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1

NASA Astrophysics Data System (ADS)

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

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

2013-09-01

2

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

3

Geometric nonlinear dynamic analysis of curved beams using curved beam element

NASA Astrophysics Data System (ADS)

Instead of using the previous straight beam element to approximate the curved beam, in this paper, a curvilinear coordinate is employed to describe the deformations, and a new curved beam element is proposed to model the curved beam. Based on exact nonlinear strain-displacement relation, virtual work principle is used to derive dynamic equations for a rotating curved beam, with the effects of axial extensibility, shear deformation and rotary inertia taken into account. The constant matrices are solved numerically utilizing the Gauss quadrature integration method. Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system. The present results are compared with those obtained by commercial programs to validate the present finite method. In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation, comparison of the results of the present formulation with those of the ADAMS software are made. Furthermore, the present results obtained from linear formulation are compared with those from nonlinear formulation, and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

Pan, Ke-Qi; Liu, Jin-Yang

2011-12-01

4

NASA Astrophysics Data System (ADS)

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

Torabizadeh, Mohammad Amin

2013-07-01

5

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

6

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

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

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

2013-08-01

7

A co-rotational total Lagrangian finite element formulation for the geometrically nonlinear dynamic analysis of spatial Euler beam with large rotations but small strain, is presented.The nodal coordinates, displacements, rotations, velocities, accelerations, and the equations of motion of the structure are defined in a fixed global set of coordinates. The beam element has two nodes with six degrees of freedom per

Kuo Mo Hsiao; Jer Yan Lin; Wen Yi Lin

1999-01-01

8

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

Stationary nonlinear Airy beams

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

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

2011-08-15

10

Vibration isolation using extreme geometric nonlinearity

NASA Astrophysics Data System (ADS)

A highly deformed, slender beam (or strip), attached to a vertically oscillating base, is used in a vibration isolation application to reduce the motion of a supported mass. The isolator is a thin strip that is bent so that the two ends are clamped together, forming a loop. The clamped ends are attached to an excitation source and the supported system is attached at the loop midpoint directly above the base. The strip is modeled as an elastica, and the resulting nonlinear boundary value problem is solved numerically using a shooting method. First the equilibrium shapes of the loop with varying static loads and lengths are studied. The analysis reveals a large degree of stiffness tunability; the stiffness is dependent on the geometric configuration, which itself is determined by the supported mass, loop length, and loop self-weight. Free vibration frequencies and mode shapes are also found. Finally, the case of forced vibration is studied, and the displacement transmissibility over a large range of forcing frequencies is determined for varying parameter values. Experiments using polycarbonate strips are conducted to verify equilibrium and dynamic behavior.

Virgin, L. N.; Santillan, S. T.; Plaut, R. H.

2008-08-01

11

Dynamic analysis of geometrically nonlinear robot manipulators

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

E. M. Bakp

1996-01-01

12

Geometrically nonlinear behavior of piezoelectric laminated plates

NASA Astrophysics Data System (ADS)

The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.

Rabinovitch, Oded

2005-08-01

13

Nonclassical nonlinear effects in thin-walled composite beams

Non-classical nonlinearities are those geometric nonlinearities in the 3-D or 2-D models, of slender elastic bodies, which transform to physical nonlinearities in a 1-D beam theory. Small parameters involving thin-walled beam geometry bring into prominence these non-classical effects which would otherwise be negligible. The objective of this work is to provide asymptotic analytical solutions for the non-classical sectional analysis of

Dineshkumar Harursampath

1999-01-01

14

Geometrically nonlinear analysis of adhesively bonded joints

NASA Technical Reports Server (NTRS)

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

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

1982-01-01

15

Nonlinearity of Pancharatnam's geometric phase in polarizing interferometers.

Earlier investigations show a time-variable nonlinear shift of the fringe pattern in a polarizing interferometer while rotating a polarizer at the exit. This effect was identified as Pancharatnam's geometrical phase and proposed for applications in interferometry and fast optical switching devices. A heterodyne analysis attributes moving fringes to a frequency difference between the interfering beams; thus changing fringe velocities point to a dynamic frequency development within the period of the uniformly rotating analyzer. This explanation offends the intuition and we undertake an experimental and theoretical investigation of the effect to solve the paradox. We determine, e.g., the complete frequency and mode spectrum of an arbitrary state of polarization P0 behind a rotating linear analyzer and behind a rotating arbitrary linear birefringent plate. We find that, in spite of a fast changing phase in the interferometer, no other (higher) frequency components appear in the spectral distribution of the intensity at the exit than the double of the rotary frequency of the analyzer: phase nonlinearities are compensated for by intensity changes. Only a phase-sensitive detector like an array of photodetectors is able to observe the nonlinearity of Pancharatnam's geometrical phase. A single detector only finds a sinusoidal intensity variation. Our insight into these relations leads us to two new applications of Pancharatnam's phase: supersensitivity of a polarizing double beam interferometer with a video camera acting as a phase detector and external tuning of a Fizeau interferometer. PMID:11970029

Hils, B; Dultz, W; Martienssen, W

1999-08-01

16

Nonlinear Geometric Effects in Bioinspired Multistable Structures

NASA Astrophysics Data System (ADS)

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

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

2013-03-01

17

Classical light beams and geometric phases.

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

Mukunda, N; Chaturvedi, S; Simon, R

2014-06-01

18

Interface Technology for Geometrically Nonlinear Analysis of Multiple Connected Subdomains

NASA Technical Reports Server (NTRS)

Interface technology for geometrically nonlinear analysis is presented and demonstrated. This technology is based on an interface element which makes use of a hybrid variational formulation to provide for compatibility between independently modeled connected subdomains. The interface element developed herein extends previous work to include geometric nonlinearity and to use standard linear and nonlinear solution procedures. Several benchmark nonlinear applications of the interface technology are presented and aspects of the implementation are discussed.

Ransom, Jonathan B.

1997-01-01

19

NASA Astrophysics Data System (ADS)

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

Fu, Yiming; Chen, Yang; Zhong, Jun

2014-10-01

20

Particular effort has been spent in the field of identification of multi-degree-of-freedom non-linear systems. The newly developed methods permit the structural analyst to consider increasingly complex systems. The aim of this paper and a companion paper is to study, by means of two methods, a continuous non-linear system consisting of an experimental cantilever beam with a geometrical non-linearity. In the

V. Lenaerts; G. Kerschen; J.-C. Golinval

2003-01-01

21

Stability of nonlinear periodic vibrations of 3D beams

The geometrically nonlinear periodic vibrations of beams with rectangular cross section under harmonic forces are investigated\\u000a using a p-version finite element method. The beams vibrate in space; hence they experience longitudinal, torsional, and nonplanar bending\\u000a deformations. The model is based on Timoshenko’s theory for bending and assumes that, under torsion, the cross section rotates\\u000a as a rigid body and is

S. Stoykov; P. Ribeiro

22

Hamilton’s principle. These equations form the basis of investigations to determine certain microstructural length scales on the bending, vibration and buckling response of beams used in micro- and nano-devices. (2) Analytical solutions of the conventional...

Mahaffey, Patrick Brian

2013-08-07

23

Gain scheduling for geometrically nonlinear flexible space structures

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

Yung, Jeremy Hoyt, 1971-

2002-01-01

24

Exact and geometrical optics energy trajectories in twisted beams

Energy trajectories, that is, integral curves of the Poynting (current) vector, are calculated for scalar Bessel and Laguerre-Gauss beams carrying orbital angular momentum. The trajectories for the exact waves are helices, winding on cylinders for Bessel beams and hyperboloidal surfaces for Laguerre-Gauss beams. In the geometrical optics approximations, the trajectories for both types of beam are overlapping families of straight

M. V. Berry; K. T. McDonald

2008-01-01

25

GAMNAS- GEOMETRIC AND MATERIAL NONLINEAR ANALYSIS OF STRUCTURES

NASA Technical Reports Server (NTRS)

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two-dimensional finite element stress analysis program developed to support fracture mechanics studies of debonding and delamination. GAMNAS options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. GAMNAS can analyze plastic deformations of isotropic materials. GAMNAS can calculate strain energy release rates using a virtual crack extension technique. The element available to the GAMMNAS user is a four-node isoparametric quadrilateral with full or reduced integration. GAMNAS has been used to investigate debonding and delamination of adhesively bonded composites. GAMNAS is written in FORTRAN 77 for batch execution and has been implemented on a PRIME 700 series computer. As currently dimensioned for a maximum global stiffness matrix of 1300 degrees of freedom and a bandwidth of 70, GAMNAS has a central memory requirement of approximately 603K of 16 bit words. GAMNAS was developed in 1983.

Whitcomb, J. D.

1994-01-01

26

Geometric and material nonlinear analysis of tensegrity structures

NASA Astrophysics Data System (ADS)

A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations, while the material nonlinearity is treated through elastoplastic stress-strain relationship. The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method. A computer program is developed to predict the mechanical responses of tensegrity systems under tensile, compressive and flexural loadings. Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program. The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications. On the other hand, its bending strength capacity is not sensitive to the self-stress level.

Tran, Hoang Chi; Lee, Jaehong

2011-12-01

27

Nonlinear geometric effects in mechanical bistable morphing structures.

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

28

Nonlinear geometric effects in mechanical bistable morphing structures

Bistable structures associated with non-linear 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 table-top experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells.

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

2012-09-08

29

Nonlinear Geometric Effects in Mechanical Bistable Morphing Structures

NASA Astrophysics Data System (ADS)

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.

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

2012-09-01

30

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

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

Boris Trogrlic; Ante Mihanovic

2008-01-01

31

Geometric Heat Equation and Nonlinear Diffusion of Shapes and Images

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

Benjamin B. Kimia; Kaleem Siddiqi

1996-01-01

32

Geometric methods in nonlinear analysis of data from brain imaging

NASA Astrophysics Data System (ADS)

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

Eghbalnia, Hamid; Assadi, Amir H.

2001-11-01

33

Geometrically nonlinear analysis of laminated elastic structures

NASA Technical Reports Server (NTRS)

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

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

1993-01-01

34

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

35

Nonlinear modeling of integrally actuated beams

A set of nonlinear, intrinsic equations describing the dynamics of beam structures undergoing large deformations is presented. The intrinsic kinematical equations are derived for the general case of a moving beam. Active force\\/strain terms are added to the equations to take into account active components. The equations are then discretized into finite elements, transformed into state-space form and finally decomposed

Johannes P. Traugott; Mayuresh J. Patil; Florian Holzapfel

2006-01-01

36

Non-linear model for stability of thin-walled composite beams with shear deformation

A geometrically non-linear theory for thin-walled composite beams is developed for both open and closed cross-sections and taking into account shear flexibility (bending and warping shear). This non-linear formulation is used for analyzing the static stability of beams made of composite materials subjected to concentrated end moments, concentrated forces, or uniformly distributed loads. Composite is assumed to be made of

Sebastián P. Machado; Víctor H. Cortínez

2005-01-01

37

Geometrical E-beam proximity correction for raster scan systems

High pattern fidelity is a basic requirement for the generation of masks containing sub micro structures and for direct writing. Increasing needs mainly emerging from OPC at mask level and x-ray lithography require a correction of the e-beam proximity effect. The most part of e-beam writers are raster scan system. This paper describes a new method for geometrical pattern correction

Nikola Belic; Hans Eisenmann; Hans Hartmann; Thomas Waas

1999-01-01

38

A galerkin solution to geometrically nonlinear shallow shell equations

NASA Astrophysics Data System (ADS)

A laminated shallow shell approach that includes von Karman geometric nonlinearity and parabolic transverse shear deformation is posed in differential operator form. Trigonometric series are assumed for each of the five shell displacement degrees of freedom for the subsequentnonlinear galerkin solution resulting in 5n(sup 2) simultaneous algebraic equations where n is the number of displacement terms assumed in the series. The galerkin nonlinear solution is computationally intensive. The response of several laminate geometries subjected to transverse loadings are found. Thicker plates and shells generally exhibit more flexible response compared to thinner geometries in both linear and nonlinear analyses. The nondimensional shell response is examined by using the Batdorf-Stein shell parameter for laminated constructions. Quasi-isotropic shallow shells undergo significant transverse shear flexibility in the thicker geometries as given by the nondimensional shell crown deflection. However, the nondimensional crown deflection in the deeper shell response is not much influenced by shell thickness. For flat plates, geometric nonlinearity lessens the influence of transverse shear flexibility when compared to linear solutions due to membrane stretching resistance.

Dennis, Scott T.

1995-04-01

39

Hybrid analytical technique for the nonlinear analysis of curved beams

NASA Technical Reports Server (NTRS)

The application of a two-step hybrid technique to the geometrically nonlinear analysis of curved beams is used to demonstrate the potential of hybrid analytical techniques in nonlinear structural mechanics. The hybrid technique is based on successive use of the perturbation method and a classical direct variational procedure. The functions associated with the various-order terms in the perturbation expansion of the fundamental unknowns, and their sensitivity derivatives with respect to material and geometric parameters of the beam, are first obtained by using the perturbation method. These functions are selected as coordinate functions (or modes) and the classical direct variational technique is then used to compute their amplitudes. The potential of the proposed hybrid technique for nonlinear analysis of structures is discussed. The effectiveness of the hybrid technique is demonstrated by means of numerical examples. The symbolic computation system Mathematica is used in the present study. The tasks performed on Mathematica include: (1) generation of algebraic expressions for the perturbation functions of the different response quantities and their sensitivity derivatives: and (2) determination of the radius of convergence of the perturbation series.

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

1992-01-01

40

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

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

41

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

42

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

43

Beams on nonlinear elastic foundation

NASA Astrophysics Data System (ADS)

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

Lukkassen, Dag; Meidell, Annette

2014-12-01

44

Nonlinear bending models for beams and plates.

A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler-Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960

Antipov, Y A

2014-10-01

45

Stochastic Reduced Order Models for Uncertain Infinite-Dimensional Geometrically Nonlinear

1 Stochastic Reduced Order Models for Uncertain Infinite-Dimensional Geometrically Nonlinear of the nonparametric stochastic modeling technique to reduced order models of geometrically nonlinear structures to a combined loading composed of a static in- plane load and a stochastic transverse excitation representative

Boyer, Edmond

46

A geometric calibration method for cone beam CT systems

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

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

2006-06-15

47

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

48

Beam stability & nonlinear dynamics. Formal report

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

Parsa, Z. [ed.

1996-12-31

49

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

NASA Technical Reports Server (NTRS)

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

Mei, Chuh; Decha-Umphai, Kamolphan

1987-01-01

50

Nonlinear diffraction from high-order Hermite-Gauss beams.

We investigate experimentally and theoretically the nonlinearly diffracted second harmonic light from the first-order Hermite-Gauss beam. We investigate the cases of loosely and tightly focused beams in a periodically poled lithium niobate crystal in the temperature range near the birefringent phase matching. Unlike the case of fundamental Gaussian beam, the nonlinear diffracted beam is spatially structured. Its shape depends on the focusing conditions and on the crystal temperature. Furthermore, for the case of tight focusing, the diffracted beam structure depends on the beam's position with respect to the domain wall. PMID:25531596

Kalinowski, Ksawery; Shapira, Asia; Libster-Hershko, Ana; Arie, Ady

2015-01-01

51

Diffractive nonlinear geometrical optics for variational wave equations and the Einstein equations

We derive an asymptotic solution of the vacuum Einstein equations that\\u000adescribes the propagation and diffraction of a localized, large-amplitude,\\u000arapidly-varying gravitational wave. We compare and contrast the resulting\\u000atheory of strongly nonlinear geometrical optics for the Einstein equations with\\u000anonlinear geometrical optics theories for variational wave equations.

John K. Hunter

2007-01-01

52

Anti-diffracting beams through the diffusive optical nonlinearity.

Anti-diffraction is a theoretically predicted nonlinear optical phenomenon that occurs when a light beam spontaneously focalizes independently of its intensity. We observe anti-diffracting beams supported by the peak-intensity-independent diffusive nonlinearity that are able to shrink below their diffraction-limited size in photorefractive lithium-enriched potassium-tantalate-niobate (KTN:Li). PMID:25607093

Di Mei, F; Parravicini, J; Pierangeli, D; Conti, C; Agranat, A J; DelRe, E

2014-12-15

53

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

54

NASA Technical Reports Server (NTRS)

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

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

55

Effect of Kerr nonlinearity on an Airy beam

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

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

2010-10-15

56

Geometric manipulation of light : from nonlinear optics to invisibility cloaks

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

Hashemi, Hila

2012-01-01

57

Direct determination of geometric alignment parameters for cone-beam scanners

This paper describes a comprehensive method for determining the geometric alignment parameters for cone-beam scanners (often called calibrating the scanners or performing geometric calibration). The method is applicable to x-ray scanners using area detectors, or to SPECT systems using pinholes or cone-beam converging collimators. Images of an alignment test object (calibration phantom) fixed in the field of view of the

C Mennessier; R Clackdoyle; F Noo

2009-01-01

58

Nonlinear beam deflection in photonic lattices with negative defects

We demonstrate both theoretically and experimentally that a nonlinear beam can be reflected by a negative defect in a photonic lattice if the incident angle is below a threshold value. Above this threshold angle, the beam simply passes through the defect. This phenomenon occurs in both one- and two-dimensional photonic lattices, and it provides a way to use the incident angle to control beam propagation in a lattice network. If the defect is absent or positive, no evident transition from reflection to transmission occurs. These nonlinear phenomena are also compared with linear nondiffracting-beam propagation in a photonic lattice with a defect, and both similarities and differences are observed. In addition, some important features in linear and nonlinear beam propagations are explained analytically by using a linear model with a delta-function defect.

