P. M. Carabetta; W. J. Bottega
2008-01-01
The problem of edge debonding of patched beam-plates subjected to transverse pressure is examined using two related mathematical\\u000a models; one which incorporates geometric nonlinearities and the other which neglects them. The models, developed in a prior\\u000a study, present the energy release rates in self-consistent functional form and yield closed form analytical solutions for\\u000a the specific problem of interest. Results of
Qing Li; Tianshu Wang; Xingrui Ma
2009-01-01
Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics\\u000a undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems\\u000a have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted\\u000a flexible beam is investigated. The Hertzian contact
Mahaffey, Patrick Brian
2013-08-07
theory and analysis that considers the nonlinear effects on the buckling response of beams. This thesis contains three new developments: (1) the conventional beam theories are generalized by accounting for nonlinear terms arising from ?zz and ?xz...
Stationary nonlinear Airy beams
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
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.
Fibich, Gadi
critical powers, the trans- verse spatial beam profile breaks up into several filaments, a phenomenon knownPredicting the filamentation of high-power beams and pulses without numerical integration and pulses. Using this method we study the filamentation pattern of a variety of input profiles, without
Geometrical Phases in Nonlinear Oscillators
Radha Balakrishnan; Indubala Satija
2004-01-01
We characterize the geometrical and topological aspects of a classical dynamical system by associating a geometric phase with a phase space trajectory. Unlike Hannay's angle, this phase can be defined for non-integrable, as well as dissipative systems. Further, the path underlying this ``anholonomy'' is not in an external parameter space, but in a certain \\
Nonlinear Computation of Shear Lag Effect of Box Beam
Wu Yaping; Su Qiang; Zhu Yanfeng; Lin Lixia; Guo Chunxiang
2010-01-01
This paper presents an initial value solution of static equilibrium differential equations of thin-walled box beams considering shear lag, shear deformation and geometric nonlinear, which was used to establish the related element stiffness matrix, geometric stiffness matrix and equivalent nodal forces vector. So that the nonlinear analysis of thin-walled box beams is admitted into the program system of matrix-displacement method.
Geometric stiffening effect on rigid-flexible coupling dynamics of an elastic beam
J. Y. Liu; J. Z. Hong
2004-01-01
In the previous work, the authors examined the effect of the geometric stiffness terms on the stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the geometrically non-linear formulations to an elastic beam with free large overall motions. The equations of motion are derived taking into account the foreshortening deformation
Dynamic analysis of geometrically nonlinear robot manipulators
E. M. Bakp
1996-01-01
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
Nonlinear combining of laser beams.
Lushnikov, Pavel M; Vladimirova, Natalia
2014-06-15
We propose to combine multiple laser beams into a single diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. Beams with total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with Kerr nonlinearity. Random fluctuations during propagation eventually trigger a strong self-focusing event and produce a diffraction-limited beam carrying the critical power. PMID:24978503
p Version nonlinear analysis of RC beams and slabs strengthened with externally bonded plates
J. S. Ahn; K. S. Woo; P. K. Basu; J. H. Park
2006-01-01
The p-version nonlinear RC finite element model has been used to analyze the nonlinear behavior of RC beams and slabs as well as RC beams and slabs strengthened by externally bonded steel or FRP plates. The numerical approach is based on the p-version shell element, including the theory of anisotropic laminated composites considering geometric and material nonlinearities. In the nonlinear
NASA Astrophysics Data System (ADS)
Fu, Yiming; Chen, Yang; Zhong, Jun
2014-10-01
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.
Interface Technology for Geometrically Nonlinear Analysis of Multiple Connected Subdomains
NASA Technical Reports Server (NTRS)
Ransom, Jonathan B.
1997-01-01
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.
NASA Technical Reports Server (NTRS)
Peterson, D.
1979-01-01
Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.
Mahaffey, Patrick Brian
2013-08-07
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...
Two-dimensional nonlinear beam shaping.
Shapira, Asia; Shiloh, Roy; Juwiler, Irit; Arie, Ady
2012-06-01
We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion. PMID:22660146
NASTRAN nonlinear vibration analysis of beam and frame structures
NASA Technical Reports Server (NTRS)
Mei, C.; Rogers, J. L., Jr.
