics Data System (ADS)

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

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

2005-10-01

349

Nonlinear tracking with almost disturbance decoupling and its application to ball and beam system  

Microsoft Academic Search

The almost disturbance decoupling and trajectory tracking of nonlinear control systems, using an observer?based feedback linearization control, is developed. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed?loop system enjoys the following characteristics: input?to?state stability with respect to disturbance inputs and almost disturbance decoupling for any initial condition and bounded

2007-01-01

350

Nonlinear magneto-optical rotation narrowing in vacuum gas cells due to interference between atomic dark states of two spatially separated laser beams  

NASA Astrophysics Data System (ADS)

We present, experimentally and theoretically, nonlinear magneto-optical rotation (NMOR) using two spatially separated laser beams, the pump laser beam for creation and the probe laser beam for detection of the coherence between ground Zeeman sublevels. Both pump and probe lasers are tuned to Fg=2?Fe=1 transition in R87b . With the specially designed spatial configuration of the pump and the probe beams we were able to obtain dispersively shaped probe laser NMOR resonances in the Rb vacuum gas cell. The theory indicates that the obtained line shapes are due to the interference between prepared atomic states and the probe laser field. The interference nature of the resonances is supported by narrowing of NMOR resonances with increased separation between laser beams, and by the shift of the central fringe from the zero magnetic field with increased angle between initial orientation of electric vectors of linearly polarized pump and probe beams.

Mijailovi?, M. M.; Gruji?, Z. D.; Radonji?, M.; Arsenovi?, D.; Jelenkovi?, B. M.

2009-11-01

351

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

SciTech Connect

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

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

2013-08-15

352

Geometric optimization  

SciTech Connect

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

Hinker, P.; Hansen, C.

1993-09-01

353

Nonlinear Equations for Bending of Rotating Beams with Application to Linear Flap-Lag Stability of Hingeless Rotors  

NASA Technical Reports Server (NTRS)

The nonlinear partial differential equations for the flapping and lead-lag degrees of freedom of a torisonally rigid, rotating cantilevered beam are derived. These equations are linearized about an equilibrium condition to study the flap-lag stability characteristics of hingeless helicopter rotor blades with zero twist and uniform mass and stiffness in the hovering flight condition. The results indicate that these configurations are stable because the effect of elastic coupling more than compensates for the destabilizing flap-lag Coriolis and aerodynamic coupling. The effect of higher bending modes on the lead-lag damping was found to be small and the common, centrally hinged, spring restrained, rigid blade approximation for elastic rotor blades was shown to be resonably satisfactory for determining flap-lag stability. The effect of pre-cone was generally stabilizing and the effects of rotary inertia were negligible.

Hodges, D. H.; Ormiston, R. A.

1973-01-01

354

Electron-beam-induced domain poling in LiNbO{sub 3} for two-dimensional nonlinear frequency conversion  

SciTech Connect

A bulk of LiNbO{sub 3} was periodically poled in two dimensions to achieve noncollinear second-harmonic generation. The sample was fabricated using an electron-beam indirect exposure. This method used a dielectric buffer layer deposited on LiNbO{sub 3} Z{sup -}polar face to trap the incident electrons. These localized electrons formed a charge droplet which generated a strong electric field and triggered the domain inversion process in the LiNbO{sub 3}. Tailored two-dimensional domain configurations enabled quasi-phase-matched frequency doubling of a Nd:YLF laser at 15 different input angles. The measured angular dependence was in agreement with calculations based on the nonlinear reciprocal lattice vectors of the poled structure.

Glickman, Yinnon; Winebrand, Emil; Arie, Ady; Rosenman, Gil [Department of Physical Electronics, School of Electrical Engineering, Tel-Aviv University, Tel-Aviv, 69978 (Israel)

2006-01-02

355

Nonlinear adaptive control of optical jitter with a new liquid crystal beam steering device  

Microsoft Academic Search

This paper presents a new approach to active control of optical jitter with a new transmissive liquid crystal beam steering device, or tilt corrector. The device is driven by a linear time-invariant feedback control loop and an adaptive control loop to maximize the jitter-rejection bandwidth. In contrast to conventional fast steering mirrors, the liquid crystal device optically redirects the laser

Pawel K. Orzechowski; Steve Gibson; Tsu-Chin Tsao; Dan Herrick; Victor Beazel

2008-01-01

356

Studies of Optical-Beam Phase-Conjugation by Nonlinear Refraction.  

National Technical Information Service (NTIS)

We demonstrated the first cw phase-conjugating mirror with gain, and made a self-oscillating resonator which emitted a diffraction-limited optical beam while severe phase aberration was present in the resonator. We demonstrated storable and erasable phase...