Wang Jiandong [College of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China); Ye Zhuoyi; Lou Cibo [TEDA Applied Physical School, Nankai University, Tianjin 300457 (China); Miller, Alexandra; Zhang Peng [Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132 (United States); Hu Yi; Chen Zhigang [TEDA Applied Physical School, Nankai University, Tianjin 300457 (China); Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132 (United States); Yang Jianke [Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401 (United States)

2011-03-15

59

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

NASA Astrophysics Data System (ADS)

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

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

2010-10-01

60

Development of geometrically-nonlinear finite element analysis for marine risers

length. 80 70 I 60 C c 50 0 0 40 V Cl 30 -' 20 X 0 10 LEGEND ? Linear Nonlinear 0 100 200 300 Load (Pounds) 400 500 FIG. 3. 2(b) ? Maximum Deflection of a Pinned-End Beam vs. Load. The maximum deflection of a 130-inch pinned-end beam... is plotted against increases in point load. 80 70 60 N e 50 C c 40 0 30 e a 20 LEGEND Linear Nonlinear 10 0 20 40 60 80 100 120 140 160 180 Distance Along Beam (Inches) FIG. 3. 2(c) ? Pinned-End Beam Shape. The deflected shape of a 180-inch...

Haas, Mark Edward

2012-06-07

61

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

NASA Technical Reports Server (NTRS)

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

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

1993-01-01

62

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

63

Nonlinear Analysis of Reinforced Concrete Beams Under Pure Torsion

A nonlinear finite element analysis is conducted using ANSYS-V10 finite element package on six reinforced concrete cantilever beams having different length vary from 0.5 to 3 m with 0.5 m increments and subjected to a concentrated torque at the free end. The beams are designed to carry the same torque. The study emphasize on the effect of beam length (span

Mohammad Najim Mahmood

2007-01-01

64

Geometrically derived anisotropy in cubically nonlinear dielectric composites

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

Tom G. Mackay; James Clerk

2003-01-01

65

Iterative nonlinear beam propagation method and its application in nonlinear devices

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

Gao, Hanhong

2011-01-01

66

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

67

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

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

Li, Nianbei

2014-01-01

68

A Global Geometric Framework for Nonlinear Dimensionality Reduction

NASA Astrophysics Data System (ADS)

Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 106 optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.

Tenenbaum, Joshua B.; de Silva, Vin; Langford, John C.

2000-12-01

69

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion

NASA Astrophysics Data System (ADS)

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

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

2011-10-01

70

Linear and nonlinear methods for detecting cracks in beams

This paper presents experimental results from the vibration of a polycarbonate beam containing a crack that opens and closes during vibration. Several techniques were employed to detect and locate the crack making use of the nonlinearity. ``Harmonic mode shapes`` proved to be more sensitive to damage than conventional mode shapes. Instantaneous frequency and time-frequency methods also showed clear signatures for the crack. The results indicate that nonlinearities may provide increased capabilities for structural damage detection and location.

Prime, M.B.; Shevitz, D.W.

1995-12-31

71

Nonlinear Analysis of Shear Dominant Prestressed Concrete Beams using ANSYS

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

Job Thomas

72

Nonlinear 3D magnetostatic solver in beam optics analyzer

Calabazas Creek Research, Inc. (CCR) has included a nonlinear magnetostatic vector finite-element solver in its trajectory and particle-in-cell (PIC) code, Beam Optics Analyzer. With its seamless integration and intuitive graphical user interface, the new 3D magnetostatic field solver in BOA will help to design electron guns with complex coil geometries and high power beams that generate self magnetic fields. Convergence

Thuc Bui; R. Lawrence Ives

2008-01-01

73

NASA Astrophysics Data System (ADS)

The dynamic instability resulting from a high-supersonic flow over a simply supported laminated flat panel subjected to uniform in-plane edge compression is studied. The structural model incorporates geometrical non-linearities, transverse shear deformation, and transverse normal stress effects, and satisfies the traction-free condition on both faces of the panel. In-plane edge restraints and small initial geometric imperfections are also considered. Aerodynamic loads based on the third-order piston theory are used and the panel flutter equations are derived via Galerkin's method. The arclength continuation method is used to determine the static equilibrium state whose dynamic stability behavior is subsequently examined. The effects of transverse shear flexibility, aerodynamic non-linearities, initial imperfections and in-plane plate theory generally overpredicts the critical flow speed and compressive load, and a shear deformation theory is required when considering panels that are flexible in transverse shear. When aerodynamic non-linearities are included, multiple flutter speeds may exist. The nature of the flutter boundary for perfect panels is determined by the method of?!multiple scales, and it is seen that the presence of aerodynamic non-linearities could result in the hard flutter phenomenon. Results indicate that non-linear aerodynamics is important for panels that are not sufficiently thin (i.e., panels characterized by a high flutter Mach number).

Chandiramani, N. K.; Librescu, L. I.; Plaut, R. H.

1996-04-01

74

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

Heidari, Mohammad; Heidari, Ali; Homaei, Hadi

2014-01-01

75

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

Heidari, Mohammad; Heidari, Ali; Homaei, Hadi

2014-01-01

76

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

NASA Astrophysics Data System (ADS)

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

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

2014-09-01

77

Analytical load-displacement relations for flexure mechanisms, formulated by integrating the individual analytical models of their building-blocks (i.e., flexure elements), help in understanding the constraint characteristics of the whole mechanism. In deriving such analytical relations for flexure mechanisms, energy based approaches generally offer lower mathematical complexity, compared to Newtonian methods, by reducing the number of unknowns-specifically, the internal loads. To facilitate such energy based approaches, a closed-form nonlinear strain energy expression for a generalized bisymmetric spatial beam flexure is presented in this paper. The strain energy, expressed in terms of the end-displacement of the beam, considers geometric nonlinearities for intermediate deformations, enabling the analysis of flexure mechanisms over a finite range of motion. The generalizations include changes in the initial orientation and shape of the beam flexure due to potential misalignment or manufacturing. The effectiveness of this approach is illustrated via the analysis of a multilegged table flexure mechanism. The resulting analytical model is shown to be accurate using nonlinear finite elements analysis, within a load and displacement range of interest. PMID:24895492

Sen, Shiladitya; Awtar, Shorya

2014-02-01

78

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

Nonlinear Diffraction from a Virtual Beam Solomon M. Saltiel,1,2,* Dragomir N. Neshev,1 Wieslaw experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic beams, a second-harmonic diffraction pattern is generated by a virtual beam propagating along

Arie, Ady

79

Nonlinear transmission line based electron beam driver

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

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

2012-12-15

80

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

81

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

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

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

2005-04-01

82

Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media Ido Dolev,1

, experiments with Airy beams in quadratic media include the generation and manipulation of Airy beams throughExperimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media Ido Dolev,1 Ido present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadratic media

Arie, Ady

83

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

NASA Astrophysics Data System (ADS)

By using polystyrene microspheres with index n=1.59 as a model system we study light focusing and transport properties of chains formed by spheres with diameters varying from 2 to 30 ?m. We used techniques of imaging based on light scattering perpendicular to the axis of the chain to visualize and study periodically focused beams in such structures. The results demonstrate good agreement with geometrical optics modeling for sufficiently large spheres, D>>10?, where D is the sphere diameter and ? is the wavelength of light. For mesoscale structures with 4

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

2012-02-01

84

Beam loading by electrons in nonlinear plasma wakes

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

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

2009-05-15

85

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 Analysis of Reinforced Concrete Beams Under Pure Torsion

NASA Astrophysics Data System (ADS)

A nonlinear finite element analysis is conducted using ANSYS-V10 finite element package on six reinforced concrete cantilever beams having different length vary from 0.5 to 3 m with 0.5 m increments and subjected to a concentrated torque at the free end. The beams are designed to carry the same torque. The study emphasize on the effect of beam length (span to depth ratio) on the torsional strength and behavior of reinforced concrete rectangular beams and the effectiveness of the torsional reinforcement in the pre and post cracking stages of loading. It was found that beams with span/depth ratio equal to or more than 4 have the same reserved torsional strength and less than those with smaller ratio, keeping the cross section and torsional reinforcements constant for all the beams. Before cracking stresses in transverse and longitudinal reinforcement are almost negligible and it is far below the yield stress even at the post cracking stages. Reinforcement attained yielding only at ultimate torque and after the wide spread of cracks in the shorter beam.

Najim Mahmood, Mohammad

87

Nonlinear evolution of the ion-ion beam instability

NASA Technical Reports Server (NTRS)

The criterion for the existence of vortex-like ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates that this instability actually evolves into such phase-space configurations. A small, but nonzero, ion temperature turns out to be essential for the saturation into stationary structures

Pecseli, H. L.; Trulsen, J.

1982-01-01

88

Analysis of a nonlinear beam in contact with a foundation

NASA Astrophysics Data System (ADS)

The paper investigates the contact between a nonlinear dynamic Gao beam and a rigid or reactive foundation. The contact is modeled with the normal compliance condition for the deformable foundation and with the Signorini condition for the rigid foundation. The existence and uniqueness of the weak solution for the problem with normal compliance are obtained. The solution of the Signorini condition for the rigid foundation is obtained by passing to the limit when the normal compliance approaches infinity.

Mbengue, Mbagne F.

2014-08-01

89

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

NASA Technical Reports Server (NTRS)

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

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

1995-01-01

90

The geometric phase and the geometrodynamics of relativistic electron vortex beams

We have studied here the geometrodynamics of relativistic electron vortex beams from the perspective of the geometric phase associated with the scalar electron encircling the vortex line. It is pointed out that the electron vortex beam carrying orbital angular momentum is a natural consequence of the skyrmion model of a fermion. This follows from the quantization procedure of a fermion in the framework of Nelson's stochastic mechanics when a direction vector (vortex line) is introduced to depict the spin degrees of freedom. In this formalism a fermion is depicted as a scalar particle encircling a vortex line. It is here shown that when the Berry phase acquired by the scalar electron encircling the vortex line involves quantized Dirac monopole we have paraxial (non-paraxial) beam when the vortex line is parallel (orthogonal) to the wavefront propagation direction. Non-paraxial beams incorporate spin-orbit interaction. When the vortex line is tilted with respect to the propagation direction the Berry phase invo...

Bandyopadhyay, Pratul; Chowdhury, Debashree

2014-01-01

91

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

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

92

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

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

2015-01-01

93

NASA Astrophysics Data System (ADS)

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

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

2015-01-01

94

Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods

Mechanistic models based on systems of nonlinear differential equations can help provide a quantitative understanding of complex physical or biological phenomena. The use of such models to describe nonlinear interactions in molecular biology has a long history; however, it is only recently that advances in computing have allowed these models to be set within a statistical framework, further increasing their usefulness and binding modelling and experimental approaches more tightly together. A probabilistic approach to modelling allows us to quantify uncertainty in both the model parameters and the model predictions, as well as in the model hypotheses themselves. In this paper, the Bayesian approach to statistical inference is adopted and we examine the significant challenges that arise when performing inference over nonlinear ordinary differential equation models describing cell signalling pathways and enzymatic circadian control; in particular, we address the difficulties arising owing to strong nonlinear correlation structures, high dimensionality and non-identifiability of parameters. We demonstrate how recently introduced differential geometric Markov chain Monte Carlo methodology alleviates many of these issues by making proposals based on local sensitivity information, which ultimately allows us to perform effective statistical analysis. Along the way, we highlight the deep link between the sensitivity analysis of such dynamic system models and the underlying Riemannian geometry of the induced posterior probability distributions. PMID:23226584

Calderhead, Ben; Girolami, Mark

2011-01-01

95

Nonlinear theory of the orotron with inclined electron beam

NASA Astrophysics Data System (ADS)

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

Nusinovich, G. S.; Sinitsyn, O. V.

2006-12-01

96

Electromagnetic and geometric characterization of accelerated ion beams by laser ablation

NASA Astrophysics Data System (ADS)

Laser ion sources offer the possibility to get ion beam useful to improve particle accelerators. Pulsed lasers at intensities of the order of 108 W/cm2 and of ns pulse duration, interacting with solid matter in vacuum, produce plasma of high temperature and density. The charge state distribution of the plasma generates high electric fields which accelerate ions along the normal to the target surface. The energy of emitted ions has a Maxwell-Boltzmann distribution which depends on the ion charge state. To increase the ion energy, a post-acceleration system can be employed by means of high voltage power supplies of about 100 kV. The post acceleration system results to be a good method to obtain high ion currents by a not expensive system and the final ion beams find interesting applications in the field of the ion implantation, scientific applications and industrial use. In this work we compare the electromagnetic and geometric properties, like emittance, of the beams delivered by pure Cu, Y and Ag targets. The characterization of the plasma was performed by a Faraday cup for the electromagnetic characteristics, whereas a pepper pot system was used for the geometric ones. At 60 kV accelerating voltage the three examined ion bunches get a current peak of 5.5, 7.3 and 15 mA, with a normalized beam emittance of 0.22, 0.12 and 0.09 ? mm mrad for the targets of Cu, Y, and Ag, respectively.

Nassisi, V.; Velardi, L.; Side, D. Delle

2013-05-01

97

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

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

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

2012-02-01

98

NASA Astrophysics Data System (ADS)

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

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

2014-11-01

99

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

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

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

2014-01-01

100

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

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

2014-01-15

101

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

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

102

NASA Astrophysics Data System (ADS)

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

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

2010-03-01

103

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

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

1997-07-01

104

This paper presents the chaotic analysis of the single-walled carbon nanotubes on elastic medium. Due to small scales of the nanotubes, the nonlocal elastic theory is applied. Besides, due to large-amplitude vibrations of the nanotubes, the geometrical nonlinearity is taken into account, so the von Kármán strain is incorporated. The results show that the period-three oscillation, the chaos and the period-one oscillation are excited by the different excitation amplitudes. In addition, the excitation amplitude of the chaos increases as the nonlocal parameter increases. These results are also validated by the steady-state time responses, the FFT spectrums, the phase portraits, and the Poincaré sections. PMID:24745231

Kuo, Yong-Lin

2014-03-01

105

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

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

106

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

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

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

2013-04-15

107

NASA Astrophysics Data System (ADS)

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

Andruet, Raul Horacio

108

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

109

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

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

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

2013-01-01

110

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

111

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

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

Dreischuh, Alexander

112

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

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

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

2014-02-15

113

Fast Calculations in Nonlinear Collective Models of Beam/Plasma Physics

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

Antonina N. Fedorova; Michael G. Zeitlin

2002-12-31

114

Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity.

The near-field dynamics of a femtosecond Bessel beam propagating in a Kerr nonlinear medium (fused silica) is investigated both numerically and experimentally. We demonstrate that the input Bessel beam experiences strong nonlinear reshaping. Due to the combined action of self-focusing and nonlinear losses the reshaped beam exhibits a radial compression and reduced visibility of the Bessel oscillations. Moreover, we show that the reshaping process starts from the intense central core and gradually replaces the Bessel beam profile during propagation, highlighting the conical geometry of the energy flow. PMID:16803062

Polesana, P; Dubietis, A; Porras, M A; Kucinskas, E; Faccio, D; Couairon, A; Di Trapani, P

2006-05-01

115

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

116

Integrability and chaos in nonlinearly coupled optical beams

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

David, D.

1989-01-01

117

NASA Astrophysics Data System (ADS)

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

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

2014-08-01

118

Propagation of Lorentz—Gaussian Beams in Strongly Nonlocal Nonlinear Media

NASA Astrophysics Data System (ADS)

In this paper the propagation of Lorentz—Gaussian beams in strongly nonlinear nonlocal media is investigated by the ABCD matrix method. For this purpose, an expression for field distribution during propagation is derived and based on it, the propagation of Lorentz—Gaussian beams is simulated in this media. Then, the evolutions of beam width and curvature radius during propagation are discussed.

Keshavarz, A.; Honarasa, G.

2014-02-01

119

NONLINEAR FINITE ELEMENT RESPONSE SENSITIVITY ANALYSIS OF STEEL-CONCRETE COMPOSITE BEAMS

The behavior of steel-concrete composite beams is strongly influenced by the type of connection between the steel beam and the concrete slab. For accurate analysis, the structural model must account properly for the interlayer slip between the components. This paper focuses on nonlinear finite element response sensi- tivity analysis using a displacement-based formulation for composite beams with deformable shear connec-

M. Barbato; A. Zona; J. P. Conte

120

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

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

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

2011-03-04

121

Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity

Propagation of Gaussian beams in the negative-index metamaterials (NIMs) with cubic nonlinearities is investigated, both theoretically and numerically. The role of the status of the incident Gaussian beam, which is scaled by a converging parameter in this paper, in beam self-focusing and self-defocusing in NIMs is specially identified. The expressions for beam self-focusing and self-defocusing for different converging parameter cases,

Yonghua Hu; Shuangchun Wen; Youwen Wang; Dianyuan Fan

2008-01-01

122

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

123

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

124

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

NASA Technical Reports Server (NTRS)

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

Kory, Carol L.