1975-01-01
A capability for the nonlinear vibration analysis of beam and frame structures suitable for use with NASTRAN level 15.5 is described. The nonlinearity considered is due to the presence of axial loads induced by longitudinal end restraints and lateral displacements that are large compared to the beam height. A brief discussion is included of the mathematical analysis and the geometrical stiffness matrix for a prismatic beam (BAR) element. Also included are a brief discussion of the equivalent linearization iterative process used to determine the nonlinear frequency, the required modifications to subroutines DBAR and XMPLBD of the NASTRAN code, and the appropriate vibration capability, four example problems are presented. Comparisons with existing experimental and analytical results show that excellent accuracy is achieved with NASTRAN in all cases.
Geometric stiffening effect on rigid-flexible coupling dynamics of an elastic beam
NASA Astrophysics Data System (ADS)
Liu, J. Y.; Hong, J. Z.
2004-12-01
In the previous work, the authors examined the effect of the geometric stiffness terms on the stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the geometrically non-linear formulations to an elastic beam with free large overall motions. The equations of motion are derived taking into account the foreshortening deformation term, therefore, the equations include the geometric mass and force matrices, which have geometric stiffening effect on the rigid-flexible coupling dynamics of the system. The numerical results obtained in this investigation reveal the significant difference between the deformations with and without stiffening effect. Furthermore, the stiffening effect on the large overall motion is investigated. An influence ratio is employed as a criterion to clarify the application range of the conventional linear modelling method, in which the stiffening effect is neglected. The effectiveness of the criterion is examined by two simulation examples.
Geometric Compensation of Focused Ion Beam Machining Using Image Processing
Hiwon Lee; Jin Han; Byung-Kwon Min; Sang Jo Lee
2008-01-01
During the process of focused ion beam (FIB) machining, the redeposition of the sputtered material during machining decreases the geometric accuracy of the process. In this paper, a new approach to reducing the geometric error in FIB machining is introduced. The new algorithm measures the amount of redeposited material after each production cycle and modifies the next process plan. Information
Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections
NASA Technical Reports Server (NTRS)
Atilgan, Ali R.; Hodges, Dewey H.
1991-01-01
A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.
Nonlinear geometric effects in mechanical bistable morphing structures
Zi Chen; Qiaohang Guo; Carmel Majidi; Wenzhe Chen; David J. Srolovitz; Mikko P. Haataja
2012-09-08
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.
Geometric Heat Equation and Nonlinear Diffusion of Shapes and Images
Benjamin B. Kimia; Kaleem Siddiqi
1996-01-01
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
Sonic boom propagation revisited: A nonlinear geometrical acoustic model
M. Berci; L. Vigevano
An analytical model which can accurately propagate a near-field sonic boom pressure signature down to the ground in a stratified atmosphere is presented. The pressure perturbations are limited to the vertical plane below a supersonic aircraft flying at constant horizontal speed. The proposed model employs geometrical acoustics to propagate the boom and combines a nonlinear treatment of both its amplitude
A geometric approach to nonlinear fault detection and isolation
Claudio De Persis; Alberto Isidori
2001-01-01
We present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems. A necessary condition for the problem to be solvable is derived in terms of an unobservability distribution, which is computable by means of suitable algorithms. The existence and regularity of such a distribution implies the existence of changes of coordinates in the state
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.; Chandrashekhara, K.; Chao, W. C.
1993-01-01
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.
Magnetically compensated supersonic beams for nonlinear optics
Stokes, K.D.; Schnurr, C.; Gardner, J.; Marable, M.; Shaw, S.; Goforth, M.; Holmgren, D.E.; Thomas, J. (Department of Physics, Duke University, Durham, North Carolina 27706 (US))
1989-12-01
Doppler frequently shifts for a laser field interacting with a diverging supersonic atomic beam are canceled using spatially varying Zeeman shifts. Dense atomic beams with long interaction path lengths and narrowline widths are obtained for spectroscopic and nonlinear-optics applications.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
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.
Y. B. Yang; S. P. Lin; C. S. Chen
2007-01-01
In the nonlinear analysis of elastic structures, the displacement increments generated at each incremental step can be decomposed into two components as the rigid displacements and natural deformations. Based on the updated Lagrangian (UL) formulation, the geometric stiffness matrix [kg] is derived for a 3D rigid beam element from the virtual work equation using a rigid displacement field. Further, by
D. M. Tang; E. H. Dowell
2004-01-01
In this paper structural equations of motion based on nonlinear beam theory and the ONERA aerodynamic stall model are used to study the effects of geometric structural nonlinearity on flutter and limit cycle oscillations (LCO) of high-aspect-ratio wings. For example, the effects of large static pre-flutter deformations in the vertical or torsional direction are considered. In particular, static deformations in
Generation of Optical Vortex Beams by Nonlinear Wave Mixing
Arie, Ady
Generation of Optical Vortex Beams by Nonlinear Wave Mixing Alon Bahabad and Ady Arie School@eng.tau.ac.il Abstract: It is shown that optical vortex beams can be generated from a non-vortex fundamental beam.0190) Nonlinear optics; (190.2620) Harmonic generation and mixing optical vortex beams; (190.4223) Nonlinear wave
A survey of the core-congruential formulation for geometrically nonlinear TL finite elements
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn
1994-01-01
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.