R. W. Hellwarth

1981-01-01

357

Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation  

Microsoft Academic Search

A nonlinear analysis of an energy harvester consisting of a multilayered cantilever beam with a tip mass is performed. The\\u000a model takes into account geometric, inertia, and piezoelectric nonlinearities. A combination of the Galerkin technique, the\\u000a extended Hamilton principle, and the Gauss law is used to derive a reduced-order model of the harvester. The method of multiple\\u000a scales is used to

A. Abdelkefi; A. H. Nayfeh; M. R. Hajj

358

The Strong Effects Of On-Axis Focal Shift And Its Nonlinear Variation In Ultrasound Beams Radiated By Low Fresnel Number Transducers  

Microsoft Academic Search

On the basis of theoretical concepts, an accurate and complete experimental and numerical examination of the on-axis distribution and the corresponding temporal profiles for low-Fresnel-number focused ultrasound beams under increasing transducer input voltage has been performed. For a real focusing transducer with sufficiently small Fresnel number, a strong initial (linear) shift of the main on-axis pressure maximum from geometrical focal

Y. N. Makov; V. Espinosa; V. J. Sa´nchez-Morcillo; J. Ramis; F. Camarena

2006-01-01

359

Evaluation of femtosecond X-rays produced by Thomson scattering under linear and nonlinear interactions between a low-emittance electron beam and an intense polarized laser light  

Microsoft Academic Search

The mechanisms of Thomson scattering under linear and nonlinear interactions are discussed theoretically and used to evaluate characters of femtosecond (fs) X-rays produced by collision between a low-emittance electron beam and an intense polarized laser light. In the evaluation, we start from the differential cross section of the Thomson scattering under the linear interaction, and calculate the effects of the

J. Yang; M. Washio; A. Endo; T. Hori

1999-01-01

360

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

NASA Astrophysics Data System (ADS)

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

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

2012-07-01

361

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

362

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

Microsoft Academic Search

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

V. A. Shchepunov; H. Wollnik

2005-01-01

363

An Airy beam as a self-similar solution to the problem of slit laser beam propagation in a linear medium and in a photorefractive crystal with diffusion nonlinearity  

NASA Astrophysics Data System (ADS)

We have analysed self-similar solutions to the propagation problem of a slit beam with a plane wavefront in a linear medium and in a photorefractive crystal with diffusion nonlinearity. It is shown that in the latter case, despite the presence of the nonlinear term in the wave equation, the linear superposition principle holds true for the solutions of this class due to saturation. At the same time, the mirror symmetry violation of the wave equation for the transverse coordinate in the nonlinear case and the requirement to the spatial localisation modify one of the localised partial solutions (Airy beam) to the corresponding linear problem and prohibit the existence of other solutions of this class.

Makarov, V. A.; Petnikova, V. M.; Shuvalov, V. V.

2013-10-01

364

Optimal Design of Nonlinear Shell Structures.  

National Technical Information Service (NTIS)

A numerical method for optimal design of nonlinear shell structures is described. The nonlinearity is only geometrical and the external load is assumed to be conservative. The nonlinear shell is analyzed using standard shell finite elements with the displ...

U. T. Ringertz

1991-01-01

365

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

SciTech Connect

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

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

2010-11-15

366

Microstructure-dependent couple stress theories of functionally graded beams  

NASA Astrophysics Data System (ADS)

A microstructure-dependent nonlinear Euler-Bernoulli and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material are developed using the principle of virtual displacements. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Kármán geometric nonlinearity. The model contains a material length scale parameter that can capture the size effect in a functionally graded material, unlike the classical Euler-Bernoulli and Timoshenko beam theories. The influence of the parameter on static bending, vibration and buckling is investigated. The theoretical developments presented herein also serve to develop finite element models and determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on post-buckling response.

Reddy, J. N.

2011-11-01

367

Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena  

NASA Astrophysics Data System (ADS)

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

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

2013-11-01

368

Geometric learning algorithms  

NASA Astrophysics Data System (ADS)

Emergent computation in the form of geometric learning is central to the development of motor and perceptual systems in biological organisms and promises to have a similar impact on emerging technologies including robotics, vision, speech, and graphics. This paper examines some of the trade-offs involved in different implementation strategies, focusing on the tasks of learning discrete classifications and smooth nonlinear mappings. The trade-offs between local and global representations are discussed, a spectrum of distributed network implementations are examined, and an important source of computational inefficiency is identified. Efficient algorithms based on k-d trees and the Delaunay triangulation are presented and the relevance to biological networks is discussed. Finally, extensions of both the tasks and the implementations are given.

Omohundro, Stephen M.

1990-06-01

369

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

NASA Astrophysics Data System (ADS)

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.

Vyatkin, A. G.; Khazanov, Efim A.

2009-09-01

370

Neurocontroller alternatives for "fuzzy" ball-and-beam systems with nonuniform nonlinear friction.  