2000-01-01

125

Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity

NASA Astrophysics Data System (ADS)

Propagation of Gaussian beams in the negative-index metamaterials (NIMs) with cubic nonlinearities is investigated, both theoretically and numerically. The role of the status of the incident Gaussian beam, which is scaled by a converging parameter in this paper, in beam self-focusing and self-defocusing in NIMs is specially identified. The expressions for beam self-focusing and self-defocusing for different converging parameter cases, and the dependence of the critical power and the focus location of self-focusing in NIMs on the converging parameter are obtained. It is found that it is the divergent rather than convergent incident beams which are self-focused more quickly in NIMs with defocusing nonlinearities, in sharp contrast with the propagation property of Gaussian beams in conventional Kerr media, in which beam self-focusing only occurs in the media with focusing nonlinearities and a convergent incident beam self-focuses more quickly than a divergent one. By adjusting the converging parameter of incident Gaussian beam or the controllable magnetic permeability of NIM, or both, one can manipulate the beam self-focusing in NIMs at will.

Hu, Yonghua; Wen, Shuangchun; Wang, Youwen; Fan, Dianyuan

2008-05-01

126

Nonlinear FE Analysis of Reinforced H.S. Concrete Continuous Beam Strengthened with CFRP Sheet

This paper is focused on the nonlinear finite element analysis of the reinforced high strength concrete continuous beam strength with carbon fiber reinforced polymer sheet. Three full scale continuous beams are analyzed under two points load; the data of analysis are compared with the experimental data provided by Akbarzadeh and Maghsoudi [1]. ANSYS V.11 program is used in FE analysis,

Majid Mohammed Ali Kadhim

2011-01-01

127

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

Nonlinear charge and current neutralization of an ion beam pulse in a pre-formed plasma Igor D of the calculation is the quantitative prediction of the degree of charge and current neutralization of the ion beam. Particle-in-cell simulations and fluid calculations of current and charge neutralization have been

Kaganovich, Igor

128

Non-Linear Effects in NLC Media Undergoing Two Beams Irradiation

A Nematic Liquid Crystal crossed by the overlap of multiple laser beams gives rise to different phenomena, such as the cancellation of reorientation and critical reorientation. A nonlinear 2D theoretical model is presented to describe these effects in the case of two laser beams impinging on a homeotropically aligned cell. By comparing the theoretical estimation of the re-orientational effect to

L. Pezzi; A. Veltri; A. De Luca; C. Umeton

2007-01-01

129

Z-scan method for nonlinear saturation intensity determination, using focused intense laser beams

NASA Astrophysics Data System (ADS)

We describe a method for determining saturation peak intensities of nonlinear intense field processes. The Z-scan method takes advantage of the balance between nonlinear response and interaction volume change as an intense laser pulse is focused onto a sample. We derive a robust geometric factor, directly relating the peak intensity at optimal target displacement from the focal plane and the corresponding saturation intensity. The Z-scan method allows obtaining saturation intensities with no need of a priori assumptions about the nonlinear process; surprisingly even for unfavorable finite depth samples. The method is demonstrated experimentally for an intense laser pulse interaction with molecular anions.

Albeck, Y.; Kandhasamy, D. M.; Strasser, D.

2014-11-01

130

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

131

NASA Astrophysics Data System (ADS)

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

Abd El Baky, Hussien

132

NASA Astrophysics Data System (ADS)

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

Haddadzadeh Hendou, Ramtin; Karami Mohammadi, Ardeshir

2014-11-01

133

NASA Astrophysics Data System (ADS)

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

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

2008-07-01

134

Refraction of nonlinear light beams in nematic liquid crystals

Optical spatial solitons in nematic liquid crystals, termed nematicons, have become an excellent test bed for nonlinear optics, ranging from fundamental effects to potential uses, such as designing and demonstrating ...

Xia, Wenjun

2013-07-01

135

Nonlinear beam-based vibration energy harvesters and load cells

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

Kluger, Jocelyn Maxine

2014-01-01

136

Modeling of Nonlinear Beam Propagation in Chiral Nematic Liquid Crystals

In this work three dimensional full-vector beam propagation method derived directly from Maxwell equations and combined with the exact equations describing director reorientation are presented. Molecules reorientation model bases on the Frank-Oseen equation with two angles (twist and azimuthal) describing molecule orientation. Solutions of light propagation in chiral nematic liquid crystals for different input beam polarization are shown. Formation of

Filip A. Sala; Miros?aw A. Karpierz

2012-01-01

137

Nonlinear Longitudinal Space Charge Oscillations in Relativistic Electron Beams

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

138

NASA Astrophysics Data System (ADS)

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

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

2014-09-01

139

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

NASA Astrophysics Data System (ADS)

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

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

2014-08-01

140

Nonlinear Models of Reinforced and Post-tensioned Concrete Beams

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

141

Experimental damage detection of cracked beams by using nonlinear characteristics of forced response

NASA Astrophysics Data System (ADS)

Experimental evaluation of the flexural forced vibrations of a steel cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed, where an actual fatigue crack was introduced instead - as usual - of a narrow slot. The nonlinear aspects of the dynamic response of the beam under harmonic excitation were considered and the relevant quantitative parameters were evaluated, in order to relate the nonlinear resonances to the presence and size of the crack. To this end, the existence of sub- and super-harmonic components in the Fourier spectra of the acceleration signals was evidenced, and their amplitudes were quantified. In particular, the acceleration signals were measured in different positions along the beam axis and under different forcing levels at the beam tip. The remarkable relevance of the above mentioned nonlinear characteristics, and their substantial independence on force magnitude and measurement point were worthily noted in comparison with the behavior of the intact beam. Thus, a reliable method of damage detection was proposed which was based on simple tests requiring only harmonically forcing and acceleration measuring in any point non-necessarily near the crack. Then, the time-history of the acceleration recorded at the beam tip was numerically processed in order to obtain the time-histories of velocity and displacement. The nonlinear features of the forced response were described and given a physical interpretation in order to define parameters suitable for damage detection. The efficiency of such parameters was discussed with respect to the their capability of detecting damage and a procedure for damage detection was proposed which was able to detect even small cracks by using simple instruments. A finite element model of the cantilever beam was finally assembled and tuned in order to numerically simulate the results of the experimental tests.

Andreaus, U.; Baragatti, P.

2012-08-01

142

Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities

NASA Astrophysics Data System (ADS)

Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged fields generated by beam-plasma instabilities can be responsible for defocusing and distorting beams propagating in background plasma. This can be problematic in inertial fusion applications where the beam is intended to propagate ballistically as the background plasma neutralizes the beam space charge and current. We used particle-in-cell (PIC) code LSP to numerically investigate the defocusing effects in an ion beam propagating in background plasma experiences as it is exposed to the non-linear fields generated by Two-Stream instability between beam ions and plasma electrons. Supported by theory and benchmarked by the numerical solutions of governing E&M equations, the simulations were used to find and check scaling laws for the defocusing forces in the parameter space of beam and plasma density as well as the beam ion mass. A transition region where the defocusing fields peak has been identified, which should be avoided in the design of experimental devices. We further proposed a diagnostic tool to identify the presence of the two-stream instability in a system with parameters similar to the National Drift Compression Experiment II (NDCX-II) and conducted proof-of concept simulations. In the case of electron beam propagating in background plasma instability driven collisionless scattering and plasma heating is observed. 1-D simulations conducted in EDIPIC were benchmarked in LSP to study the excitation and time-evolution of electron-electron Two-Stream instability. Coupling of electron dynamics via non-linear ponderomotive force created by instability generated fields with ion cavities and Ion-Acoustic mode excitation was observed. Furthermore 2-D simulations of an electron-beam in a background plasma was performed. Many of the effects in observed in 1-D simulations were replicated. Morever generation of oblique modes with transverse wave numbers were observed in the simulations, which resulted in significant transverse scattering of beam electrons and the time evolution of the turbulent spectrum was studied via Fourier techniques. It is plausible that the

Tokluoglu, Erinc K.

143

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

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

2012-07-15

144

NASA Astrophysics Data System (ADS)

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

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

2015-01-01

145

NASA Astrophysics Data System (ADS)

Many experiments at neutron scattering facilities require nearly monochromatic neutron beams. In such experiments, one must accurately measure the mean wavelength of the beam. We seek to reduce the systematic uncertainty of this measurement to approximately 0.1%. This work is motivated mainly by an effort to improve the measurement of the neutron lifetime determined from data collected in a 2003 in-beam experiment performed at NIST. More specifically, we seek to reduce systematic uncertainty by calibrating the neutron detector used in this lifetime experiment. This calibration requires simultaneous measurement of the responses of both the neutron detector used in the lifetime experiment and an absolute black neutron detector to a highly collimated nearly monochromatic beam of cold neutrons, as well as a separate measurement of the mean wavelength of the neutron beam. The calibration uncertainty will depend on the uncertainty of the measured efficiency of the black neutron detector and the uncertainty of the measured mean wavelength. The mean wavelength of the beam is measured by Bragg diffracting the beam from a nearly perfect silicon analyzer crystal. Given the rocking curve data and knowledge of the directions of the rocking axis and the normal to the scattering planes in the silicon crystal, one determines the mean wavelength of the beam. In practice, the direction of the rocking axis and the normal to the silicon scattering planes are not known exactly. Based on Monte Carlo simulation studies, we quantify systematic uncertainties in the mean wavelength measurement due to these geometric errors. Both theoretical and empirical results are presented and compared.

Coakley, K. J.; Dewey, M. S.; Yue, A. T.; Laptev, A. B.

2009-12-01

146

Numerical methods for axisymmetric and 3D nonlinear beams

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

Gianmarco F. Pinton; Gregg E. Trahey

2005-01-01

147

A coupled electromechanical finite element formulation for active control of geometrically non-linear transient response of laminated composite plate is studied. First-order shear deformation theory and von Karman type non-linear strain displacements are used. The plate is discritized using eight-noded quadratic isoparametric elements with five mechanical degrees of freedom and one electrical degree of freedom per node. Newton-Raphson iterative method in

Shravankumar B. Kerur; Anup Ghosh

2011-01-01

148

Collisionless beam-plasma instabilities are expected to play a crucial role during the early phase of the relativistic electron transport in the Fast Ignition scheme. This Letter presents a theoretical study of these instabilities in a two-dimensional geometry, highlighting the role of unstable modes propagating obliquely to the beam direction. The main features identified through a linearized analysis in a very general kinetic framework are examined by means of a particle-in-cell simulation. Good agreement between the two approaches is observed in the linear phase. Beam trapping is found to account for the nonlinear wave saturation.

Gremillet, L.; Benisti, D.; Lefebvre, E.; Bret, A. [Departement de Physique Theorique et Appliquee, CEA/DIF, Boite Postale 12, 91680 Bruyeres-le-Chatel (France); ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)

2007-04-15

149

Beam Loading in the Nonlinear Regime of Plasma-Based Acceleration

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

Tzoufras, M.; Lu, W. [Department of Electrical Engineering, University of California, Los Angeles, California 90095 (United States); Tsung, F. S.; Huang, C. [Department of Physics and Astronomy, University of California, Los Angeles, California 90095 (United States); Mori, W. B. [Department of Electrical Engineering, University of California, Los Angeles, California 90095 (United States); Department of Physics and Astronomy, University of California, Los Angeles, California 90095 (United States); Katsouleas, T. [Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089 (United States); Vieira, J.; Fonseca, R. A.; Silva, L. O. [GoLP/Instituto de Plasmas e FuSao Nuclear, Instituto Superior Tecnico, 1049-001 Lisboa (Portugal)

2008-10-03

150

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

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

151

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

152

Two-dimensional nonlinear dynamics of bidirectional beam-plasma instability

Solar wind electrons near 1 AU feature wide-ranging asymmetries in the superthermal tail distribution. Gaelzer et al. (2008) recently demonstrated that a wide variety of asymmetric distributions results if one considers a pair of counterstreaming electron beams interacting with the core solar wind electrons. However, the nonlinear dynamics was investigated under the simplifying assumption of one dimensionality. In the present

J. Pavan; L. F. Ziebell; R. Gaelzer; P. H. Yoon

2009-01-01

153

The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities

NASA Astrophysics Data System (ADS)

Very high energy gamma-rays from extragalactic sources produce pairs from the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the "oblique" instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here we show with numerical calculations that the effective damping rate is 8 × 10-4 the growth rate of the linear instability, which is sufficient for the "oblique" instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wave numbers and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long-wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long-wavelength modes, this scenario represents the "worst case" scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the "oblique" instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.

Chang, Philip; Broderick, Avery E.; Pfrommer, Christoph; Puchwein, Ewald; Lamberts, Astrid; Shalaby, Mohamad

2014-12-01

154

Thermodynamic bounds on nonlinear electrostatic perturbations in intense charged particle beams

This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (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

155

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

156

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

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

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

2005-06-01

157

This paper analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces by Incremental Harmonic Balance (IHB) method. Attention is paid to the fundamental resonance as the force frequency is close to the first frequencies omega{sub 1} of the system. Galerkin method is used to discretize the governing equations and the IHB method is used to illustrate the nonlinear dynamic behavior of the axially moving beam. The stable and unstable periodic solutions for given parameters are determined by the multivariable Floquet theory. Hsu's method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration.

Huang, J. L.; Chen, S. H. [Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275 (China); Su, R. K. L. [Department of Civil Engineering, University of Hong Kong, Pokfulam (Hong Kong); Lee, Y. Y. [Department of Building and Construction, City University of Hong Kong (Hong Kong)

2010-05-21

158

Elasto-dynamics of multihulls in nonlinear beam seas-a multibody-BEM approach

NASA Astrophysics Data System (ADS)

Many floating structures in naval architecture and ocean engineering cannot be modelled as a single rigid body. Even for ships, models of interconnected bodies may be necessary for an adequate description of the dynamics. The dynamic behavior of these floating structures is significantly influenced by fluid-structure interactions. So far, most available methods for analyzing these interactions are restricted to single bodies, small wave amplitudes and small body motions, or both. In the present paper, a two-dimensional boundary integral approach with fully nonlinear boundary conditions on the free surface is used to investigate the dynamic behavior of catamarans in nonlinear beam seas. In the model introduced here, the two hulls of a catamaran are connected by elastic beams. Beams and hulls are modelled as multibody systems. The results of numerical simulations are shown for selected configurations.

Kral, R.; Kreuzer, E.; Schlegel, V.

2003-05-01

159

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

NASA Technical Reports Server (NTRS)

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

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

1991-01-01

160

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

NASA Astrophysics Data System (ADS)

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

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

2015-02-01

161

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

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

Albert C. Fannjiang

2004-03-05

162

Geometrical correction of the e-beam proximity effect for raster scan systems

Increasing demands on pattern fidelity and CD accuracy in e- beam lithography require a correction of the e-beam proximity effect. The new needs are mainly coming from OPC at mask level and x-ray lithography. The e-beam proximity limits the achievable resolution and affects neighboring structures causing under- or over-exposion depending on the local pattern densities and process settings. Methods to

Nikola Belic; Hans Eisenmann; Hans Hartmann; Thomas Waas

1999-01-01

163

NASA Astrophysics Data System (ADS)

We present observations of polar mesospheric summer echoes (PMSE) using the Middle Atmosphere Alomar Radar System in Northern Norway (69.30° N, 16.04° E). The radar is able to resolve PMSE at high spatial and temporal resolution and to perform pulse-to-pulse beam steering. In this experiment, 81 oblique beam directions were used with off-zenith angles up to 25°. For each beam pointing direction and range gate, coherent radar imaging was applied to determine the mean backscatter location. The location of the mean scatterer in the beam volume was calculated by the deviation from the nominal off-zenith angle of the brightest pixel. It shows that in tilted beams with an off-zenith angle greater than 5°, structures appear at the altitudinal edges of the PMSE layer. Our results indicate that the mean influence of the location of the maximum depends on the tilt of the beam and on the observed area of the PMSE layer. At the upper/lower edge of the PMSE layer, the mean backscatter has a greater/smaller off-zenith angle than the nominal off-zenith angle. This effect intensifies with greater off-zenith beam pointing direction, so the beam filling factor plays an important role in the observation of PMSE layers for oblique beams.

Sommer, S.; Stober, G.; Chau, J. L.; Latteck, R.

2014-11-01

164

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

165

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

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

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

1993-01-01

166

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

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

2014-08-22

167

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

168

Effect of geometric elastic non-linearities on the impact response of flexible multi-body systems

NASA Astrophysics Data System (ADS)

The intermittent motion behavior of large scale geometrically non-linear flexible multi-body systems due to impact loading is investigated. Impacts and the associated impulsive forces are incorporated into the dynamic formulation by using a generalized momentum balance. The solution of the momentum equation provides the jump discontinuities in the system velocities and reaction forces. Flexible components in the system are discretized by using the finite element method. Because of the large rotations of the system components, a set of reference co-ordinates are employed to describe the motion of a selected body reference. The rigid body modes of the finite element shape functions are eliminated by using a set of reference conditions and accordingly a unique displacement field is defined. In order to account for the inertia and elastic non-linearities which are, respectively, the results of the large rotations and finite deformations, the system inertia and stiffness characteristics have to be iteratively updated. Two numerical examples of different nature are presented. The first example is a high speed slider crank mechanism with a flexible connecting rod. In the second example, however, the dynamic response of a flexible multi-body aircraft during the touch down impact is predicted.

Bakr, E. M.; Shabana, A. A.

1987-02-01

169

Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion

process. The electron-beam poling was performed in a scanning electron microscope JEOL 6400 , which electron-beam poling,1 electric-field poling,2 and high-voltage atomic force microscop AFM .3Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion

Arie, Ady

170

Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red), which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures. PMID:24022688

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

2013-01-01

171

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

Lee, S. Y.