Injection of beam shaped locally with nonlinear optics.
Wang, C.-X.; Accelerator Systems Division (APS)
2007-01-01
We discuss nonlinear beam shaping by octupole and sextupole to fold the tails of a Gaussian beam into its core, for the purpose of improving betatron injection in storage rings by significantly reducing the beam width at the injection septurn and thus reducing beam centroid offset from the stored beam. Necessary conditions as well as challenges for such nonlinear injections are explored.
Nonlinear spectroscopy with twisted beams
David L. Andrews; Mohamed Babiker; Colin R. Bennett; Luciana Davila-Romero
2002-01-01
The propensity of conventional optical beams to convey angular momentum is very well known. As a spin-1 elementary particle any photon can assume a polarisation state with a well defined 'spin' angular momentum of plus or minus 1 in the direction of propagation, corresponding to a circular polarisation of either left or right helicity. The mechanical effects of photonic angular
Dynamics of Airy beams in nonlinear media
NASA Astrophysics Data System (ADS)
Allayarov, I. M.; Tsoy, E. N.
2014-08-01
The dynamics of truncated Airy beams in optical media with Kerr nonlinearity is studied in the framework of the nonlinear Schrödinger (NLS) model. It is demonstrated that an intense Airy beam with zero total momentum can generate static solitons, as well as moving solitons. The parameters of these solitons are calculated using the Zakharov-Shabat scattering problem associated with the NLS equation. It is found that solitons take the main part of the initial power, while only a small fraction of the power is transformed into a self-accelerating linear packet. The threshold parameters of the Airy beam for the soliton formation are obtained. It is shown that the threshold for the formation of the first static soliton is also a threshold of the solitonless regime.
Beams on nonlinear elastic foundation
NASA Astrophysics Data System (ADS)
Lukkassen, Dag; Meidell, Annette
2014-12-01
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.
Focused optical and acoustic beams in media with nonlinear absorption
O. V. Rudenko; A. A. Sukhorukov
1996-01-01
Optical and acoustic beams are known to be useful for medical and biological applications, such as diagnostics, surgery, etc. At high intensities both nonlinear lens effects and nonlinear absorption can be significant for the beams. The nonlinear absorption arises due to two-photon optical processes or acoustic shock wave formation. The present work is devoted to the theoretical description of nonlinear
Geometrically nonlinear analysis of layered composite plates and shells
NASA Technical Reports Server (NTRS)
Chao, W. C.; Reddy, J. N.
1983-01-01
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.
Nonlinear $\\delta f$ Method for Beam-Beam Simulation
Cai, Y; Tzenov, Stephan I; Tajima, T; Cai, Yunhai; Chao, Alexander W.; Tzenov, Stephan I.; Tajima, Toshi
2000-01-01
We have developed an efficacious algorithm for simulation of the beam-beam interaction in synchrotron colliders based on the nonlinear $\\delta f$ method, where $\\delta f$ is the much smaller deviation of the beam distribution from the slowly evolving main distribution $f_0$. In the presence of damping and quantum fluctuations of synchrotron radiation it has been shown that the slowly evolving part of the distribution function satisfies a Fokker-Planck equation. Its solution has been obtained in terms of a beam envelope function and an amplitude of the distribution, which satisfy a coupled system of ordinary differential equations. A numerical algorithm suited for direct code implementation of the evolving distributions for both $\\delta f$ and $f_0$ has been developed. Explicit expressions for the dynamical weights of macro-particles for $\\delta f$ as well as an expression for the slowly changing $f_0$ have been obtained.