PubMed

The ball-and-beam problem is a benchmark for testing control algorithms. In the World Congress on Neural Networks, 1994, Prof. L. Zadeh proposed a twist to the problem, which, he suggested, would require a fuzzy logic controller. This experiment uses a beam, partially covered with a sticky substance, increasing the difficulty of predicting the ball's motion. We complicated this problem even more by not using any information concerning the ball's velocity. Although it is common to use the first differences of the ball's consecutive positions as a measure of velocity and explicit input to the controller, we preferred to exploit recurrent neural networks, inputting only consecutive positions instead. We have used truncated backpropagation through time with the node-decoupled extended Kalman filter (NDEKF) algorithm to update the weights in the networks. Our best neurocontroller uses a form of approximate dynamic programming called an adaptive critic design. A hierarchy of such designs exists. Our system uses dual heuristic programming (DHP), an upper-level design. To our best knowledge, our results are the first use of DHP to control a physical system. It is also the first system we know of to respond to Zadeh's challenge. We do not claim this neural network control algorithm is the best approach to this problem, nor do we claim it is better than a fuzzy controller. It is instead a contribution to the scientific dialogue about the boundary between the two overlapping disciplines. PMID:18249772

Eaton, P H; Prokhorov, D V; Wunsch, D I

2000-01-01

371

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

SciTech Connect

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

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

1997-08-01

372

High Energy Laser Beam Propagation in the Atmosphere: The Integral Invariants of the Nonlinear Parabolic Equation and the Method of Moments  

NASA Technical Reports Server (NTRS)

The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.

Manning, Robert M.

2012-01-01

373

Transient counter-beam propagation in a nonlinear Fabry-Perot cavity  

NASA Astrophysics Data System (ADS)

By adapting Moretti's self-consistent numerical approach to integrating the Euler equation of compressible flow, a unified complete temporal and spatial description of superfluorescence and optical bi-stability was undertaken. (The simulation includes material initialization as well as refractive transverse and longitudinal field boundary conditions appropriate to the cylindrical laser cavity). The respecting of physical causality in Moretti's method was maintained; but by using an improved derivative estimator at both the predictor and corrector levels, the overall accuracy was improved. The physical model includes nonplanar two-way Maxwell-Bloch propagation with spontaneous sources. The problem of dynamic transverse effects as they relate to soliton collisions is addressed. The calculations are based upon an extension of Mattar's previous semi-classical model for diffraction and phase effects in self-induced transparency at thick optical absorptions. The computational algorithm relies on the use of characteristics, but is strictly a finite-difference scheme. This explicit scheme involves the simultaneous integration along the time coordinate for both forward and backward wave. However, directional derivatives must be considered to appropriately take into account the mutual influence of the two light beams without violating the laws of forbidden signals. Particular case is exercised to maintain at least a second-order accuracy using one-sided approximations to spatial derivatives. Each forward/backward field derivative will be related to its respective directional history. A numerical approach in which the discretization is not consistent with these physical facts will inevitably fail. Thus the numerical algorithm must discriminate between different domains of dependence of different physical parameters. The physical process can now be analyzed with a degree of realism not previously attainable. Significant agreement with experimental observations is reported from the planar or time-independent analysis counterpart confined to the central portion of the beam.

Mattar, F. P.; Moretti, G.; Franceour, R. E.

1981-06-01

374

Geometrized Gravitation Theories.  

National Technical Information Service (NTIS)

General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). For a ...

A. A. Logunov V. N. Folomeshkin

1977-01-01

375

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

376

Generation of a dark hollow beam by a nonlinear ZnSe crystal and its propagation properties in free space: Theoretical analysis  

NASA Astrophysics Data System (ADS)

A new nonlinear optical method to generate a dark hollow beam (DHB) with a dielectric ZnSe crystal is proposed. From Huygens-Fresnel diffraction theory, we calculate the intensity distributions of the DHB and its propagating properties in free space, and study the dependences of the optimal propagation position and the dark-spot size (DSS) of the hollow beam on the waist radius of the incident Gaussian laser beam. Our study shows that the intensity distribution of the DHB presents symmetrical distribution with increasing the propagation distance, the optimal distance zopt becomes farther and the DSS becomes larger with the increase of the waist radius w of the incident Gaussian laser beam. This generated DHB will have applications in the optical guiding and trapping of macroscopic objects, atoms or molecules.

Du, Xiangli; Yin, Yaling; Zheng, Gongjue; Guo, Chaoxiu; Sun, Yu; Zhou, Zhongneng; Bai, Shunjie; Wang, Hailing; Xia, Yong; Yin, Jianping

2014-07-01

377

A Simple Constant Strain Energy Release Rate Loading Method for Double Cantilever Beam Specimens  

Microsoft Academic Search

A simple loading arrangement is proposed to permit nearly constant strain energy release rate testing of double cantilever beam specimens. The inexpensive arrangement may be well suited to long term and environmental exposure testing of these specimens. An added advantage of the technique is that it also provides an attractive method to measure debond length. The geometrically nonlinear loading device

David A. Dillard; John Z. Wang; Hari Parvatareddy

1993-01-01

378

A case study of analysis methods for large deflections of a cantilever beam  

NASA Technical Reports Server (NTRS)

A load case study of geometric nonlinear large deflections of a cantilever beam is presented. The bending strain must remain elastic. Closed form solution and finite element methods of analysis are illustrated and compared for three common load cases. A nondimensional nomogram for each case is presented in the summary.

Craig, L. D.