2014-04-07

172

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

Various researchers have predicted situations where the acoustical or optical radiation force on a sphere centered on a Bessel beam is opposite the direction of beam propagation. We develop the analogy between acoustical and optical radiation forces of arbitrary-order helicoidal and ordinary Bessel beams to gain insight into negative radiation forces. The radiation force is expressed in terms of the asymmetry of the scattered field, the scattered power, the absorbed power, and the conic angle of the Bessel beam and is related to the partial-wave coefficients for the scattering. Negative forces only occur when the scattering into the backward hemisphere is suppressed relative to the scattering into the forward hemisphere. Absorbed power degrades negative radiation forces. PMID:22060448

Zhang, Likun; Marston, Philip L

2011-09-01

173

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

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

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

2009-09-04

174

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

Controlling the propagation of intense optical wavepackets in transparent media is not a trivial task. During propagation, low- and high-order non-linear effects, including the Kerr effect, multiphoton absorption and ionization, lead to an uncontrolled complex reshaping of the optical wavepacket that involves pulse splitting, refocusing cycles in space and significant variations of the focus. Here we demonstrate both numerically and experimentally that intense, abruptly autofocusing beams in the form of accelerating ring-Airy beams are able to reshape into non-linear intense light-bullet wavepackets propagating over extended distances, while their positioning in space is extremely well defined. These unique wavepackets can offer significant advantages in numerous fields such as the generation of high harmonics and attosecond physics or the precise micro-engineering of materials. PMID:24131993

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

2013-01-01

175

Nonlinear finite element analysis of steel fiber reinforced concrete deep beams

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

176

A comparison between nonlinear cantilever and buckled beam for energy harvesting

NASA Astrophysics Data System (ADS)

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

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

2013-09-01

177

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

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

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

2015-01-01

178

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

179

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

180

Geometrically nonlinear analysis of hyperelastic solids by high-order tetrahedral finite elements

NASA Astrophysics Data System (ADS)

The purpose of this study is to develop a computer code for accurate prediction of the mechanical behavior of hyperelastic solids under large deformation and finite strains. It is used, in the present work, the Lagrangian positional version of the Finite Element Method, in which the degrees of freedom are current positions instead of displacements. The main mechanical variables are the Green-Lagrange strain and the second Piola-Kirchhoff stress tensors. Isoparametric tetrahedral solid finite element of any approximation degree is employed with full integration in order to obtain accuracy. In order to be general, it is developed a numerical strategy to determine the shape functions coefficients of any order, following tetrahedral basis. The solid equilibrium is achieved at the current position by means of the Minimal Potential Energy Principle regarding positions and is solved by the Newton-Raphson iterative scheme. It is important to mention that the adopted constitutive laws are nonlinear, isotropic and homogeneous hyperelastic, normally used in mechanical analysis of elastomers, with the near compressibility assumption. It is applied the Flory decomposition, i.e., the multiplicative split of the deformation gradient into a volumetric and an isochoric part. A parallel processing strategy is used to increase the simulation speed and memory capacity, justifying the use of high order elements for solid analysis. Results confirm that the developed computer code is capable of predicting the static behavior of complex problems, such as Cook's membrane and partially loaded block. The shape functions generator code exhibits simplicity and, thus, it may be easily implemented in other finite elements. The increase in the order of approximation and the mesh refinement improve accuracy and, therefore, the proposed methodology together with parallel computing indicate a safe way for further developments in plasticity and damage mechanics for large strain and deformations.

Pascon, João P.; Coda, Humberto B.

2010-06-01

181

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

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

1998-03-15

182

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

We report on the generation of a narrow divergence (?_{?}<2.5??mrad), multi-MeV (E_{max}?18??MeV) and ultrahigh peak brilliance (>1.8×10^{20}??photons?s^{-1}?mm^{-2}??mrad^{-2} 0.1% BW) ?-ray beam from the scattering of an ultrarelativistic laser-wakefield accelerated electron beam in the field of a relativistically intense laser (dimensionless amplitude a_{0}?2). The spectrum of the generated ?-ray beam is measured, with MeV resolution, seamlessly from 6 to 18 MeV, giving clear evidence of the onset of nonlinear relativistic Thomson scattering. To the best of our knowledge, this photon source has the highest peak brilliance in the multi-MeV regime ever reported in the literature. PMID:25494074

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

2014-11-28

183

A nonlinear OPC technique for laser beam control in turbulent atmosphere

NASA Astrophysics Data System (ADS)

A viable beam control technique is critical for effective laser beam transmission through turbulent atmosphere. Most of the established approaches require information on the impact of perturbations on wavefront propagated waves. Such information can be acquired by measuring the characteristics of the target-scattered light arriving from a small, preferably diffraction-limited, beacon. This paper discusses an innovative beam control approach that can support formation of a tight laser beacon in deep turbulence conditions. The technique employs Brillouin enhanced fourwave mixing (BEFWM) to generate a localized beacon spot on a remote image-resolved target. Formation of the tight beacon doesn't require a wavefront sensor, AO system, or predictive feedback algorithm. Unlike conventional adaptive optics methods which allow wavefront conjugation, the proposed total field conjugation technique is critical for beam control in the presence of strong turbulence and can be achieved by using this non-linear BEFWM technique. The phase information retrieved from the established beacon beam can then be used in conjunction with an AO system to propagate laser beams in deep turbulence.

Markov, V.; Khizhnyak, A.; Sprangle, P.; Ting, A.; DeSandre, L.; Hafizi, B.

2013-05-01

184

NASA Astrophysics Data System (ADS)

Using the frame matrix representation of the Grassmann manifold, we derive a nonlinear realization of the general linear group. We show that its super-extension reproduces the ?-field which appears in the recent work on a supersymmetric extension of local Lorentz symmetry by Abe and Nakanishi. This clarifies the geometrical meaning of the ?-field and we discuss its properties on the basis of this interpretation. The similarity of this ?-field and the vierbein field is pointed out.

Kanno, Hiroaki

185

The important nonlinear effects which limit high energy laser propagation through the atmosphere are reviewed. The two most important effects are thermal blooming (or thermal defocussing) and air breakdown within the beam. A third, less important effect is stimulated raman scattering. The possibility of transmitting laser beams through fogs, clouds or haze by boring holes through these atmospheric media with

S. Edelberg

1976-01-01

186

Multi-harmonic measurements and numerical simulations of nonlinear vibrations of a beam with non-clamped steel beam with non-ideal boundary conditions. A multi-harmonic comparison of simulations of the model. Then, two numerical methods, the Harmonic Balance Method and a time-integration method

Boyer, Edmond

187

Linear, nonlinear and mixed-regime analysis of electrostatic MEMS

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

Gang Li; N. R. Aluru

2001-01-01

188

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

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

2012-05-15

189

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

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

2013-12-15

190

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

191

NASA Astrophysics Data System (ADS)

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

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

2012-02-01

192

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

193

Model for nonlinear evolution of localized ion ring beam in magnetoplasma

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

194

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

195

NASA Astrophysics Data System (ADS)

A nonneutral plasma is a many-body collection of charged particles in which there is not overall charge neutrality. Such systems are characterized by intense self-electric fields and, in high-current configurations, by intense self-magnetic fields. Nonneutral plasmas, like electrically neutral plasmas, exhibit a broad range of collective properties. This presentation summarizes several recent advances in understanding the collective processes and nonlinear dynamics of intense charged particle beams and nonneutral plasmas. Particular emphasis is placed on: basic experimental investigations of nonneutral plasmas confined in the Paul Trap Simulator Experiment (PTSX), a compact laboratory device with oscillatory wall voltages, used to simulate intense beam propagation through a periodic quadrupole field over equivalent distances of tens of kilometers; and analytical and numerical studies of the nonlinear dynamics and collective processes in intense one-component beams propagating in periodic-focusing accelerators and transport systems, such as next-generation accelerators for ion-beam-driven high energy density physics and heavy ion fusion, and high energy physics applications. The topics covered include: nonlinear stability theorem for quiescent beam propagation; electrostatic Harris and electromagnetic Weibel instabilities in highly anisotropic, intense one-component beams; and the electron-ion two-stream (electron cloud) instability for an intense ion beam propagating through a partially neutralizing electron background. In the longitudinal drift compression and transverse compression regions, collective processes associated with the interaction of an intense ion beam with a charge-neutralizing background plasma are discussed.

Davidson, Ronald

2008-11-01

196

NASA Technical Reports Server (NTRS)

Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

Noor, A. K.; Peters, J. M.

1981-01-01

197

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

198

Nonlinear response of a clamped beam and plate to high levels of excitation

NASA Astrophysics Data System (ADS)

Acoustic fatigue failure in aerospace structures has been a concern for many years. New prediction techniques are needed for the new materials and structural concepts of interest and higher sound pressure levels encountered for the hypersonic flight regime. The objective of this program of work is to improve the fundamental understanding of the nonlinear behavior of beams and plates excited from low to high levels of excitation. Experiments have been conducted utilizing a clamped-clamped (C-C) beam statically tested and shaker driven at increasing levels of excitation. Similarly, a C-C-C-C plate was acoustically excited in a progressive wave tube. The total strains and the components, bending and axial, were measured for increasing levels of excitation. The bending strain response modes induced exhibited a peak broadening and frequency increase with an increase in excitation levels. The bending strain amplitudes were slightly less than the total strains measured. While the axial strains increased with increasing excitation levels, they did not increase as rapidly as expected. The static test resulted in a linear relationship between the strain and the loads over the level of interest. The dynamic tests resulted in a nonlinear relationship between the response strains and the excitation levels.

Wolfe, Howard F.; White, Robert G.

199

NASA Astrophysics Data System (ADS)

We present a new pump probe laser beams configuration for the nonlinear optical characterization of microemulsions. We detect the variation of the on-axis optical intensity of the probe beam as generated by the concentration profile induced in an optically thin film of microemulsion by the pump beam. A mathematical model has been introduced to describe the phenomenon. The technique allows the determination of both Kerr-like optical nonlinearity and time constants and, therefore, it gives information both on cluster dimension and their shape. We discuss its application to WAD (water/AOT/decane, where AOT denotes sodium-bis-di-ethyl-sulfosuccinate) with the application of a strong electric field of optical source. Comparison between theoretical predictions and experimental results confirms the presence of giant optical nonlinearity in the absence of turbidity divergence. Chainlike shape of clusters, of the kind already reported with the application of strong electric field, could justify this result.

Vicari, L.

2002-11-01

200

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

201

NASA Astrophysics Data System (ADS)

Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.

Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan

2012-12-01

202

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

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

2014-04-28

203

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

NASA Astrophysics Data System (ADS)

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

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

2007-10-01

204

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

205

A Creep Non-Linear FEM Analysis of Glulam Timber

This work is focused on a creep formulation in bending for timber beams, of glue laminated (glulam) type, which is suited to be implemented in both geometrical and material non-linear Finite Element Method (FEM) models. It studies the performance of timber beams by accounting the deformation under increments of time and stress in a long-term. The proposed creep formulation uses

V. De Luca; A. Della Chiesa

2012-01-01

206

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

207

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

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

2014-03-21

208

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

209

A special purpose 3D concrete finite element is employed in this research to model the complex nonlinear behaviour of reinforced concrete beams with no shear reinforcement. The theory is based on the 5 parameter plasticity failure surface due to Willam-Warnke and takes into account the tensile cracking in three orthogonal directions plus crushing status of certain Gaussian integration point. A

Sonia L. Parvanova; Konstantin S. Kazakov; Irina G. Kerelezova; Gospodin K. Gospodinov; Mogens P. Nielsen

210

In the present work, mechanical behavior of a functionally graded cantilever micro-beam subjected to a nonlinear electrostatic pressure and temperature changes has been studied. It has been assumed that the top surface is made of pure metal and the bottom surface from a metal–ceramic mixture. The ceramic constituent percent of the bottom surface varies from 0% to 100%. In addition

Behzad Mohammadi-Alasti; Ghader Rezazadeh; Ali-Mohammad Borgheei; Saeid Minaei; Rahim Habibifar

2011-01-01

211

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

Karaton, Muhammet

2014-01-01

212

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

213

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

Karaton, Muhammet

2014-01-01

214

SELF-FOCUSING AND DIFFRACTION OF LIGHT IN A NONLINEAR MEDIUM

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

S A Akhmanov; Anatolii P Sukhorukov; R V Khokhlov

1968-01-01

215

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

216

NASA Technical Reports Server (NTRS)

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

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

1984-01-01

217

NASA Astrophysics Data System (ADS)

Weld geometric characteristics in laser overlapping spot welding of 0.6-mm AISI 304 stainless steel sheets were investigated. A pulsed Nd:YAG laser with maximal average power of 150 W was used for welding experiments with different laser beam energies in the range of 3.5 J to 6.2 J, keeping all other processing parameters constant. The main objective of these experiments was to study the effect of energy changes and to identify the welding mode in dependency on the beam effective peak power density. Each weld surface and its cross section were analyzed using a laser scanning confocal microscope. The spot diameter on the specimen, weld width, and penetration depth were measured. Three-dimensional surface reconstruction was realized to describe the effect of energy changes on weld surface properties.

Lapsanska, Hana; Chmelickova, Hana; Hrabovsky, Miroslav

2010-10-01

218

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

2012-03-01

219

A coaxial electromagnetic shock tube was developed to produce a non-ideal plasma target with ??0.1 (?: Plasma coupling constant) for non-linear interaction experiments between ion beams and plasmas. To evaluate the shock velocity, we photographed the trajectory of the shock front along the tube by a streak camera. From these measurements, we found that the shock waves are strong enough

K. Katagiri; J. Hasegawa; S. Nishinomiya; H. Ikagawa; Y. Oguri

2008-01-01

220

Ultra-high brilliance multi-MeV $\\gamma$-ray beam from non-linear Thomson scattering

We report on the generation of a narrow divergence ($\\theta\\approx 2.5$ mrad), multi-MeV ($E_\\text{MAX} = 18$ MeV) and ultra-high brilliance ($\\approx 2\\times10^{19}$ photons s$^{-1}$ mm$^{-2}$ mrad $^{-2}$ 0.1\\% BW) $\\gamma$-ray beam from the scattering of an ultra-relativistic laser-wakefield accelerated electron beam in the field of a relativistically intense laser (dimensionless amplitude $a_0\\approx2$). The spectrum of the generated $\\gamma$-ray beam is measured, with MeV resolution, seamlessly from 6 MeV to 18 MeV, giving clear evidence of the onset of non-linear Thomson scattering. The photon source has the highest brilliance in the multi-MeV regime ever reported in the literature.

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

2014-01-01

221

A model for the nonlinear mechanism responsible for cochlear amplification.

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

Fessel, Kimberly; Holmes, Mark H

2014-12-01

222

NASA Astrophysics Data System (ADS)

We report the optimized geometrical structures using the ab initio method, and the calculated frequency dependence of the third-order nonlinear optical polarizabilities ? in the different optical processes of the third-harmonic generation, electric-field induced second-harmonic generation, and degenerate four-wave mixing using the INDO/SDCI method coupled with the sum-over-states method for C59Si and two isomers of C58Si2 heterofullerenes. The optimized structures show that the stabilization of the para isomer of C58Si2 is larger than that of the dia isomer of C58Si2, and the geometrical modifications of C59Si and C58Si2 isomers occur in the vicinity of the Si-doped atom after the replacement of one or two C atoms by Si atoms in the C60 fullerene. The calculated hyperpolarizabilities at nonresonant frequency show the varied trends in the order of C59Si~ dia isomer of C58Si2< para isomer of C58Si2 at ground state and the charge transfers of two-photon states make significant contributions to third-order optical polarizabilities for the para isomer of C58Si2. The enhancement of first excited singlet state is about one or two order of magnitude at nonresonant frequency. The susceptibilities of ?(-??,?,-?) of these Si-doped fullerene films are estimated to be about 10-10 esu at first excited state and 10-11 esu at ground state in nonresonant frequency.

Cheng, W.-D.; Wu, D.-S.; Zhang, H.; Chen, D.-G.; Wang, H.-X.

2002-08-01

223

Actuating characteristic of laminated PVDF actuators used on a beam with large deformation

Actuating characteristic of laminated PVDF actuator (LPA) partially covered on a beam is studied in this paper. Considering large deformation of the beam, coupled dynamic equations of the system are derived based on Hamilton principle. The formulas of nonlinear actuating forces are obtained and the parametric study is then conducted to evaluate the effects of geometric and physical properties of

Ya-hong Zhang; Shi-lin Xie; Xi-nong Zhang

2008-01-01

224

NASA Astrophysics Data System (ADS)

Realizing that nonlinearity is a frequent occurrence in engineering structures and that linear experimental modal analysis (EMA) is of limited usefulness in this context, the present paper is an attempt to develop nonlinear EMA by targeting the extraction of nonlinear normal modes (NNMs) from time series of nonlinear mechanical systems. Based on a nonlinear extension of phase resonance testing, the proposed methodology excites the structure to isolate a single NNM during the experiments. Thanks to the invariance principle, the energy dependence of that nonlinear mode (i.e., the NNM modal curves and their oscillation frequencies) can be extracted from the resulting free decay response using time-frequency analysis. This paper is devoted to the experimental demonstration and robustness of this procedure. To this end, an experimental cantilever beam with a geometrical nonlinearity is considered, and the ability of the proposed methodology to extract its NNMs from the measured responses is assessed.

Peeters, M.; Kerschen, G.; Golinval, J. C.