Geometric Nonlinear Finite Element Analysis of Active Fibre Composite Bimorphs
NASA Astrophysics Data System (ADS)
Kernaghan, Robert
Active fibre composite-actuated bimorphic actuators were studied in order to measure deflection performance. The deflection of the actuators was a function of the actuating electric potential applied to the active material as well as the magnitude of the axial preload applied to the bimorphic structure. This problem required the use of geometric nonlinear modeling techniques. Geometric nonlinear finite element analysis was undertaken to determine the deflection performance of Macro Fibre Composite (MFC)- and Hollow Active Fibre (HAFC)-actuated bimorphic structures. A physical prototype MFC-actuated bimorphic structure was manufactured in order to verify the results obtained by the finite element analysis. Theses analyses determined that the bimorphic actuators were capable of significant deflection. The analyses determined that the axial preload of the bimorphic actuators significantly amplified the deflection performance of the bimorphic actuators. The deflection performance of the bimorphic actuators suggest that they could be candidates to act as actuators for the morphing wing of a micro unmanned air vehicle.
A consistent interface element formulation for geometrical and material nonlinearities
NASA Astrophysics Data System (ADS)
Reinoso, J.; Paggi, M.
2014-12-01
Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with coupled material and geometrical nonlinearities. The present work proposes a consistent derivation of a new interface element for large deformation analyses. The resulting compact derivation leads to an operational formulation that enables the accommodation of any order of kinematic interpolation and constitutive behavior of the interface. The derived interface element has been implemented into the finite element codes FEAP and ABAQUS by means of user-defined routines. The interplay between geometrical and material nonlinearities is investigated by considering two different constitutive models for the interface (tension cut-off and polynomial cohesive zone models) and small or finite deformation for the continuum. Numerical examples are proposed to assess the mesh independency of the new interface element and to demonstrate the robustness of the formulation. A comparison with experimental results for peeling confirms the predictive capabilities of the formulation.
T. Rahman
2009-01-01
In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is often done using finite element based incremental-iterative procedures. However standard finite element based nonlinear analysis of many practical structures is still
Nonlinear interaction of optical beams in gradient waveguides
NASA Astrophysics Data System (ADS)
Sukhorukova, Anna K.; Sukhorukov, Anatoly P.
2010-06-01
We investigate the interaction of two optical beams at different frequencies in an optical gradient waveguide. The index has a parabolic profile, and the nonlinearity belongs to a defocusing type. The total reflection of a tilted signal beam from a negative inhomogeneity induced by pump-beam occurs while both beams are trapped in the refractive index trough is considered. We derive the equation for the rays, taking into account cubic nonlinearity and transverse inhomogeneity. Trajectories of the signal beam at different ratios of the values of the nonlinearity, heterogeneity and the initial angle of inclination are plotted. The critical angle of total reflection in a gradient waveguide with negative nonlinearity is found. The interaction of co-axis beams is also discussed. The waveguiding propagation of a pump beam under the balance between defocusing with negative nonlinearity and focusing with parabolic inhomogeneity is presented. The wide signal beam can split by narrow pump beam.
Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations
NASA Technical Reports Server (NTRS)
Hodges, D. H.
1985-01-01
Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.
B. P. Patel; M. Ganapathi; M. Touratier
1999-01-01
Nonlinear free flexural vibrations and post-buckling of laminated orthotropic beams resting on a class of two parameter elastic foundation are studied using a three-noded shear flexible beam element. Geometric nonlinearity is considered using von Karman’s strain–displacement relations. The formulation includes the effects of transverse shear deformation, in-plane and rotary inertia terms. Exact numerical integration is employed for evaluating all the
A geometric calibration method for cone beam CT systems
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
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.
Sensitive measurement of optical nonlinearities using a single beam
MANSOOR SHEIK-BAHAE; ALI A. SAID; T.-H. Wei; D. J. Hagan; E. W. Van Stryland
1990-01-01
A sensitive single-beam technique for measuring both the nonlinear refractive index and nonlinear absorption coefficient for a wide variety of materials is reported. The authors describe the experimental details and present a comprehensive theoretical analysis including cases where nonlinear refraction is accompanied by nonlinear absorption. In these experiments, the transmittance of a sample is measured through a finite aperture in
Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics
NASA Astrophysics Data System (ADS)
Bun Tse, Bosco Chun
This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.
Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions
NASA Astrophysics Data System (ADS)
Ma, NiuJing; Wang, RongHui; Han, Qiang; Lu, YiGang
2014-08-01
An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The first approximation solution of the non-resonance is obtained by means of the method of multiple scales. The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method. The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS. Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.