1994-01-01

379

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

NASA Astrophysics Data System (ADS)

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

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

2011-02-01

380

Explicit analytical approximation to large-amplitude non-linear oscillations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia  

Microsoft Academic Search

This paper is concerned with analytical treatment of non-linear oscillations of planar, flexural large amplitude free vibrations\\u000a of a slender, inextensible cantilever beam carrying a lumped mass with rotary inertia at an intermediate position along its\\u000a span. An analytic approximate technique, namely Optimal Homotopy Asymptotic Method (OHAM) is employed for this purpose. It\\u000a is proved that OHAM provide accurate solutions

Nicolae Heri?anu; Vasile Marinca

2010-01-01

381

Influence of axial loads on the nonplanar vibrations of cantilever beams  

NASA Astrophysics Data System (ADS)

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

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

2012-11-01

382

The effects of external applied voltage on the nonlinear optical properties of a dye-doped nematic liquid crystal by using a single beam  

NASA Astrophysics Data System (ADS)

We report the experimental data of typical liquid crystals (6CHBT and w1680) in the nematic phase doped with and without Sudan dyes. We investigated the effect of an ac-applied voltage on the nonlinear behavior of dye doped liquid crystal (DDLC). The z-scan technique is used to measure the amplitude and the sign of the nonlinear refractive indices DDLC. The amplitude of negative nonlinear refractive indices was (~10-5cm2/W). The nonlinear absorption coefficient ? of DDLC was measured by using open aperture z- scan technique. Also the optical limiting (OL) response of DDLC was obtained. The novel effects on the far-field diffraction patterns of a Gaussian beam were depended on the external applied field. The measurements were performed using a CW He:Ne laser and CW Nd:Yag laser tuned at 632.8 nm and 532 nm, respectively. Also Gaussian beam propagated through a thin cell (sample thickness =11.8 ?m).

Majles Ara, M. H.; Bahramian, R.; Abolhasani, M.

2008-11-01

383

Visualizing the Geometric Series.  

ERIC Educational Resources Information Center

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

Bennett, Albert B., Jr.

1989-01-01

384

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem  

NASA Technical Reports Server (NTRS)

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Muravyov, Alexander A.

1999-01-01

385

Nonlinear and linear wave phenomena in narrow pipes  

NASA Astrophysics Data System (ADS)

Phenomena arising in the course of wave propagation in narrow pipes are considered. For nonlinear waves described by the generalized Webster equation, a simplified nonlinear equation is obtained that allows for low-frequency geometric dispersion causing an asymmetric distortion of the periodic wave profile, which qualitatively resembles the distortion of a nonlinear wave in a diffracted beam. Tunneling of a wave through a pipe constriction is investigated. Possible applications of the phenomenon are discussed, and its relation to the problems of quantum mechanics because of the similarity of the basic equations of the Klein-Gordon and Schrödinger types is pointed out. The importance of studying the tunneling of nonlinear waves and broadband signals is indicated.

Rudenko, O. V.; Shvartsburg, A. B.

2010-07-01

386

Study of nonlinear ohmic heating and ponderomotive force effects on the self-focusing and defocusing of Gaussian laser beams in collisional underdense plasmas  

SciTech Connect

In the present paper, the propagation characteristics of a linearly polarized gaussian laser beam in a non-isothermal underdense collisional plasma is studied. By considering the effects of the ponderomotive force and ohmic heating of plasma electrons as the nonlinear mechanisms, the second order differential equation of the dimensionless beam width parameter has been obtained and solved at several initial ion temperatures. Furthermore, by using the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the gaussian laser pulse, the perturbed electron density n{sub e}/n{sub 0e} is obtained and its variation in terms of the dimensionless plasma length is analyzed at different initial ion temperatures. Our results show that the dimensionless beam width parameter is strongly influenced by the initial plasma ion temperature. It is found that, for the self-focusing regime, the plasma electron density perturbation continuously oscillates between the initial density distribution and a minimum, and for the defocusing regime, the plasma electron density perturbation continuously oscillates between the initial density distribution and a maximum.

Etehadi Abari, M.; Shokri, B. [Physics Department and Laser-Plasma Research Institute of Shahid Beheshti University, G.C., Evin, Tehran (Iran, Islamic Republic of)

2012-11-15

387

Geometric representations of graphs  

Microsoft Academic Search

The study of geometrically defined graphs, and of the reverse ques- tion, the construction of geometric representations of graphs, leads to unexpected connections between geometry and graph theory. We survey the surprisingly large variety of graph properties related to ge- ometric representations, construction methods for geometric represen- tations, and their applications in proofs and algorithms.

Laszlo Lovasz; Katalin Vesztergombi

1999-01-01

388

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

SciTech Connect

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

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

2013-02-15

389

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

Microsoft Academic Search

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

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

2009-01-01

390

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

391

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

392

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

Microsoft Academic Search

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

393

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

SciTech Connect

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

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

2012-11-15

394

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

395

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

SciTech Connect

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

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

2006-04-01

396

Geometric Modelling with CASL  

Microsoft Academic Search

This paper presents an experiment that demonstrates the feasibility of successfully applying CASL to design 3D geometric modelling\\u000a software. It presents an abstract specification of a 3D geometric model, its basic constructive primitives together with the\\u000a definition of the rounding high-level operation. A novel methodology for abstractly specifying geometric operations is also\\u000a highlighted. It allows one to faithfully specify the

Franck Ledoux; Agnès Arnould; Pascale Le Gall; Yves Bertrand

2001-01-01

397

Nonlinear diffractive optical elements.  