2011-05-01

225

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

226

NASA Astrophysics Data System (ADS)

We analyze a new scheme for generating squeezed states in a short semiconductor AlxGa 1-xAs waveguide with chi (3) nonlinearity at below half the band-gap energy. We find that for a Gaussian pulse the amount of squeezing achievable is limited by the squeezed-state detection phase mismatch caused by the pump self-phase modulation and is also degraded slightly by the pump-probe phase mismatch that is due to the different nonlinear refractive indices experienced by the pump and the probe beams. We show theoretically that the amount of squeezing observed can be increased by use of either a short pulse or a pulse with matched phase variation as the local oscillator. In a centimeter-long AlxGa1-x As waveguide more than 85% (8.2 dB) of squeezing potentially can be obtained, limited mainly by two-photon absorption.

Ho, Seng-Tiong; Zhang, Xiaolong; Udo, Maria K.

1995-09-01

227

Optimization of nonlinear structural resonance using the incremental harmonic balance method

NASA Astrophysics Data System (ADS)

We present an optimization procedure for tailoring the nonlinear structural resonant response with time-harmonic loads. A nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinear vibration analysis. An optimization procedure based on a gradient-based algorithm is developed and we use the adjoint method for efficient computation of design sensitivities. We consider several examples in which we find optimized beam width distributions that minimize or maximize fundamental or super-harmonic resonant responses.

Dou, Suguang; Jensen, Jakob Søndergaard

2015-01-01

228

This paper shows the analysis and design of feedforward neural networks using the coordinate-free system of Clifford or geometric algebra. It is shown that real-, complex-, and quaternion-valued neural networks are simply particular cases of the geometric algebra multidimensional neural networks and that some of them can also be generated using support multivector machines (SMVMs). Particularly, the generation of radial basis function for neurocomputing in geometric algebra is easier using the SMVM, which allows one to find automatically the optimal parameters. The use of support vector machines in the geometric algebra framework expands its sphere of applicability for multidimensional learning. Interesting examples of nonlinear problems show the effect of the use of an adequate Clifford geometric algebra which alleviate the training of neural networks and that of SMVMs. PMID:18249926

Bayro-Corrochano, E J

2001-01-01

229

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

230

Nonlinear dynamic response of shallow arches to harmonic forcing

Buckled beams and shallow arches exhibit nonlinear force-deflection curves as a result of their geometric shape. These structural components share the common characteristic of nonlinear load-deflection curves, exhibiting both stable and unstable equilibrium states. Previous work has shown that with the application of sufficiently large static or dynamic loads, snap-buckling can occur, in which the structure suddenly jumps from one

Kim Billy Blair

1992-01-01

231

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

NASA Astrophysics Data System (ADS)

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 based on excitons. We also found that when a DC electric field was added on the sample of CdS, the nonlinear absorption increased as the applied DC electric field was increased.

Li, Zhengang; Xiong, Guangnan; Zhao, Zhihong; Fan, Xiwu

1994-04-01

232

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

233

Nonlinear Plasma Waves Excitation by Intense Ion Beams in Background Plasma

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

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

2004-04-15

234

NASA Astrophysics Data System (ADS)

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

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

235

Nonlinear parametric amplification and attenuation in a base-excited cantilever beam

actuated by piezoelectric and electrostatic elements [3]. Subsequent to this work, a number of studies have the nonlinear behavior of a representative parametrically amplified macroscale structure. Specifically excitations [11]. This work reported near-resonant amplifier gains of 1.4Â1.6 and showed that with careful

Rhoads, Jeffrey F.

236

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

/slip implementation, the tendon/mooring disconnection (breakage/unlatch) module with the tendon down-stroke check, and the contact spring with the initial gap with the friction force implemented. The nonlinear coupling may happen in many places for the offshore...

Yang, Chan K.

2010-07-14

237

Steady-progressive-wave solutions are sought to the nonlinear wave equation derived previously [J. Fluids Struct. 16 (2002) 597] for flexural motions of an elastic beam traveling in an air-filled tube along its center axis at a subsonic speed. Fluid-structure interactions are taken into account through aerodynamic loading on the lateral surface of the beam subjected to small but finite deflection but

Yosuke Watanabe; Nobumasa Sugimoto

2003-01-01

238

NASA Astrophysics Data System (ADS)

Stress generated during thin film deposition is a critical issue for many applications. In general, the possible origins of the residual stress include intrinsic and extrinsic stresses. Since high residual stresses can cause detrimental effects on the film, such as delamination and wrinkle, it is of great importance to quantify the residual stress for the optimal design and the evaluation of its mechanical behavior. In this study, a method combining focused ion beam (FIB) milling and geometric phase analysis (GPA) is developed to assess the residual stress of thin films. The procedures of the residual stress measurement using this method include grating fabrication and slot milling by FIB, high-resolution scanning electron microscope (SEM) imaging of the grating before and after stress relaxation, and deformation analysis by GPA. The residual stress can be inferred from the released deformation using the reference displacements of the finite element model. As an application, this method was utilized to measure the residual stress in a TiAlSiN film, and the measured result is in good agreement with that obtained by the curvature method. In order to analyze the measurement error, the influence factors of Ga+ bombardment and the deposited platinum layer on the stress calculation are also discussed in detail.

Zhu, Ronghua; Xie, Huimin; Dai, Xianglu; Zhu, Jianguo; Jin, Aizi

2014-09-01

239

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

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

2013-08-15

240

Nonlinear airship aeroelasticity

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

N. Bessert; O. Frederich

2005-01-01

241

NASA Astrophysics Data System (ADS)

A commonly observed feature of the field-aligned flow of ions on closed geomagnetic field lines is that the pitch angle distributions are considerably broadened. Such pitch angle distributions facilitate in trapping ions and thus contribute to the process of plasmaspheric refilling. Since counterstreaming ion beams are a common feature of the early stage refilling as shown by models, we have investigated the role of ion-beam-driven instabilities in broadening the pitch angle distribution of the ion beams. The study is performed using a 2.5-dimensional particle-in-cell code. It is shown that for sufficiently fast ion beams as expected in the outer region of the plasmasphere, the ion cyclotron modes, which appear at frequencies less than the ion-cyclotron frequency ?i in the rest frame of the nondrifting electrons, are the dominant unstable wave modes. In the early stage of the instability a nearly purely growing mode dominates, which efficiently mediates in transferring a part of the parallel drift energy into the perpendicular energy, significantly broadening the ion pitch angle distribution. The transfer abruptly saturates when Jn(k??if)->0, where Jn( ) is the Bessel function of an appropriate order n, k? is the perpendicular wave number of the dominant mode, and ?if is the maximum value of the Larmor radius of the beam ions in anomalous cyclotron resonance with the wave. This behavior of the dominant mode in conjunction with the conservation of ion energy allows a method for including such wave-particle interaction effects in mesoscale models for the plasmaspheric refilling. The perpendicular acceleration of ions by this instability reduces the parallel drift only by a relatively small fraction, leaving the counterstreaming intact. However, the perpendicular acceleration produces a pitch angle distribution which is inducive for the trapping of the counterstreaming ions in the plasmaspheric flux tubes.

Singh, Nagendra; Leung, W. C.

242

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

243

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

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

1997-08-01

244

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

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

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

2010-11-15

245

Nonlinear optics: Diffraction cancellation

NASA Astrophysics Data System (ADS)

The unusual nonlinear optical properties of rapidly cooled disordered ferroelectric crystals allow beam spreading to be completely suppressed, irrespective of the beam width and intensity, offering potentially important applications in imaging and all-optical beam control.

Sukhorukov, Andrey

2011-01-01

246

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

247

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

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

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

2009-09-30

248

NASA Astrophysics Data System (ADS)

We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega

Belashov, Vasily

249

NSDL National Science Digital Library

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

2011-01-01

250

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

251

Competing nonlinearities in quadratic nonlinear waveguide arrays

Competing nonlinearities in quadratic nonlinear waveguide arrays Frank Setzpfandt,1, * Dragomir N demonstrate experimentally the existence of competing focusing and defocusing nonlinearities in a double- tively. If an optical system, however, exhibits so- called competing nonlinearities a laser beam can ex

252

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

253

Dynamic analysis of 3D beams with joints in presence of large rotations

In this paper we present a way to extend the earlier static master–slave formulation for beams and joints [1] to dynamic problems. The dynamic master–slave approach is capable of (i) handling the problems of linear elasticity in a geometrically non-linear environment, (ii) accounting for the non-linear kinematics of arbitrary types of joints and (iii) performing the numerical time integration while

G. Jelenic; M. A. Crisfield

2001-01-01

254

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

255

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.

2008-09-01

256

NASA Astrophysics Data System (ADS)

Polarisation singularities in the electric field at a sum-frequency generated in the bulk of an isotropic gyrotropic medium with a quadratic nonlinearity are predicted to appear in the case of the collinear interaction of two uniformly elliptically polarised Gaussian beams. The parameters of the fundamental waves are found, corresponding to the formation of lines with circular and linear polarisations (C- and L-lines) in the cross section of the beam at the sum-frequency as well as to the appearance of the regions in the signal beam where the polarisation state varies smoothly from the left-hand circularly polarised state to the right-hand circularly polarised. In this case, the ellipticity degree of the polarisation ellipse takes all possible values, while its orientation remains unchanged.

Makarov, Vladimir A.; Perezhogin, I. A.; Potravkin, N. N.

2011-02-01

257

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

Y. Zhu; Y. X. Zhang

2010-01-01

258

18.385 Nonlinear Dynamics and Chaos, Fall 2002

Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear ...

Rosales, Rodolfo

259

NASA Astrophysics Data System (ADS)

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

Oguama, Ferdinand Anayo

260

NSDL National Science Digital Library

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

NCTM Illuminations

2000-01-01

261

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

262

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

Lajimi, Seyed Amir Mousavi

2014-01-01

263

Geometric Algebra: the framework for geometric computations

Geometric Algebra: the framework for geometric computations Leo Dorst Intelligent Autonomous and in computation. Q: How do they relate? A: They are all aspects of geometric algebra! This connection can unify and simplify geometric programs. 2 #12; 2 What's new in geometric algebra? The uni#12;cation is achieved

Dorst, Leo

264

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

265

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

Eric Chisolm

2012-05-27

266

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

Chisolm, Eric

2012-01-01

267

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

268

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

269

Advances in dynamic relaxation techniques for nonlinear finite element analysis

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

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

1995-05-01

270

Non-isothermal elastoviscoplastic analysis of planar curved beams

NASA Technical Reports Server (NTRS)

The development of a general mathematical model and solution methodologies, to examine the behavior of thin structural elements such as beams, rings, and arches, subjected to large nonisothermal elastoviscoplastic deformations is presented. Thus, geometric as well as material type nonlinearities of higher order are present in the analysis. For this purpose a complete true abinito rate theory of kinematics and kinetics for thin bodies, without any restriction on the magnitude of the transformation is presented. A previously formulated elasto-thermo-viscoplastic material constitutive law is employed in the analysis. The methodology is demonstrated through three different straight and curved beams problems.

Simitses, G. J.; Carlson, R. L.; Riff, R.

1988-01-01

271

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

272

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

273

Linearizing Intra-Train Beam-Beam Deflection Feedback

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

Smith, S.R.; /SLAC

2006-02-22

274

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

275

The mixing action of two crossed ultrasonic beams has been studied. The theoretical treatment of Taylor and Rollins is extended to include the all-pure-mode cases for the prosess L (omega1)-Tomega2omega1- omega2-->Tomega1- omega2omega2 in cubic single crystals. Five such cases exist in cubic crystals; two in the (001) mixing plane and with L (omega1) propagated in either of two fixed directions

Russel W. Dunham; Hillard B. Huntington

1970-01-01

276

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

277

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

278

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

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

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

2015-01-01

279

Geometrically nonlinear analysis of laminated elastic structures

NASA Technical Reports Server (NTRS)

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

Reddy, J. N.

1984-01-01

280

Processing textured surfaces via anisotropic geometric diffusion

A multiscale method in surface processing is presented which carries over image processing methodology based on nonlinear diffusion equations to the fairing of noisy, textured, parametric surfaces. The aim is to smooth noisy, triangulated surfaces and accompanying noisy textures - as they are delivered by new scanning technology - while enhancing geometric and texture features. For an initial textured surface

Ulrich Clarenz; Udo Diewald; Martin Rumpf

2004-01-01

281

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

282

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

283

Nonlinear dynamic response of submarine pipelines in contact with the ocean floor

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

284

NASA Astrophysics Data System (ADS)

In this paper, a new switch control strategy based on an energy threshold is proposed for the synchronized switch damping techniques in multimode control. This strategy is derived from the total converted energy of a synchronized switch damping (SSD) system in a given time window. Using the new strategy the voltage is inverted only at those extrema where the effective distance, which is proportional to the converted energy between two neighboring extrema, exceeds the threshold. The new switch control strategy is used in both the synchronized switch damping on inductor (SSDI) technique and the synchronized switch damping on voltage source (SSDV) technique, which are applied to the two-mode control of a composite beam. Their control performances are compared with those of the single-mode control and those of classical SSDI and SSDV techniques in two-mode control. The experimental results show that voltage inversion is prevented at some of the displacement extrema to increase the total converted energy, and exhibit better global damping effect than classical SSDI and classical SSDV, respectively. In single mode, the best control performance is achieved when the voltage is inverted at every extremum. But in multimodal control, the total converted energy in a given time window is increased and the control performance is improved when some extrema are skipped.

Ji, Hongli; Qiu, Jinhao; Zhu, Kongjun; Badel, Adrien

2010-07-01

285

Transition from linear- to nonlinear-focusing regime in filamentation

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

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

2014-01-01

286

Transition from linear- to nonlinear-focusing regime in filamentation

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

287

Reconciling Geometric Planners with

Hierarchical Planning People Detection Structure Discovery Collaborative Manipulation Skill Learning #12Reconciling Geometric Planners with Physical Manipulation Siddhartha Srinivasa Senior Research Geometric Planners with Physical Manipulation Siddhartha Srinivasa Senior Research Scientist Intel

North Carolina at Chapel Hill, University of

288

On geometric factors for neutral particle analyzers

NASA Astrophysics Data System (ADS)

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

Stagner, L.; Heidbrink, W. W.

2014-11-01

289

On geometric factors for neutral particle analyzers.

Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories. PMID:25430216

Stagner, L; Heidbrink, W W

2014-11-01

290

Hybrid Matrix Geometric Algebra

\\u000a The structures of matrix algebra and geometric algebra are completely compatible and in many ways complimentary, each having\\u000a their own advantages and disadvantages. We present a detailed study of the hybrid 2 × 2 matrix geometric algebra M(2,IG) with elements in the 8 dimensional geometric algebra IG=IG\\u000a 3 of Euclidean space. The resulting hybrid structure, isomorphic to the geometric algebra

Garret Sobczyk; Gordon Erlebacher

2004-01-01

291

Geometric Systems in Architecture

NSDL National Science Digital Library

Lessons that include deriving formulas for volume by building rectangular prisms, identifying geometric solids by constructing cubes, tetrahedrons, and octahedrons, and identifying geometric patterns found in ceiling and wall tiles. Additional lessons deal with geometric systems manifested in the crystal structure of minerals. Students are introduced to three-dimensional figures in nature, in the classroom, and in architecture.

Decaprio, Sheryl A.

2007-04-09

292

ArithmeticGeometric Progression

VMCAI'05 The ArithmeticÂGeometric Progression Abstract Domain JÃ©rÃ´me Feret Ã?cole Normale SupÃ©rieure; Overview 1. Introduction 2. Case study 3. ArithmeticÂgeometric progressions 4. Benchmarks 5. ConclusionÂgeometric progressions 4. Benchmarks 5. Conclusion JÃ©rÃ´me Feret, LIENS 13 January, 2005 #12; Arithmetic

Feret, JÃ©rÃ´me

293

Nonlinear 3d frame element with multi-axial coupling under consideration of local effects

of nonlinear geometry reduces the lateral load capacity ofNonlinear geometric response Structures subjected to extreme loads,nonlinear geometry effects to be suitable for the simulation of structures under extreme load

Le Corvec, Veronique

2012-01-01

294

Bloch-sphere representation of three-vertex geometric phases

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

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

2011-11-15

295

Optimization of piezoelectric cantilever energy harvesters including non-linear effects

NASA Astrophysics Data System (ADS)

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

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

2014-08-01

296

Geometric Gyrokinetic Theory for Edge Plasma

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

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

2007-01-18

297

Nonlinear space charge wave theory of distortion in a Klystron

We present a new view of nonlinear distortion in a klystron based on an analytically solvable nonlinear Eulerian model. The nonlinear contributions to the analytic solutions for the beam modulations are \\

John G. Wöhlbier; John H. Booske

2005-01-01

298

Beam halo in high-intensity beams

In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which in projection to the 2-D phase spaces results in a 2-component beam consisting of an inner core and a diffuse outer halo. The beam-halo is of concern for a next generation of cw, high-power proton linacs that could be applied to intense neutron generators for nuclear materials processing. The author describes what has been learned about beam halo and the evolution of space-charge dominated beams using numerical simulations of initial laminar beams in uniform linear focusing channels. Initial results are presented from a study of beam entropy for an intense space-charge dominated beam.

Wangler, T.P.

1993-01-01

299

Beam halo in high-intensity beams

In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which in projection to the 2-D phase spaces results in a 2-component beam consisting of an inner core and a diffuse outer halo. The beam-halo is of concern for a next generation of cw, high-power proton linacs that could be applied to intense neutron generators for nuclear materials processing. The author describes what has been learned about beam halo and the evolution of space-charge dominated beams using numerical simulations of initial laminar beams in uniform linear focusing channels. Initial results are presented from a study of beam entropy for an intense space-charge dominated beam.