QINGHUA QIN; JIANXUN ZHANG; ZHENGJIN WANG; T. J. WANG
2011-01-01
The objective of this work is to study the large deflection of geometrically asymmetric metal foam core sandwich beam under transverse loading by a fiat punch. A yield criterion is proposed for geometrically asymmetric metal foam core sandwich structures, and then analytical solution for the large deflection of a fully clamped slender sandwich beam is obtained, in which the interaction
Nonlinear free vibrations of beams in space due to internal resonance
NASA Astrophysics Data System (ADS)
Stoykov, S.; Ribeiro, P.
2011-08-01
The geometrically nonlinear free vibrations of beams with rectangular cross section are investigated using a p-version finite element method. The beams may vibrate in space, hence they may experience longitudinal, torsional and non-planar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The geometrical nonlinearity is taken into account by considering Green's nonlinear strain tensor. Isotropic and elastic beams are investigated and generalised Hooke's law is used. The equation of motion is derived by the principle of virtual work. Mostly clamped-clamped beams are investigated, although other boundary conditions are considered for validation purposes. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. One constant term, odd and even harmonics are assumed in the Fourier series and convergence with the number of harmonics is analysed. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of backbone curves. Coupling between modes is investigated, internal resonances are found and the ensuing multimodal oscillations are described. Some of the couplings discovered lead from planar oscillations to oscillations in the three dimensional space.
Nonlinear formation of holographic images of obscurations in laser beams
words: Nonlinear optics, self-focusing, optical damage, fusion lasers. 1. Introduction In highNonlinear formation of holographic images of obscurations in laser beams C. Clay Widmayer, David of obscurations in laser beams. The predictions of the model are found to be in good agreement with measurements
Nonlinear Flexural Deflection of Thermoplastic Foam Core Sandwich Beam
Kwang Joon Yoon; C. K. Kim; Hoon C. Park
2002-01-01
Nonlinear flexural deflection behavior of foam core sandwich beams hasbeen experimentally investigated. The experimental data were compared with the predicted results obtained from a proposed analytical method and the finite element analysis. Sandwich beams with thermoplastic foam core and carbon\\/epoxy fabric faces were manufactured using the vacuum bagging process. To investigate the effect of the face thickness on the nonlinear
Nonlinear Dynamics of a Beam on Elastic Foundation
F. Pellicano; F. Mastroddi
1997-01-01
The nonlinear dynamics of a simply supported beam resting on a nonlinear spring bed with cubic stiffness is analyzed. The continuous differential operator describing the mathematical model of the system is discretized through the classical Galerkin procedure and its nonlinear dynamic behavior is investigated using the method of Normal Forms. This model can be regarded as a simple system describing
Development of geometrically-nonlinear finite element analysis for marine risers
Haas, Mark Edward
1987-01-01
DEVELOPMENT OF GEOMETRICALLY-NONLINEAR FINITE ELEMENT ANALYSIS FOR MARINE RISERS A Thesis MARK EDWARD HAAS Submitted to the Graduate College of Texas AE-M Hniversity in partial fulfillment of the requirements for the degree oi' MASTER.... Hogan (Member) James R. . organ (5'Iem er) James K. N on (Memb ) Donald A. Max ell (Interim Head oI Department) August l 98i ABSTRACT Development of Geometrically-Nonlinear Finite Element Analysis for Marine Risers (August 1987) Mark Edward...
Zhu Jufen; Chen Wanji
1997-01-01
Based on a large deformation variational principle with relaxed interelement continuity requirement in the total Lagranginan description, a refined triangular thin plate element for geometric nonlinear analysis has been developed. By introducing special element displacement functions into the geometric stiffness matrix, the membrane locking phenomenon is relieved effectively. The numerical results are presented to show that the present element possesses
NASA Astrophysics Data System (ADS)
Akbari, M. R.; Nimafar, M.; Ganji, D. D.; Akbarzade, M. M.
2014-12-01
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.
Geometric studies on variable radius spiral cone-beam scanning Yangbo Yea)
Virginia Tech
spiral cone-beam scanning is given in the context of electron-beam CT/micro-CT. Then, necessary, much of the efforts have been limited to high spatial resolution. In the 1990s, a num- ber of microGeometric studies on variable radius spiral cone-beam scanning Yangbo Yea) and Jiehua Zhu
Geometrical representation of Gaussian beams propagating through complex paraxial optical systems
L. C. Andrews; W. B. Miller; J. C. Ricklin
1993-01-01
This paper investigates the propagation and diffraction of Gaussian laser beams through a complex system of paraxial optical elements by applying geometric representation of two pairs of nondimensional beam parameters. The various diagrams presented provide a visual technique for characterizing diffractive propagation of Gaussian beam waves and design of laser systems.