PubMed

We propose diffractive optical elements with a spatially-varying nonlinear refractive index. Such a component acts as a diffractive optical element whose properties depend on the intensity of the incoming beam. We present a method for designing such elements, and as specific examples we study three types of nonlinear diffractive optical elements: Nonlinear Fresnel Zone Plates, Two-foci Nonlinear Fresnel Zone Plate, and Fresnel Zone Plate to Grating interpolator. PMID:19547443

Manela, Ofer; Segev, Mordechai

2007-08-20

398

Bloch-sphere representation of three-vertex geometric phases  

SciTech Connect

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

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

2011-11-15

399

Geometrical method of decoupling  

NASA Astrophysics Data System (ADS)

The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E?, B?, and P?, which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of) transformations must be symplectic and hence canonical. When used iteratively, the decoupling algorithm can also be applied to n-dimensional systems and requires O(n2) iterations to converge to a given precision.

Baumgarten, C.

2012-12-01

400

Diffraction-limited polarized emission from a multimode Yb-doped fiber amplifier after nonlinear beam cleanup  

Microsoft Academic Search

The multimode and depolarized output beam of a highly multimode diode-pumped Yb-doped fiber amplifier is converted to a diffraction limited, linearly polarized beam by a self-referencing two wave mixing process in an infrared sensitive photorefractive crystal (Rh:BaTiO3). Up to 11.6W singlemode output is achieved with a 78% multimode to singlemode photorefractive conversion efficiency.

Laurent Lombard; Arnaud Brignon; Jean-Pierre Huignard; Eric Lallier; Gaelle Lucas-Leclin; Patrick M. Georges; Gilles Pauliat; Gerald Roosen

2004-01-01

401

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

Microsoft Academic Search

Ion implantation has been shown to produce a high density of metal colloids in glasses and crystalline materials. The high-precipitate volume fraction and small size of metal nanoclusters formed leads to values for the third-order susceptibility much greater than those for metal doped solids. This has stimulated interest in use of ion implantation to make nonlinear optical materials. On the

S. S. Sarkisov; E. K. Williams; M. Curley; C. C. Smith; D. Ila; P. Venkateswarlu; D. B. Poker; D. K. Hensley

1997-01-01

402

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

NASA Astrophysics Data System (ADS)

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

Saberian, E.; Esfandyari-Kalejahi, A.; Rastkar-Ebrahimzadeh, A.; Afsari-Ghazi, M.

2013-03-01

403

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

SciTech Connect

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

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

2013-03-15

404

Geometric Shapes in Architecture  

NSDL National Science Digital Library

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

Fox, Lauretta J.

2007-02-22

405

Geometric Dimensioning Sentence Structure.  

ERIC Educational Resources Information Center

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

McCuistion, Patrick J.

1991-01-01

406

Parallel processors and nonlinear structural dynamics algorithms and software  

NASA Technical Reports Server (NTRS)

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

Belytschko, Ted

1989-01-01

407

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

NASA Technical Reports Server (NTRS)

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

1976-01-01

408

Experimental Study on Energy Absorption Characteristics of Reinforced Concrete Beams in Emphasis of Initial Non-linear Stage  

NASA Astrophysics Data System (ADS)

The non-linear behavior of reinforced concrete members have been pursued experimentally by many researchers and Clough-model and Takeda-model are perceived to be working models to describe the non-linear behavior. However, still remains a room where the possibility to enhance the damping capacity of reinforced concrete members are pursued by applying exquisite model such as Degrading Tri-linear model. In this paper, results of experiment are reported which cover the difference in yielding type (shear yielding or flexural yielding) material strength. Emphasis is placed in the range of deformation prior to the yielding of reinforcing bars. The test results are compared with proposed models and it is concluded that Takeda model keeps firm precedence and Degrading Tri-linear model should be excluded on the reason of its over estimate of damping capacity in the smaller deformation range.

Serizawa, Kojiro; Hannuki, Toshio; Akiyama, Hiroshi

409

Analytical method for describing the paraxial region of finite amplitude sound beams.  

PubMed

A special analytical method, which combines the parabolic approximation (KZ equation) with nonlinear geometrical acoustics, is developed to model nonlinear and diffraction effects near the axis of a finite amplitude sound beam. The corresponding system of nonlinear equations describing waveform evolution is derived. For the case of an initially sinusoidal wave radiated by a Gaussian source, an analytic solution of the coupled equations is obtained for the paraxial region of the beam. The axial solution is expressed in both the time and frequency domains, and is analyzed in detail for both unfocused and focused beams in their preshock regions. Harmonic propagation curves are compared with finite difference solutions of the KZ equation, and good agreement is obtained for a variety of parameter values. PMID:9069621

Hamilton, M F; Khokhlova, V A; Rudenko, O V

1997-03-01

410

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

Microsoft Academic Search

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

411

Geometric continuum regularization of quantum field theory  

SciTech Connect

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

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

1989-11-08

412

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

413

Geometrically Induced Interactions and Bifurcations  

NASA Astrophysics Data System (ADS)

In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.