Wangler, T.P.

1993-06-01

300

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

Yury A. Rossikhin; Marina V. Shitikova

301

NASA Technical Reports Server (NTRS)

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

Gray, Carl E., Jr.

1988-01-01

302

NASA Technical Reports Server (NTRS)

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

Rizzi, Stephen A.; Przekop, Adam

2004-01-01

303

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

304

Geometric Effects in an Elastic Tensegrity Structure

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

I. J. Oppenheim; W. O. Williams

2000-01-01

305

Geometric Algebra for Physicists

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

Chris Doran; Anthony Lasenby

2003-01-01

306

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

307

Localisation of Geometric Anisotropy

The class of 2-D nonseparable geometrically anisotropic localisation operators is defined, containing highly anisotropic nearly unidirectional localisation operator s, as well as isotropic localisation operators. A continuum of anisotropic operators between the extremes of near unidirectionality and isotropy are treated in a single class. The eigensystem of any given operator in this family is determined, thus specifying geometrically anisotropic optimally

Sofia C. Olhede

2008-01-01

308

Hierarchies of Geometric Entanglement

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

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

2007-01-01

309

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

Harrington, J. Patrick

310

NONLINEAR MODEL EVALUATION VIA SYSTEM IDENTIFICATION OF A MOORED STRUCTURAL SYSTEM

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

S. Narayanan; S. C. S. Yim

311

Nonlinear resonances of a single-wall carbon nanotube cantilever

NASA Astrophysics Data System (ADS)

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

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

2015-03-01

312

A Babylonian Geometrical Algebra.

ERIC Educational Resources Information Center

A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)

Bidwell, James K.

1986-01-01

313

AJ Geometric Formulas Calculator

NSDL National Science Digital Library

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

Jimmy Raymond

314

Focusing of intense ion beams from pinched-beam diodes

Geometric focusing of proton and deuteron beams extracted from pinched-beam diodes to current densities above 70 KA\\/sq cm is demonstrated by a variety of experimental techniques. Time-dependent computer simulations of the electron and ion flow show good agreement with experiment.

S. A. Goldstein; G. Cooperstein; Roswell Lee; D. Mosher; S. J. Stephanakis

1978-01-01

315

We describe theoretically the quantum properties of atype-II Optical Parametric Oscillator containing a birefringent plate which induces a linear coupling between the orthogonally polarized signal and idler beams and results in phase locking between these two beams. As in a classical OPO, the signal and idler waves show large quantum correlations which can be measured experimentally due to the phase locking between the two beams. We study the influence of the waveplate on the various criteria characterizing quantum correlations. We show in particular that the quantum correlations can be maximized by using optimized quadratures.

Laurent Longchambon; Julien Laurat; Thomas Coudreau; Claude Fabre

2003-11-19

316

Reliability and failure analyses of composite beams and plates containing stress concentrations

NASA Astrophysics Data System (ADS)

Size effects in brittle composite structures such as beams and plates with and without stress raisers are investigated experimentally and analytically. For stress analysis of isotropic beams under four-point bending and composite plates under in-plane loading, a finite element analysis program F2DELAST based on 2-D elasticity theory was developed and verified. For composite beams under four-point bending, ABAQUS is used. For stress and failure analysis of laminated composite plates under transverse loading, a nonlinear finite element analysis program FNCOMPLT which accounts for the geometrical nonlinearity in von Karman sense and transverse shear deformation was developed. Both the finite element programs written by the author and the ABAQUS were used for stress analysis. For post-processing purposes, PATRAN and I-DEAS are used. Linear and nonlinear stress analyses were performed for the case of composite plates under transverse loading. A methodology for reliability analysis is developed for composite beams and plates with and without stress concentration under various loading conditions and various finite element reliability analysis programs were written. The materials used for the analysis are mainly carbon-carbon composites, however graphite-epoxy composites are also used. The Weibull model was extended to account for the 3-D stress field including interlaminar stresses. The effect of interlaminar stresses on the total reliability is investigated. Various failure theories for composite materials are reviewed.

Yeo, Incheol

317

NASA Astrophysics Data System (ADS)

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

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

2014-07-01

318

Geometric algebra: a computation framework for geometrical applications

Abstract Geometric algebra is a consistent computational,framework,in which to define geometric primitives and their relationships. This algebraic approach contains all geometric operators and permits specification of constructions in a coordinate-free manner. Thus, the ideas of geometric algebra are important for developers of CAD systems. This paper gives an introduction to the elements of geometric algebra, which contains primitives of any

L. Dorst; S. Mann

2001-01-01

319

Geometric algebra: a computational framework

Geometric algebra: a computational framework for geometrical applications (part I: algebra) Leo Dorst and Stephen Mann Abstract Geometric algebra is a consistent computational framework in which of geometric algebra are important for developers of CAD systems. This paper gives an introduction

Waterloo, University of

320

Geometric algebra: a computational framework

Geometric algebra: a computational framework for geometrical applications (part II: applications) Leo Dorst and Stephen Mann Abstract Geometric algebra is a consistent computational framework in which. It shows how using well-chosen geometric algebra models, we can eliminate special cases in incidence

Dorst, Leo

321

Geometric integration by playing with matrices Luigi Brugnano and Felice Iavernaro

driven nonlinear pendulum Chaos 22, 033138 (2012) Small signal stability analysis of photovoltaic array significant attempt of performing geometrical integration can be led back to the early works of G. Dahlquist

Brugnano, Luigi

322

A geometric representation scheme suitable for shape optimization

NASA Technical Reports Server (NTRS)

A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.

Tortorelli, Daniel A.

1990-01-01

323

Nonlinear Optics and Applications

NASA Technical Reports Server (NTRS)

Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)

2007-01-01

324

Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

NASA Technical Reports Server (NTRS)

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

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

2003-01-01

325

NONLINEAR SYSTEM IDENTIFICATION OF A MOORED STRUCTURAL SYSTEM

This paper addresses the practical application of a multiple- input\\/single-output nonlinear system identification technique on ocean structural systems. An ocean structure exhibiting nonlinear behavior due to geometric nonlinearity of mooring line angles and the complexity of hydrodynamic excitations is chosen for this analytical study. Given the input wave characteristics, wave force and the system response, the method identifies the hydrodynamic

S. Narayanan; S. C. S. Yim; P. A. Palo

326

Inflation from geometrical tachyons

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

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

2005-10-15

327

NASA Astrophysics Data System (ADS)

It is well known that solutions to nonlinear hyperbolic wave equations can exhibit ``steepening,'' and can ``break'' in a finite time. Most commonly the physical situations being modeled dictate that shock formation occurs at the breaking point. However, it has long been acknowledged that another interpretation of the breaking event is the formation of ``multi-valued'' solutions [1]. In fact, in electron beam devices Lagrangian methods are commonly used to compute solutions when the electron beam velocity and density becomes multi-valued. Recently an Eulerian technique for computing multi-valued solutions was developed in the context of geometrical optics [2]. In [3] this technique is applied to the Euler-Poisson equations which may be used to model, among other systems, nonlinear electron beam evolution in Klystron amplifiers. In this paper we apply the technique to the Traveling Wave Tube (TWT). The moment formulation used in the technique provides insights into spectral mixing in the electron beam at the onset of TWT saturation and beyond; such insights are not available in a conventional Lagrangian model. We discuss the numerical technique, and the insights it has generated into TWT physics. [1] G.B. Whitham. Linear and Nonlinear Waves, Wiley 1974. [2] S. Jin and X.T. Li. Physica D 182, 46--85 (2003). [3] X.T. Li, J.G. Wöhlbier, et al. Phys. Rev. E 70, 016502 (2004).

Wohlbier, J. G.; Sengele, S.

2004-11-01

328

Lagrange geometric interpolation by rational spatial cubic Bezier curves

, Slovenia b IMFM, Jadranska 19, Ljubljana, Slovenia c IAM, University of Primorska, Muzejski trg 2, Koper is a challenging task since it involves anal- ysis of systems of nonlinear equations. Several results on existence the rational geometric interpolation is a even more challenging topic and even less results are known. A nice

Zagar, Emil

329

A geometric view on early and middle level visual coding

. The assumption is then validated by noting that human observers and cortical neurons are sensitive to parametersA geometric view on early and middle level visual coding Erhardt Barth Institute for Signal://www.isip.mu-luebeck.de Keywords: motion, MT neurons, nonlinear features, curvature tensor Abstract As opposed to dealing

330

Estimation of Geometric Entities and Operators from Uncertain Data

In this text we show how points, point pairs, lines, planes, circles, spheres, and rotation, translation and dilation operators and their uncertainty can be evaluated from uncertain data in a unifled manner using the Geometric Algebra of conformal space. This extends previous work by Forstner et al. (3) from points, lines and planes to non-linear enti- ties and operators, while

Christian Perwass; Christian Gebken; Gerald Sommer

2005-01-01

331

GEOMETRIC NUMERICAL SCHEMES FOR THE KDV EQUATION DENYS DUTYKH

GEOMETRIC NUMERICAL SCHEMES FOR THE KDV EQUATION DENYS DUTYKH , MARX CHHAY, AND FRANCESCO FEDELE-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries (KdV) equation methods for computing the long-time KdV dynamics, and thus more suitable to model complex nonlinear wave

Paris-Sud XI, UniversitÃ© de

332

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

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

Martin Rumpf

2000-01-01

333

Nonlinear optomechanical pressure

NASA Astrophysics Data System (ADS)

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

Conti, Claudio; Boyd, Robert

2014-03-01

334

Aerospace plane guidance using geometric control theory

NASA Technical Reports Server (NTRS)

A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.

Van Buren, Mark A.; Mease, Kenneth D.

1990-01-01

335

NASA Technical Reports Server (NTRS)

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

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

1991-01-01

336

ERIC Educational Resources Information Center

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

Smart, Julie; Marshall, Jeff

2007-01-01

337

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

338

Geometric computing in computer graphics using conformal geometric algebra

Abstract Early in the development,of Computer Graphics it was realized that projective geometry,was well suited for the representation of transformations. Now, it seems that another change of paradigm is lying ahead of us based on Geometric Computing using Conformal Geometric Algebra. Due to its geometric intuitiveness, elegance and simplicity, the underlying Conformal Geometric Algebra appears to be a promising mathematical,tool

Dietmar Hildenbrand

2005-01-01

339

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

NASA Astrophysics Data System (ADS)

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

Dakel, Mzaki; Baguet, Sébastien; Dufour, Régis

2014-05-01

340

System identification-guided basis selection for reduced-order nonlinear response analysis

NASA Astrophysics Data System (ADS)

Reduced-order nonlinear simulation is often times the only computationally efficient means of calculating the extended time response of large and complex structures under severe dynamic loading. This is because the structure may respond in a geometrically nonlinear manner, making the computational expense of direct numerical integration in physical degrees of freedom prohibitive. As for any type of modal reduction scheme, the quality of the reduced-order solution is dictated by the modal basis selection. The techniques for modal basis selection currently employed for nonlinear simulation are ad hoc and are strongly influenced by the analyst's subjective judgment. This work develops a reliable and rigorous procedure through which an efficient modal basis can be chosen. The method employs proper orthogonal decomposition to identify nonlinear system dynamics, and the modal assurance criterion to relate proper orthogonal modes to the normal modes that are eventually used as the basis functions. The method is successfully applied to the analysis of a planar beam and a shallow arch over a wide range of nonlinear dynamic response regimes. The error associated with the reduced-order simulation is quantified and related to the computational cost.

Rizzi, Stephen A.; Przekop, Adam

2008-08-01

341

Nonlinear tension-bending deformation of a shape memory alloy rod

NASA Astrophysics Data System (ADS)

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

Shang, Zejin; Wang, Zhongmin

2012-11-01

342

Nonlinear free vibration of piezoelectric nanobeams incorporating surface effects

NASA Astrophysics Data System (ADS)

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

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

2014-03-01

343

Geometric Algebra: A Computational Framework for Geometrical Applications (Part 1)

Geometric algebra is a consistent computational framework in which to de- fine geometric primitives and their relationships. This algebraic approach con- tains all geometric operators and permits specification of constructions in a totally coordinate-free manner. Since it contains primitives of any dimensionality (rather than just vectors) it has no special cases: all intersections of primitives are com- puted with one

Leo Dorst; Stephen Mann

2002-01-01

344

Nonlinear vibrational microscopy

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

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

2000-01-01

345

Foundations of Geometric Algebra computing

NASA Astrophysics Data System (ADS)

Geometric Algebra has the power to lead easily from the geometric intuition of solving an engineering application to its efficient implementation on current and future computing platforms. It is easy to develop new algorithms in areas such as computer graphics, robotics, computer animation and computer simulation. Owing to its geometric intuitiveness, compactness and simplicity, algorithms based on Geometric Algebra can lead to enhanced quality, a reduction in development time and solutions that are more easily understandable and maintainable. Often, a clear structure and greater elegance result in lower runtime performance. However, based on our computing technology, Geometric Algebra implementations can even be faster and more robust than conventional ones. We present an example on how easy it is to describe algorithms in Geometric Algebra and introduce our technology for the integration of Geometric Algebra into standard programming languages. We really do hope that this technology can support the widespread use of Geometric Algebra Computing technology in many engineering fields.

Hildenbrand, Dietmar

2012-09-01

346

, multi-way transportation, and multi-commodity b-matching: with linear or nonlinear, congestion optimization problems where the feasible solutions are the integer points satisfying a system of linear and geometric methods, we were able to show that Graver bases enable to solve linear and nonlinear integer

Onn, Shmuel

347

NASA Astrophysics Data System (ADS)

A simple and shear-flexible rectangular composite layered plate element and nonlinear finite element analysis procedures are developed in this paper for nonlinear analysis of fiber reinforced plastic (FRP)-reinforced concrete slabs. The composite layered plate element is constructed based on Mindlin-Reissner plate theory and Timoshenko’s composite beam functions, and transverse shear effects and membrane-bending coupling effects are accounted for. Both geometric nonlinearity and material nonlinearity of the materials, which incorporates tension, compression, tension stiffening and cracking of the concrete, are included in the new model. The developed element and the nonlinear finite element analysis procedures are validated by comparing the computed numerical results of numerical examples with those obtained from experimental investigations and from the commercial finite element analysis package ABAQUS. The element is then employed to investigate the nonlinear structural behavior and the cracking progress of a clamped two-way FRP-reinforced concrete slab. The influences of reinforcement with different materials, ratio and layout in tension or compressive regions on structural behavior of the clamped slabs are investigated by parametric studies.

Zhu, Y.; Zhang, Y. X.

2010-08-01

348

Geometric Phases for Coherent States

We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled coherent states, several interesting results followed by considering different cases for the parameters. The effects of entanglement and harmonic potential on the geometric phase are discussed.

Da-Bao Yang; Jing-Ling Chen; Chunfeng Wu; C. H. Oh

2011-10-19

349

The classical geometrization electromagnetism

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

C. A. Duarte

2015-02-11

350

CORRESPONDENCE PROBLEMS IN GEOMETRIC VISION

CORRESPONDENCE PROBLEMS IN GEOMETRIC VISION OLOF ENQVIST Faculty of Engineering CentreTryck, Lund 2009 #12;Preface This thesis concerns optimal methods for geometric vision problems. Two important and branch and bound to handle the correspon- dence problems arising in geometric vision. The thesis consists

Lunds Universitet

351

Tevatron beam-beam simulations at injection energy

Major issues at Tevatron injection are the effects of 72 long-range beam-beam interactions together with the machine nonlinearity on protons and anti-protons. We look at particle tracking calculations of Dynamic Aperture (DA) under present machine conditions. Comparisons of calculations with observations and experiments are also presented in this report.

Meiqin Xiao; Bela Erdelyi; Tanaji Sen

2003-05-28

352

GEOMETRIC STIFFNESS AND STABILITY OF RIGID BODY MODES

The objective of this study is to examine the effect of geometric stiffness forces on the stability of elastic and rigid body modes. A simple rotating beam model is used to demonstrate the effect of axial forces and dynamic coupling between the modes of displacement on the rigid body motion. The effect of longitudinal deformation due to bending is systematically

H. El-Absy; A. A. Shabana

1997-01-01

353

Geometrical Wake of a Smooth Flat Collimator

A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems - a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator.

Stupakov, G.V.; /SLAC

2011-09-09

354

Korteweg deVries equation for longitudinal disturbances in coasting charged-particle beams

NASA Astrophysics Data System (ADS)

This paper employs a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius rw. The average axial electric field is expressed as

Davidson, Ronald C.

2004-05-01

355

Geometric phase gate on an optical transition for ion trap quantum computation

We propose a geometric phase gate of two ion qubits that are encoded in two levels linked by an optical dipole-forbidden transition. Compared to hyperfine geometric phase gates mediated by electric dipole transitions, the gate has many interesting properties, such as very low spontaneous emission rates, applicability to magnetic field insensitive states, and use of a co-propagating laser beam geometry.