Binder, Bernd

2010-01-01

414

Non-linear cyclic model of top and seat with web angle for steel beam-to-column conections  

Microsoft Academic Search

The use of steel connections is inherent of every structural steel building. Savings in connection costs as well as improved connection quality has an impact on all types of buildings. Several analytical models have been developed in the last years to represent the cyclic behaviour of beam-to-column connections. However very few models have been substantiated by test results under cyclic

L. Calado

2003-01-01

415

Input-output linearisation of nonlinear systems with ill-defined relative degree: the ball and beam revisited  

Microsoft Academic Search

We establish that for SISO systems lack of well-defined relative degree is not an obstacle to exact inversion. Sufficient conditions for the existence of exact linearising inputs are derived. Exact tracking solutions of a number of example systems, including the ball and beam system studied by Hauser et al. (1992), are analysed. It is shown that linearising inputs may be:

D. J. Leith; W. E. Leithead

2001-01-01

416

Beam-Bem interactions  

SciTech Connect

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

Kim, Hyung Jin; /Fermilab

2011-12-01

417

Geometric Differential Equations.  

National Technical Information Service (NTIS)

The purpose of the report is to present, however briefly, the contributions of a few outstanding authors to the development of geometric differential equations. The first author considered is Poincare, the true founder of the topic.

S. Lefschetz

1971-01-01

418

Geometric intrinsic symmetries  

SciTech Connect

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

419

Geometric correlations and multifractals.  

National Technical Information Service (NTIS)

There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. Thes...

R. E. Amritkar

1991-01-01

420

3D Multispecies Nonlinear Perturbative Particle Simulation of Intense Nonneutral Particle Beams (Research supported by the Department of Energy and the Short Pulse Spallation Source Project and LANSCE Division of LANL.)  

NASA Astrophysics Data System (ADS)

The Beam Equilibrium Stability and Transport (BEST) code, a 3D multispecies nonlinear perturbative particle simulation code, has been developed to study collective effects in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations. A Darwin model is adopted for transverse electromagnetic effects. As a 3D multispecies perturbative particle simulation code, it provides several unique capabilities. Since the simulation particles are used to simulate only the perturbed distribution function and self-fields, the simulation noise is reduced significantly. The perturbative approach also enables the code to investigate different physics effects separately, as well as simultaneously. The code can be easily switched between linear and nonlinear operation, and used to study both linear stability properties and nonlinear beam dynamics. These features, combined with 3D and multispecies capabilities, provides an effective tool to investigate the electron-ion two-stream instability, periodically focused solutions in alternating focusing fields, and many other important problems in nonlinear beam dynamics and accelerator physics. Applications to the two-stream instability are presented.

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

1999-11-01

421

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

NASA Technical Reports Server (NTRS)

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

Rizzi, Stephen A.; Przekop, Adam

2005-01-01

422

Bessel light beam self-diffraction in heavily doped n-InP under conditions of high optical nonlinearity  

NASA Astrophysics Data System (ADS)

Self-diffraction of Bessel light bema in heavily doped n-InP has been experimentally studied. It is found that additional rings which have double structure appear in spatial spectrum of diffracted light. At certain conditions Gaussian like central maximum can be also observed in spatial spectrum. Numerical simulations have been performed for the case of Raman-Nath regime and saturation nonlinearity. The results of simulations are in a good agreement with experimental data. The double structure of the diffraction rings can be explained in terms of the existence of forbidden directions for light diffraction.

Ryzhevich, Anatol A.; Utkin, Ilya A.

2002-07-01

423

Information Intrinsic Geometric Flows  

NASA Astrophysics Data System (ADS)

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

Barbaresco, Frédéric

2006-11-01

424

Determination and analysis of non-linear index profiles in electron-beam-deposited MgOAl2O3ZrO2 ternary composite thin-film optical coatings  

NASA Astrophysics Data System (ADS)

Thickness-dependent index non-linearity in thin films has been a thought provoking as well as intriguing topic in the field of optical coatings. The characterization and analysis of such inhomogeneous index profiles pose several degrees of challenges to thin-film researchers depending upon the availability of relevant experimental and process-monitoring-related information. In the present work, a variety of novel experimental non-linear index profiles have been observed in thin films of MgOAl2O3ZrO2 ternary composites in solid solution under various electron-beam deposition parameters. Analysis and derivation of these non-linear spectral index profiles have been carried out by an inverse-synthesis approach using a real-time optical monitoring signal and post-deposition transmittance and reflection spectra. Most of the non-linear index functions are observed to fit polynomial equations of order seven or eight very well. In this paper, the application of such a non-linear index function has also been demonstrated in designing electric-field-optimized high-damage-threshold multilayer coatings such as normal- and oblique-incidence edge filters and a broadband beam splitter for p-polarized light. Such designs can also advantageously maintain the microstructural stability of the multilayer structure due to the low stress factor of the non-linear ternary composite layers.