K. Kim; C. F. Roos; L. Aolita; H. Häffner; V. Nebendahl; R. Blatt

2008-01-01

356

NASA Astrophysics Data System (ADS)

We develop an explicit solution of problem describing collinear four-waves mixing in medium with cubic nonlinear response. This solution is carried out for set of Schrödinger equations using plane wave approximation for the case of phase matching for interacting waves. This solution allows to do full analysis of four-wave interaction modes in dependence of the problem parameters. We have shown, in particular, an existence of bistable mode for energy conversion from pump waves to signal wave under certain conditions. In general case, there are greater than 10 various modes of four-wave interaction. Knowledge about these modes is very important for spectroscopic experiment results understanding using four-waves mixing because its result depends on them in strong way. Analytical solutions and derived modes can explain complicated regime of four-wave interaction which may be appeared at high intensity of interacting waves.

Trofimov, Vyacheslav A.; Kuchik, Igor E.; Levitskiy, Nikita V.

2014-05-01

357

This paper summarizes the presentations and discussions of the Beam-Beam'03 workshop, held in Montauk, Long Island, from May 19 to 23, 2003. Presentations and discussions focused on halo generation from beam-beam interactions; beam-beam limits, especially coherent limits and their effects on existing and future hadron colliders; beam-beam compensation techniques, particularly for long-range interactions; and beam-beam study tools in theory, simulation, and experiment.

FISCHER,W.SEN,T.

2003-05-19

358

Geometric phase in Bohmian mechanics

Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2{pi}. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.

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

2010-10-15

359

Geometric numerical schemes for the KdV equation

Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries (KdV) equation. In this work, we show that geometrical schemes are as much robust and accurate as Fourier-type pseudo-spectral methods for computing the long-time KdV dynamics, and thus more suitable to model complex nonlinear wave phenomena.

Dutykh, Denys; Fedele, Francesco

2012-01-01

360

Filamentation nonlinear optics

NASA Astrophysics Data System (ADS)

A filamenting femtosecond laser pulse self-stabilizes the intensity fluctuation inside the filament core due to intensity clamping and generates an excellent spatial beam quality inside the core due to self-spatial filtering. The high quality of the core can be sampled by nonlinear processes. A few experimental examples are shown: self-phase modulation, four-wave mixing, third-harmonic generation and waveguide writing in glass.

Chin, S. L.; Théberge, F.; Liu, W.

2007-02-01

361

Representing geometrical knowledge.

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

Anderson, J A

1997-01-01

362

High current beam transport with multiple beam arrays

Highlights of recent experimental and theoretical research progress on the high current beam transport of single and multiple beams by the Heavy Ion Fusion Accelerator Research (HIFAR) group at the Lawrence Berkeley Laboratory (LBL) are presented. In the single beam transport experiment (SBTE), stability boundaries and the emittance growth of a space charge dominated beam in a long quadrupole transport channel were measured and compared with theory and computer simulations. Also, a multiple beam ion induction linac (MBE-4) is being constructed at LBL which will permit study of multiple beam transport arrays, and acceleration and bunch length compression of individually focused beamlets. Various design considerations of MBE-4 regarding scaling laws, nonlinear effects, misalignments, and transverse and longitudinal space charge effects are summarized. Some aspects of longitudinal beam dynamics including schemes to generate the accelerating voltage waveforms and to amplify beam current are also discussed.

Kim, C.H.

1985-05-01

363

NASA Astrophysics Data System (ADS)

Integer sequences where each element is determined by a previous randomly chosen element are investigated analytically. In particular, the random geometric series xn = 2xp with 0 les p les n - 1 is studied. At large n, the moments grow algebraically, langxsnrang ~ nbgr(s) with bgr(s) = 2s - 1, while the typical behaviour is xn ~ nln 2. The probability distribution is obtained explicitly in terms of the Stirling numbers of the first kind and it approaches a log-normal distribution asymptotically.

Ben-Naim, E.; Krapivsky, P. L.

2004-06-01

364

NASA Astrophysics Data System (ADS)

A general lumped mass finite element structural dynamics model was developed for a three-dimensional elastic beam with an arbitrary and large base movement. The six degrees of freedom of the base movement can incorporate either a prescribed arbitrary motion of the base or as coupling of the beam with other substructures. The beam can be pretwisted and have a mass center offset from the elasticity center in order to model some specific structures such as helicopter blades. The equations of motion were derived using the virtual work principle. Large deflections and small strains of the beam were assumed so that the geometrical nonlinearities are included. The centrifugal stiffness terms caused by the large base movement were specifically considered so that the dynamics model is applicable for both nonlinear and linear analyses. This dynamics model is expected to provide a general and fundamental element for rotating beams and beam-like multibody structures. Numerical examples are presented to validate the model and demonstrate its great modelling flexibility in a companion paper.

Du, H.; Hitchings, D.; Davies, G. A. O.

1992-10-01

365

Experimental and numerical characterization of the structural dynamics of flapping beams

NASA Astrophysics Data System (ADS)

The nonlinear structural dynamics of a slender beam in flapping motion is examined both experimentally and computationally. In the experiments the periodic flapping motion is imposed on the clamped edge of the cantilever beam using a 4-bar crank-and-rocker mechanism. Aluminum beams with nominal dimensions of 150 mm×25 mm×0.4 mm are tested in air over a range of flapping frequencies up to 1.3 times the linear first modal frequency at two different flapping amplitudes, 15° and 30°. The response of the beam is characterized experimentally through bending strain and tip displacement data obtained from foil strain gage and high-speed camera, respectively. It was determined that for the particular combination of beam specimen (dimensions, material properties) and forcing parameters investigated, all experimental responses were periodic. The frequency response curves based upon the experimental bending strain data reveal a secondary superharmonic peak in addition to the primary resonance peak. As the flapping frequency is increased, the response of the beam is observed to change from symmetric (with respect to equilibrium position) periodic vibrations with a period equal to the flapping period to asymmetric periodic vibrations with higher harmonic content featuring local oscillations in the time histories. Experimental tip displacement results show that the beam spends more time during stroke reversals when the flapping frequency is near primary and secondary resonance regions. In addition to experiment, numerical simulations are performed using two-node, isoparametric degenerate-continuum based geometrically nonlinear beam elements. The HHT-? version of the Newmark finite difference scheme is used to discretize the problem in time and a linear viscous damping model is assumed. Overall the numerical simulations agree well with the experiments and capture most of the nonlinear dynamical features of the beam response. It is, however, found that in resonance regions the simulation overpredicts response magnitudes, possibly due to the use of the linear damping model and linear elastic constitutive model. Additional numerical simulations of the beam tip response reveal dynamics which include periodic, asymmetric periodic, quasi-periodic and aperiodic motions.

Ozcelik, Orhan; Attar, Peter J.; Altan, M. Cengiz; Johnston, Jordan W.

2013-10-01

366

MODAL ANALYSIS OF A CRACKED BEAM

This paper addresses the problem of vibrations of a cracked beam. In general, the motion of such a beam can be very complex. This phenomenon can be attributed to the presence of the non-linearity due to the opening and closing of cracks. The focus of this paper is the modal analysis of a cantilever beam with a transverse edge crack.

M. Chati; R. Rand; S. Mukherjee

1997-01-01

367

The progress of non-linear FE-methods allows it nowadays to simulate the load-bearing behaviour of steel shells taking geometric and material nonlinearities and imperfections into account. In this paper it is investigated for the basic buckling case of uniform external pressure, which equivalent geometric imperfections have to be applied in the numerical analysis (GMNIA) to achieve the experimentally determined buckling resistances.

Werner Schneider; Andreas Brede

2005-01-01

368

Generalized nonlinear models of suspension bridges

NASA Astrophysics Data System (ADS)

This paper generalizes some results established in [J. Malik, Nonlinear models of suspension bridges, J. Math. Anal. Appl., in press]. The geometric nonlinearity connected with the torsion of a road bed is included in the generalized model. The basic variational equations are derived from the principle of minimum energy. The existence of a solution to the generalized problem is proved. The existence is based on the Brouwer fixed-point theorem.

Malik, Josef

2006-12-01

369

Engineering Graphics in Geometric Algebra

NASA Astrophysics Data System (ADS)

We illustrate the suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications. A number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics such as vector algebra and vector fields, quaternions, kinematics and projective geometry, and it easily deals with geometric objects, operations, and transformations. Not only are these properties important for computational engineering, but also for the computational point-of-view they provide. We also include the potential of geometric algebra for optimizations and highly efficient implementations.

Rockwood, Alyn; Hildenbrand, Dietmar

370

Manifestation of the geometric phase in neutron spin-echo experiments

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

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

2010-07-15

371

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

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

Michela Ponticorvo; Orazio Miglino

2010-01-01

372

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

Goldberg, P.W.

1993-04-01

373

Geometric algebra: a computational framework for geometrical applications. 2

Every vector space with an inner product has a geometric algebra, whether or not you choose to use it. This article shows how to call on this structure to define common geometrical constructs, ensuring a consistent computational framework. The goal is to show you that this can be done and that it is compact, directly computational, and transcends the dimensionality

Stephen Mann; Leo Dorst

2002-01-01

374

Nonlinear finite-difference time-domain modeling of linear and nonlinear corrugated waveguides

A multidimensional, nonlinear finite-difference time-domain (NL-FDTD) simulator, which is constructed from a self-consistent solution of the full-wave vector Maxwell equations and dispersive (Lorentz), nonlinear (finite-time-response Raman and instantaneous Kerr) materials models, is used to study finite-length, corrugated, optical waveguide output couplers and beam steerers. Multiple-cycle, ultrashort-optical-pulse interactions with these corrugated, nonlinear, dispersive waveguides are characterized. An all-optical nonlinear beam-steering device is designed, and its output-coupling performance is characterized with this NL-FDTD simulator.

Ziolkowski, R.W.; Judkins, J.B. (Electromagnetics Laboratory, Department of Electrical and Computer Engineering, The University of Arizona, Tucson, Arizona 85721 (United States))

1994-09-01

375

Solitary waves in particle beams

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

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

1996-07-01

376

Nonlinear dynamics experiments

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

Fischer, W.

2011-01-01

377

Soliton mode locking by nonlinear Faraday rotation

NASA Astrophysics Data System (ADS)

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

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

1996-11-01

378

Auto calibration of a cone-beam-CT

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

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

2012-10-15

379

Stochastic nonlinear stabilization

NASA Astrophysics Data System (ADS)

The fact that many physical systems are nonlinear and subject to disturbances motivates the study of stochastic nonlinear control, with stabilization as the most basic question. Because of a fundamental technical difficulty in the Lyapunov analysis, research attention since the 1960's has been moved from stabilization to optimization. The development of differential geometric nonlinear control theory in the 1980's and a recent discovery of a simple constructive formula for Lyapunov stabilization for deterministic nonlinear systems has inspired a large amount of research in adaptive, robust, and optimal nonlinear control. These achievements naturally led to re-examining the stochastic nonlinear stabilization problem, which is the topic of this dissertation. In this dissertation, we first introduce a new set of stability definitions in class K formalism, in order to connect the results in stochastic nonlinear control with the results in modern deterministic nonlinear control literature, and to introduce the new concept of Noise-to-State Lyapunov function. Then we rigorously prove a stochastic version of the convergence result of LaSalle and Yoshizawa. When we consider systems with unknown noise covariance, we extend Sontag's concept of input-to-state stability (ISS) to stochastic systems by introducing the concept Noise-to-State Lyapunov functions (ns-lf). For systems with a control input as well as stochastic noise (affine in both), we extend the ISS-control Lyapunov functions to stochastic systems, introduce ns-control Lyapunov functions (ns-clf), and prove that there exists a feedback law continuous away from the origin that guarantees the controlled system has an ns-lf if there exists an ns-clf. After addressing the stabilization issue, we pursue inverse optimality since direct optimal control problem involves a formidable computational task---solving HJB PDE. We show that if we know an ns-clf, then the inverse optimal control problem is solvable for general stochastic systems affine in control. Based on these theorems, we proceed with controller design for the stochastic strict-feedback systems---both state-feedback and output-feedback. Using back-stepping design method, we design closed form stabilizing and inverse optimal controllers when the noise has unity intensity. For the system with unknown covariance noise, we develop adaptive stabilization and disturbance attenuation schemes without a priori knowledge of a bound on the covariance.

Deng, Hua

380

Vibrational Control of a Nonlinear Elastic Panel

NASA Technical Reports Server (NTRS)

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

Chow, P. L.; Maestrello, L.

1998-01-01

381

Acceleration control of Airy beams with optically induced photonic lattices

NASA Astrophysics Data System (ADS)

We analyze how an optically induced photonic lattice affects and modifies the acceleration of Airy beams. Various conditions for the propagation and existence of Airy beams are considered in both linear and nonlinear regimes. We investigate how the strength of a medium's nonlinearity and the lattice intensity influence beam diffraction as well as reduction of beam acceleration. It is shown that the transverse acceleration of Airy beams, when propagating in a photonic lattice, can be reduced to the point of creating a beam similar to discrete solitons. Acceleration control of Airy beams near lattice boundaries is also investigated. We observe a novel type of Airy surface mode, localized in the lattice corner.

Piper, Aleksandra; Timotijevi?, Dejan V.; Jovi?, Dragana M.

2013-11-01

382

Nonlinear analysis of smart composite plate and shell structures

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

Lee, Seung Joon

2005-08-29

383

Phase-Space Nonlinear Control Toolbox: The Maglev Experience

We describe the Phase-Space Nonlinear Control Toolbox, a suite of computational tools for synthesizingand evaluating control laws for a broad class of nonlinear dynamical systems. The Toolboxcomprises computational algorithms for identifying optimal control reference trajectories in the phasespace of dynamical systems and experimental methods for evaluating performance of the control laws.These algorithms combine knowledge of the geometric theory of modern

Zhao Feng; Shiou C. Loh; Jeff A. May

1997-01-01

384

Error detection and control for nonlinear shell analysis

NASA Technical Reports Server (NTRS)

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

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

1990-01-01

385

Chiral symmetry breaking as a geometrical process

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

Bittencourt, Eduardo; Novello, Mário

2014-01-01

386

Chiral symmetry breaking as a geometrical process

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

Eduardo Bittencourt; Sofiane Faci; Mário Novello

2014-06-08

387

Geometric Algebra for Subspace Operations

The set theory relations ?, \\\\,?,n, and ? have corollaries in subspace relations. Geometric algebra is introduced as a useful framework to explore these subspace operations. The relations ?, \\\\, and ? are easily subsumed by geometric algebra for Euclidean metrics. A short computation shows that the meet (n) and join (?) are resolved in a projection operator representation with

T. A. Bouma; L. Dorst; H. G. J. Pijls

2002-01-01

388

Thematic Mapper geometric correction processing

NASA Technical Reports Server (NTRS)

The Thematic Mapper Image Processing System is described from the point of view of geometric correction. The system performance requirements are discussed, and the Landsat-D flight segment is described. The ground processing and overall geometric system performance is addressed. Those aspects of the Thematic Mapper Image Processing System that differ significantly from those of the MSS System are emphasized.

Beyer, E. P.

1984-01-01

389

Circle actions in geometric quantisation

NASA Astrophysics Data System (ADS)

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

Solha, Romero

2015-01-01

390

Negative radiation forces act opposite to the direction of propagation, or net momentum, of a beam but have previously been challenging to definitively demonstrate. We report an experimental acoustic tractor beam generated by an ultrasonic array operating on macroscopic targets (>1 cm) to demonstrate the negative radiation forces and to map out regimes over which they dominate, which we compare to simulations. The result and the geometrically simple configuration show that the effect is due to nonconservative forces, produced by redirection of a momentum flux from the angled sides of a target and not by conservative forces from a potential energy gradient. Use of a simple acoustic setup provides an easily understood illustration of the negative radiation pressure concept for tractor beams and demonstrates continuous attraction towards the source, against a net momentum flux in the system. PMID:24836252

Démoré, Christine E M; Dahl, Patrick M; Yang, Zhengyi; Glynne-Jones, Peter; Melzer, Andreas; Cochran, Sandy; MacDonald, Michael P; Spalding, Gabriel C

2014-05-01

391

NASA Astrophysics Data System (ADS)

Negative radiation forces act opposite to the direction of propagation, or net momentum, of a beam but have previously been challenging to definitively demonstrate. We report an experimental acoustic tractor beam generated by an ultrasonic array operating on macroscopic targets (>1 cm) to demonstrate the negative radiation forces and to map out regimes over which they dominate, which we compare to simulations. The result and the geometrically simple configuration show that the effect is due to nonconservative forces, produced by redirection of a momentum flux from the angled sides of a target and not by conservative forces from a potential energy gradient. Use of a simple acoustic setup provides an easily understood illustration of the negative radiation pressure concept for tractor beams and demonstrates continuous attraction towards the source, against a net momentum flux in the system.

Démoré, Christine E. M.; Dahl, Patrick M.; Yang, Zhengyi; Glynne-Jones, Peter; Melzer, Andreas; Cochran, Sandy; MacDonald, Michael P.; Spalding, Gabriel C.

2014-05-01

392

Linear and Nonlinear Subdivision Schemes in Geometric Modeling

schemes. Important examples such as the B-spline schemes and the interpolatory 4-point scheme by repeated refinements. While these methods are simple to implement, their analysis is rather complicated number of mask coefficients. Therefore, such schemes are easy to implement, but their analysis is rather

Dyn, Nira

393

Geometrical non-linear analysis of tensegrity systems

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

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

1999-01-01

394

Coherence delay augmented laser beam homogenizer

The geometrical restrictions on a laser beam homogenizer are relaxed by ug a coherence delay line to separate a coherent input beam into several components each having a path length difference equal to a multiple of the coherence length with respect to the other components. The components recombine incoherently at the output of the homogenizer, and the resultant beam has a more uniform spatial intensity suitable for microlithography and laser pantogography. Also disclosed is a variable aperture homogenizer, and a liquid filled homogenizer.

Rasmussen, P.; Bernhardt, A.

1993-06-29

395

Coherence delay augmented laser beam homogenizer

The geometrical restrictions on a laser beam homogenizer are relaxed by ug a coherence delay line to separate a coherent input beam into several components each having a path length difference equal to a multiple of the coherence length with respect to the other components. The components recombine incoherently at the output of the homogenizer, and the resultant beam has a more uniform spatial intensity suitable for microlithography and laser pantogography. Also disclosed is a variable aperture homogenizer, and a liquid filled homogenizer.

Rasmussen, Paul (Livermore, CA); Bernhardt, Anthony (Berkeley, CA)

1993-01-01

396

Geometric algebra, qubits, geometric evolution, and all that

The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that case. Generalization of formal complex plane to an an arbitrary plane in three dimensions and of usual Hopf fibration to the map generated by an arbitrary unit value element of even sub-algebra of the three-dimensional Geometric Algebra are resulting in more profound description of qubits compared to quantum mechanical Hilbert space formalism.

Soiguine, Alexander M

2015-01-01

397

Analysis and modeling of a stripline beam kicker and septum

A fast stripline beam kicker and septum are used to dynamically switch a high current electron beam between two beamlines. The transport of the beam through these structures is determined by the quality of the applied electromagnetic fields as well as temporal effects due to the wakefields produced by the beam. In addition, nonlinear forces in the structure will lead

G J Caporaso; Y J Chen; B R Poole; L F Wang

1998-01-01

398

Controlling Second Harmonic Efficiency of Laser Beam Interactions

NASA Technical Reports Server (NTRS)

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

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

2011-01-01

399

Stochastic pump effect and geometric phases in dissipative and stochastic systems

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

Sinitsyn, Nikolai [Los Alamos National Laboratory

2008-01-01

400

Twisted Gaussian Schell-model beams

The authors introduce a new class of partially coherent axially symmetric Gaussian Schell-model (GSM) beams incorporating a new twist phase quadratic in configuration variables. This phase twists the beam about its axis during propagation and is shown to be bounded in strength because of the positive semidefiniteness of the cross-spectral density. Propagation characteristics and invariants for such beams are derived and interpreted, and two different geometric representations are developed. Direct effects of the twist phase on free propagation as well as in parabolic index fibers are demonstrated. Production of such twisted GSM beams, starting with Li-Wolf anisotropic GSM beams, is described. 34 refs., 3 figs.

Simon, R. (Inst. of Mathematical Sciences, Madras (India)); Mukunda, N. (Indian Inst. of Science, Bangalore (India) Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore (India))

1993-01-01

401

Pressure control of a two-stage turbocharged diesel engine using a novel nonlinear IMC approach

This paper deals with nonlinear multivariable output feedback control of a two-stage turbocharged diesel engine. The feedback structure of internal model control (IMC) is used in combination with a nonlinear feedforward controller based on geometric nonlinear control design methods. Input saturations as well as measured disturbances are taken into account and a severe rank deficiency is handled. This novel control

Dieter Schwarzmann; Rainer Nitsche; Jan Lunze; Andreas Schanz

2006-01-01

402

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

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

Balsa Terzic, Yuhong Zhang

2010-05-01

403

Simulation of wavefront reconstruction in beam reshaping system for rectangular laser beam

NASA Astrophysics Data System (ADS)

A new method to calculating the wavefront of slap laser is studied in this paper. The method is based on the ray trace theory of geometrical optics. By using the Zemax simulation software and Matlab calculation software, the wavefront of rectangular beam in beam reshaping system is reconstructed. Firstly, with the x- and y-slope measurement of reshaping beam the direction cosine of wavefront can be calculated. Then, the inverse beam path of beam reshaping system is built by using Zemax simulation software and the direction cosine of rectangular beam can be given, too. Finally, Southwell zonal model is used to reconstruct the wavefront of rectangular beam in computer simulation. Once the wavefront is received, the aberration of laser can be eliminated by using the proper configuration of beam reshaping system. It is shown that this method to reconstruct the wavefront of rectangular beam can evidently reduce the negative influence of additional aberration induced by beam reshaping system.

Zhou, Qiong; Liu, Wenguang; Jiang, Zongfu

2014-05-01

404

Geometrically frustrated magnets Arnab Sen, TIFR

Geometrically frustrated magnets Arnab Sen, TIFR Theoretical Physics Colloquium Collaborators: K and A. Vishwanath, PRL 100, 097202 (2008). July 7, 2009 Arnab Sen, TIFR Geometrically frustrated magnets (virtual hoppings). Arnab Sen, TIFR Geometrically frustrated magnets #12;Unfrustrated magnets Usually

405

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

NASA Astrophysics Data System (ADS)

Modal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis (EMA) methodology of nonlinear mechanical structures. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes (LNMs). A nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single NNM during the experiments. With the help of time-frequency analysis, the energy dependence of NNM modal curves and their frequencies of oscillation are then extracted from the time series. The proposed methodology is demonstrated using two numerical benchmarks, a two-degree-of-freedom system and a planar cantilever beam with a cubic spring at its free end.

Peeters, M.; Kerschen, G.; Golinval, J. C.

2011-01-01

406

Repeating Decimals and Geometric Series

NSDL National Science Digital Library

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

2011-01-01

407

Antenna with Dielectric Having Geometric Patterns

NASA Technical Reports Server (NTRS)

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

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

2013-01-01

408

NSDL National Science Digital Library

Students learn about stress and strain by designing and building beams using polymer clay. They compete to find the best beam strength to beam weight ratio, and learn about the trade-offs engineers make when designing a structure.

Integrated Teaching And Learning Program

409

Generalized inverses of nonlinear mappings and the nonlinear geodetic datum problem

. \\u000a Motivated by the existing theory of the geometric characteristics of linear generalized inverses of linear mappings, an attempt\\u000a is made to establish a corresponding mathematical theory for nonlinear generalized inverses of nonlinear mappings in finite-\\u000a dimensional spaces. The theory relies on the concept of fiberings consisting of disjoint manifolds (fibers) in which the domain\\u000a and range spaces of the

A. Dermanis

1998-01-01

410

Optimal spatiotemporal reduced order modeling for nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

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

LaBryer, Allen

411

Original and diffracted transition radiation for diagnostics of relativistic electron beams

NASA Astrophysics Data System (ADS)

The effect of finite geometrical size and angular divergence of an electron beam on original Resonance X-ray Transition Radiation (RTR) and Diffracted RTR (DTR) has been calculated for 900 MeV electron beam. It is shown that the spectral-angular distributions of RTR and DTR are very sensitive to the geometrical and angular parameters of the electron beam and that it could be used for fine diagnostic of relativistic electron or other charged particle beams.

Kaplin, V. V.; Uglov, S. R.

1998-10-01

412

Evolution of an Airy beam in a saturated medium

NASA Astrophysics Data System (ADS)

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

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

2014-11-01

413

Hidden symmetry and nonlinear paraxial atom optics

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

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

2009-12-15

414

NASA Technical Reports Server (NTRS)

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

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

2004-01-01

415

Guitars, Violins, and Geometric Sequences

ERIC Educational Resources Information Center

This article describes middle school mathematics activities that relate measurement, ratios, and geometric sequences to finger positions or the placement of frets on stringed musical instruments. (Contains 2 figures and 2 tables.)

Barger, Rita; Haehl, Martha

2007-01-01

416

Geometric algorithms for reconfigurable structures

In this thesis, we study three problems related to geometric algorithms of reconfigurable structures. In the first problem, strip folding, we present two universal hinge patterns for a strip of material that enable the ...

Benbernou, Nadia M

2011-01-01

417

Current Concept of Geometrical Accuracy

NASA Astrophysics Data System (ADS)

Within the solving VEGA 1/0615/12 research project "Influence of 5-axis grinding parameters on the shank cutte?s geometric accuracy", the research team will measure and evaluate geometrical accuracy of the produced parts. They will use the contemporary measurement technology (for example the optical 3D scanners). During the past few years, significant changes have occurred in the field of geometrical accuracy. The objective of this contribution is to analyse the current standards in the field of geometric tolerance. It is necessary to bring an overview of the basic concepts and definitions in the field. It will prevent the use of outdated and invalidated terms and definitions in the field. The knowledge presented in the contribution will provide the new perspective of the measurement that will be evaluated according to the current standards.

Görög, Augustín; Görögová, Ingrid

2014-06-01

418

Algorithms of NCG geometrical module

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

Gurevich, M. I.; Pryanichnikov, A. V., E-mail: prianik@adis.vver.kiae.ru [National Research Centre Kurchatov Institute (Russian Federation)

2012-12-15

419

Geometric Algebra for Subspace Operations

The set theory relations \\\\in, \\\\backslash, \\\\Delta, \\\\cap, and \\\\cup have\\u000acorollaries in subspace relations. Geometric Algebra is introduced as the ideal\\u000aframework to explore these subspace operations. The relations \\\\in, \\\\backslash,\\u000aand \\\\Delta are easily subsumed by Geometric Algebra for Euclidean metrics. A\\u000ashort computation shows that the meet (\\\\cap) and join (\\\\cup) are resolved in a\\u000aprojection operator

T. A. Bouma; L. Dorst; H. G. J. Pijls

2001-01-01

420

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

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

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

2014-03-01

421

Beam hysteresis via reorientational self-focusing.

We theoretically investigate light self-trapping in nonlinear dielectrics with a reorientational response subject to threshold, specifically nematic liquid crystals. Beyond a finite excitation, two solitary waves exist for any given power, with an hysteretic dynamics due to feedback between beam size, self-focusing and the nonlinear threshold. Soliton stability is discussed on the basis of the system free energy. PMID:25361096

Alberucci, Alessandro; Piccardi, Armando; Kravets, Nina; Assanto, Gaetano

2014-10-15

422

Jacobi equations and particle accelerator beam dynamics

A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi equation of an affine averaged Lorentz connection. We introduce a specific notion reference trajectory as integral curves of the main velocity vector field. A perturbation caused by the statistical nature of the bunch of particles is considered.

Ricardo Gallego Torrome

2012-03-27

423

Nonlinear bend stiffener analysis using a simple formulation and finite element method

NASA Astrophysics Data System (ADS)

Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risers against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies, the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.

Tong, Dong Jin; Low, Ying Min; Sheehan, John M.

2011-12-01

424

Multiscale geometric modeling of macromolecules I: Cartesian representation.

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

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

2014-01-01

425

Multiscale geometric modeling of macromolecules I: Cartesian representation

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

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

2014-01-15

426

Multiscale geometric modeling of macromolecules I: Cartesian representation

NASA Astrophysics Data System (ADS)

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

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

2014-01-01

427

Geometric algebra, spacetime physics and gravitation

Geometric algebra, spacetime physics and gravitation By S. F. GUL L, A. N. LASENBY AND C. J. L Clifford's `geometric algebra' is presented as the natural language for expressing geometrical ideas are discussed. 1. Introduction For some time we have been convinced that geometric algebra is the best available

Cambridge, University of

428

Geometric Context from a Single Image

Many computer vision algorithms limit their performance by ignoring the underlying 3D geometric structure in the image. We show that we can estimate the coarse geometric properties of a scene by learning appearance-based mod- els of geometric classes, even in cluttered natural scenes. Geometric classes describe the 3D orientation of an image region with respect to the camera. We provide

Derek Hoiem; Alexei A. Efros; Martial Hebert

2005-01-01

429

Optimization of beam configuration in laser fusion based on the laser beam pattern

A simple method based on the laser beam pattern is proposed and numerically demonstrated to optimize a beam configuration for direct drive laser fusion. In this method, both the geometrical factor G{sub l} and the single beam factor B{sub l} are considered. By diminishing the product of B{sub l}·G{sub l}, the irradiation nonuniformity can be decreased to the order of 10{sup ?5}. This optimization method can be applied on the design of irradiation systems for an arbitrary number of beams and any axially symmetric beam patterns.

Xu, Teng; Xu, Lixin; Wang, Anting; Gu, Chun; Wang, Shengbo; Liu, Jing; Wei, Ankun [Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China)] [Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China)

2013-12-15

430

Chaotic dynamics of flexible Euler-Bernoulli beams

NASA Astrophysics Data System (ADS)

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c2) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q0 and frequency ?p of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.

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

2013-12-01

431

Chaotic dynamics of flexible Euler-Bernoulli beams.

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c(2)) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q(0) and frequency ?(p) of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics. PMID:24387569

Awrejcewicz, J; Krysko, A V; Kutepov, I E; Zagniboroda, N A; Dobriyan, V; Krysko, V A

2013-12-01

432

Chaotic dynamics of flexible Euler-Bernoulli beams

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ?{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl [Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland and Department of Vehicles, Warsaw University of Technology, 84 Narbutta St., 02-524 Warsaw (Poland); Krysko, A. V., E-mail: anton.krysko@gmail.com [Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation); Kutepov, I. E., E-mail: iekutepov@gmail.com; Zagniboroda, N. A., E-mail: tssrat@mail.ru; Dobriyan, V., E-mail: Dobriy88@yandex.ru; Krysko, V. A., E-mail: tak@san.ru [Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation)

2013-12-15

433

Holographic generation of non-diffractive beams

NASA Astrophysics Data System (ADS)

An Airy beam is a non-diffractive wave which propagates along a ballistic trajectory without any external force. Although it is impossible to implement ideal Airy beams because they carry infinite power, so-called finite Airy beams can be achieved by tailoring infinite side lobes with an aperture function and they have similar propagating characteristics with those of ideal Airy beams. The finite Airy beam can be optically generated by several ways: the optical Fourier transform system with imposing cubic phase to a broad Gaussian beam, nonlinear generation of Airy beams, curved plasma channel generation, and electron beam generation. In this presentation, a holographic generation of the finite Airy beams will be discussed. The finite Airy beams can be generated in virtue of holographic technique by `reading' a hologram which is recorded by the interference between a finite Airy beam generated by the optical Fourier transform and a reference plane wave. Moreover, this method can exploit the unique features of holography itself such as successful reconstruction with the imperfect incidence of reference beam, reconstruction of phase-conjugated signal beam, and multiplexing, which can shed more light on the characteristics of finite Airy beams. This method has an advantage in that once holograms are recorded in the photopolymer, a bulky optics such as the SLM and lenses are not necessary to generate Airy beams. In addition, multiple Airy beams can be stored and reconstructed simultaneously or individually.

Lee, Byoungho; Choi, Dawoon; Hong, Keehoon; Lee, Kyookeun; Kim, Kyoung-Youm

2014-11-01

434

Nonlinear Mode-Coupling in Nanomechanical Systems

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

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

2013-01-01

435

Rapid assessment of nonlinear optical propagation effects in dielectrics.

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process. PMID:25564243

Hoyo, J Del; de la Cruz, A Ruiz; Grace, E; Ferrer, A; Siegel, J; Pasquazi, A; Assanto, G; Solis, J

2015-01-01

436

Rapid assessment of nonlinear optical propagation effects in dielectrics

NASA Astrophysics Data System (ADS)

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

437

Simultaneous Spatial and Temporal Focusing in Nonlinear Microscopy.

Simultaneous spatial and temporal focusing (SSTF), when combined with nonlinear microscopy, can improve the axial excitation confinement of wide-field and line-scanning imaging. Because two-photon excited fluorescence depends inversely on the pulse width of the excitation beam, SSTF decreases the background excitation of the sample outside of the focal volume by broadening the pulse width everywhere but at the geometric focus of the objective lens. This review theoretically describes the beam propagation within the sample using Fresnel diffraction in the frequency domain, deriving an analytical expression for the pulse evolution. SSTF can scan the temporal focal plane axially by adjusting the GVD in the excitation beam path. We theoretically define the axial confinement for line-scanning SSTF imaging using a time-domain understanding and conclude that line-scanning SSTF is similar to the temporally-decorrelated multifocal multiphoton imaging technique. Recent experiments on the temporal focusing effect and its axial confinement, as well as the axial scanning of the temporal focus by tuning the GVD, are presented. We further discuss this technique for axial-scanning multiphoton fluorescence fiber probes without any moving parts at the distal end. The temporal focusing effect in SSTF essentially replaces the focusing of one spatial dimension in conventional wide-field and line-scanning imaging. Although the best axial confinement achieved by SSTF cannot surpass that of a regular point-scanning system, this trade-off between spatial and temporal focusing can provide significant advantages in applications such as high-speed imaging and remote axial scanning in an endoscopic fiber probe. PMID:18496597

Durst, M E; Zhu, G; Xu, C

2008-04-01

438

NASA Astrophysics Data System (ADS)

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

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

2012-12-01

439

A very general beam solution of the paraxial wave equation in circular cylindrical coordinates is presented. We call such a field a circular beam (CiB). The complex amplitude of the CiB is described by either the Whittaker functions or the confluent hypergeometric functions and is characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the CiB are the standard, elegant, and generalized Laguerre-Gauss beams; Bessel-Gauss beams; hypergeometric beams; hypergeometric-Gaussian beams; fractional-order elegant Laguerre-Gauss beams; quadratic Bessel-Gauss beams; and optical vortex beams. PMID:18197231

Bandres, Miguel A; Gutiérrez-Vega, Julio C

2008-01-15

440

Inflationary perturbation theory is geometrical optics in phase space

NASA Astrophysics Data System (ADS)

A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "?N" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ?, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.

Seery, David; Mulryne, David J.; Frazer, Jonathan; Ribeiro, Raquel H.

2012-09-01