Sahoo, N. K.; Thakur, S.; Senthilkumar, M.; Das, N. C.

2005-02-01

425

Nonlinear aerostatic stability analysis of suspension bridges  

Microsoft Academic Search

Nonlinear aerostatic stability analysis of long-span suspension bridges is studied by including directly the three combined effects of: (1) nonlinear three-component displacement-dependent wind loads, (2) geometric nonlinearity, and (3) material nonlinearity. The nonlinear three-component displacement-dependent wind loads are included through the static aerodynamic coefficients as a function of angle of attack. The various structural bucklings, such as flexural buckling, torsional

Virote Boonyapinyo; Yingsak Lauhatanon; Panitan Lukkunaprasit

2006-01-01

426

NONLINEAR OPTICAL PHENOMENA: Determination of the third-order correlation function by noncollinear two-beam third-harmonic generation  

Microsoft Academic Search

A method was developed for determination of the third-order correlation function G(3)(0, tau) on the basis of noncollinear two-beam generation of the third harmonic in a cell containing an atomic metal vapour. The advantages of the proposed method are its simplicity, validity in a wide range of wavelengths, and ability to reveal the asymmetry of an ultrashort pulse in one

Grigorii G. Grigoryan; A. O. Melikyan; D. G. Sarkisyan; A. S. Sarkisyan

1995-01-01

427

Global nonlinear electroelastic dynamics of a bimorph piezoelectric cantilever for energy harvesting, sensing, and actuation  

NASA Astrophysics Data System (ADS)

Inherent nonlinearities of piezoelectric materials are inevitably pronounced in various engineering applications such as sensing, actuation, their combined applications for vibration control, and most recently, energy harvesting from dynamical systems. The existing literature focusing on the dynamics of electroelastic structures made of piezoelectric materials have explored such nonlinearities in a disconnected way for the separate problems of mechanical and electrical excitation such that nonlinear resonance trends have been assumed to be due to different additional terms in constitutive equations by different researchers. Similar manifestations of softening nonlinearities have been attributed to purely elastic nonlinear terms, coupling nonlinearities, hysteresis, or a combination of these effects, by various authors. However, a reliable nonlinear constitutive equation for a given piezoelectric material is expected to be rather unique and valid regardless of the application, e.g. energy harvesting, sensing, or actuation. A systematic approach focusing on the two-way coupling can result in a sound mathematical framework. To this end, the present work investigates the nonlinear dynamic behavior of a bimorph piezoelectric cantilever under low-to-high mechanical and electrical excitation levels in energy harvesting, sensing, and actuation. A physical model is proposed including both ferroelastic hysteresis, stiffness, and electromechanical coupling nonlinearities. A lumped parameter electroelastic model is developed by accounting for these nonlinearities to analyze the primary resonance of a cantilever using the method of harmonic balance. Strong agreement between the model and experimental investigation is found, providing solid evidence that the the dominant source of observed softening nonlinear effects in geometrically linear piezolectric cantilever beams is well represented by a quadratic term resulting from ferroelastic hysteresis. Electromechanical coupling and cubic softening nonlinearities are observed to become effective only near the physical limits of the brittle and stiff bimorph cantilever used in the experiments, revealing that the quadratic nonlinearity associated with hysteresis has the primary role in nonlinear nonconservative dynamic behavior.

Leadenham, Stephen; Erturk, Alper

2014-04-01

428

Nonlinear dynamic response of submarine pipelines in contact with the ocean floor  

SciTech Connect

The nonlinear dynamic response of a submarine pipeline to wave and current excitation is investigated by the finite-element method. The pipeline, in contact with soft clay on the ocean floor, is modeled as a continuous beam. Small-deflection theory with geometric stiffening is employed. Pipeline tension, used in the geometric stiffness matrix, is calculated using pipeline stretch. The hydrodynamic forces are calculated using the modified Morison equation. The excitation involves a long-crested regular wave propagating perpendicular to the pipeline axis with or with out the current. The distributed drag and lift forces are converted into multisegment concentrated forces by means of the beam shape functions, and the inertia force is treated as a uniformly distributed force on each element. The soil-resistance forces due to lateral sliding on a plane surface are calculated using either an elasto-plastic or a hysteretic pipeline-soil interaction model. The Newmark Method is used to integrate the nonlinear equations of dynamic equilibrium using an iterative scheme within each time step. It is found from this study that the use of geometric stiffness is necessary for pipelines in a marine environment. The significant effect of geometric stiffening on pipeline responses for cases involving current is demonstrated.

Chung, C.K.

1986-01-01

429

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

SciTech Connect

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

Batra, Karuna; Mitra, Sugata; Subbarao, D.; Sharma, R.P.; Uma, R. [Center for Energy Studies, Indian Institute of Technology, Delhi, New Delhi 110016 (India)

2005-01-01

430

Linearizing Intra-Train Beam-Beam Deflection Feedback  

SciTech Connect

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

431

Nonlinear Spline Functions.  

National Technical Information Service (NTIS)

A mathematical characterization of nonlinear interpolating spline curves is developed through a variational calculus approach, based on the Euler-Bernoulli large-deflection theory for the bending of thin beams or elastica. Algorithms previously used for c...

M. A. Malcolm

1973-01-01

432

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

PubMed

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

Jin, Lihui; Shi, Jicong

2004-03-01

433

Berry phase in nonlinear systems  

SciTech Connect

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

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

2010-05-15

434

Approximate periodically focused solutions to the nonlinear Vlasov-Maxwell equations for intense beam propagation through an alternating-gradient field configuration  

NASA Astrophysics Data System (ADS)

This paper considers an intense non-neutral ion beam propagating in the z direction through a periodic-focusing quadrupole or solenoidal field with transverse focusing force, -[?x\\(s\\)xe^x+?y\\(s\\)ye^y], on the beam ions. Here, s=?bct is the axial coordinate, \\(?b-1\\)mbc2 is the directed axial kinetic energy of the beam ions, and the (oscillatory) lattice coefficients satisfy ?x\\(s+S\\)=?x\\( s\\) and ?y\\(s+S\\)=?y\\( s\\), where S=const is the periodicity length of the focusing field. The theoretical model employs the Vlasov-Maxwell equations to describe the nonlinear evolution of the distribution function fb\\(x,y,x',y',s\\) and the (normalized) self-field potential ?\\(x,y,s\\) in the transverse laboratory-frame phase space \\(x,y,x',y'\\). Here, H^\\(x,y,x', y',s\\)=\\(1/2\\) \\(x'2+y'2\\)+\\( 1/2\\)[?x\\( s\\)x2+?y\\(s\\)y2]+?\\(x,y,s\\) is the (dimensionless) Hamiltonian for particle motion in the applied field plus self-field configurations, where \\(x,y\\) and \\(x',y'\\) are the transverse displacement and velocity components, respectively, and ?\\(x,y,s\\) is the self-field potential. The Hamiltonian is formally assumed to be of order ?, a small dimensionless parameter proportional to the characteristic strength of the focusing field as measured by the lattice coefficients ?x\\(s\\) and ?y\\(s\\). Using a third-order Hamiltonian averaging technique developed by P. J. Channell [Phys. Plasmas 6, 982 (1999)], a canonical transformation is employed that utilizes an expanded generating function that transforms away the rapidly oscillating terms. This leads to a Hamiltonian, H\\(X~,Y~,X~',Y~',s\\)=\\(1/2\\) \\(X~'2+Y~'2\\)+\\(1/ 2\\)?f\\(X~2+Y~2\\)+? \\(X~,Y~,s\\), correct to order ?3 in the ``slow'' transformed variables \\(X~,Y~,X~',Y~'\\). Here, the transverse focusing coefficient in the transformed variables satisfies ?f=const, and the asymptotic expansion procedure is expected to be valid for a sufficiently small phase advance (?beam equilibrium distribution functions, F0b\\(H0\\), with ?/?s=0=?/??, are calculated in the transformed variables, and the results are transformed back to the laboratory frame. Corresponding properties of the periodically focused distribution function fb\\(x,y,x',y',s\\) are calculated correct to order ?3 in the laboratory frame, including statistical averages such as the mean-square beam dimensions, \\(s\\) and \\( s\\), the unnormalized transverse beam emittances, ?x\\(s\\) and ?y\\(s\\), the self-field potential, ?\\(x,y,s\\), the number density of beam particles, nb\\(x,y,s\\), and the transverse flow velocity, Vb\\(x,y,s\\). As expected, the beam cross section in the laboratory frame is a pulsating ellipse for the case of a periodic-focusing quadrupole field or a pulsating circular cross section for the case of a periodic-focusing solenoidal field.

Davidson, Ronald C.; Qin, Hong; Channell, Paul J.

1999-07-01

435

Algebraic geometric codes  

NASA Technical Reports Server (NTRS)

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

Shahshahani, M.

1991-01-01

436

Nonlinear investigation of beam-wave interaction in double-groove loaded folded-waveguide traveling-wave tube  

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

437

Geometrical Monte Carlo simulation of atmospheric turbulence  

NASA Astrophysics Data System (ADS)

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

Yuksel, Demet; Yuksel, Heba

2013-09-01

438

Nonlinear prism coupling with nonlocality.  

PubMed

The characteristics of prism coupling of finite-width beams into nonlinear waveguides composed of media with diffusive nonlinearities (thermal, etc.) are calculated by including a one-dimensional diffusion equation for the nonlocal nonlinearity. The resulting longitudinal feedback leads to bistability, and the threshold value for the minimum diffusion length varies inversely with the angular detuning. PMID:19753005

Vitrant, G; Reinisch, R; Paumier, J C; Assanto, G; Stegeman, G I

1989-08-15

439

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

440

1500 System Geometric Dictionary.  

ERIC Educational Resources Information Center

A general description is provided of the "geometric dictionary," a graphic display aid, used by the Computer-Assisted Instruction Laboratory at the Pennsylvania State University. The purpose of the description is to enable the reader to duplicate and use the dictionary on any cathode ray tube terminal of the IBM 1500 system. The major advantages…

Peloquin, Paul V.