Effect of Kerr nonlinearity on an Airy beam
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
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.
Influence of geometric nonlinearities in the dynamics of flexible treelike structures
NASA Astrophysics Data System (ADS)
Ider, S. K.; Amirouche, F. M. L.
1989-12-01
A comprehensive computer algorithm used in the dynamic analysis of multibody systems is presented. The procedures developed combine Kane's equations, the strain energy, and modal analysis to describe the elastic bodies. The equations of motion are expressed in a form in which their coefficients are based on the partial velocity and partial angular velocity arrays and are easily coded for computers. The nonlinear geometric stiffness matrix is developed for three-dimensional beams that account for the couplings between the deformation components having significant effects in high-speed systems. The method presented in this paper is tailored for structures with variable cross-sectional beam elements such as spacecraft antennae, helicopter rotor blades, robot systems, and mechanisms. The effects of rotary inertia as well as shear deformation are automatically included into the equations of motion. A method for obtaining the shape function matrix consisting of assumed dynamic modes is also presented. In addition, the preceding formulations are used in a simulation of a space-based robotic manipulator, and the results are compared with those obtained by Kane et al.
Developing the eikonal method in nonlinear electrodynamics based on the geometrization principle
NASA Astrophysics Data System (ADS)
Krivchenkov, I. V.
2007-01-01
We derive the eikonal equation for an electromagnetic wave propagating in an external electromagnetic field according to the laws of nonlinear electrodynamics. Based on Logunov’s geometrization principle, we determine the metric tensors of the effective Riemannian spaces for the Born-Infeld electrodynamics, nonlinear Heisenberg-Euler electrodynamics, and a parameterized post-Maxwellian electrodynamics. We analyze the main properties of these nonlinear electrodynamics.
DETECTION OF FATIGUE CRACKS IN FLEXIBLE GEOMETRICALLY NON-LINEAR BARS BY VIBRATION MONITORING
S. L. Tsyfansky; V. I. Beresnevich
1998-01-01
The results of mathematical simulation of flexural vibrations of a geometrically non-linear cracked bar under external harmonic excitation are presented. It is shown, that thanks to the influence of elastic non-linearity of the crack, new non-linear properties which are impossible in the initial undamaged structure, appear in the system (self-excitation of subharmonic regimes, appearance of even-numbered harmonic components in frequency
Namita Nanda; J. N. Bandyopadhyay
2009-01-01
The nonlinear transient response of composite shells with\\/without cutouts and initial geometric imperfection is investigated using the finite element method. The present formulation considers doubly curved shells incorporating von Kármán type nonlinear strains into the first order shear deformation theory. The analysis is carried out using quadratic C0 eight-noded isoparametric element. The governing nonlinear equations are solved by using the
Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method
NASA Astrophysics Data System (ADS)
Ghorbanpour Arani, A.; Atabakhshian, V.; Loghman, A.; Shajari, A. R.; Amir, S.
2012-07-01
In the present work, effect of von Kàrmàn geometric nonlinearity on the vibration behavior of a single-walled boron nitride nanotube (SWBNNT) is investigated based on nonlocal piezoelasticity theory. The SWBNNT is considered as a nanobeam within the framework of Timoshenko beam (TB). Loading is composed of a temperature change and an imposed axially electric potential throughout the SWBNNT. The interactions between the SWBNNT and its surrounding elastic medium are simulated by Winkler and Pasternak foundation models. The higher order governing equations of motion are derived using Hamilton's principle and the numerical solution of equations is obtained using Differential Quadrature (DQ) method. The effects of geometric nonlinearity, elastic foundation modulus, electric potential field, temperature change and nonlocal parameter on the frequency of the SWBNNT are studied in detail.
A simple theory of geometrical stiffness with applications to beam and shell problems
J. H. Argyrls; P. C. Dunne
Geometrical stiffness is the basis for any attempt to study the behaviour of slender beams and thin shells under conditions\\u000a in which large deflections may occur with small strains. Not all problems require high accuracy in the representation of the\\u000a geometrical stiffness. These are generally certain self-equilibrating stress systems (natural modes) which are the principal\\u000a contributors to the geometrical stiffness.
Geometric structure of multiple time-scale nonlinear dynamical systems
Sanjay Bharadwaj
1999-01-01
A new methodology to analyze time-scale structure of smooth finite-dimensional nonlinear dynamical systems is developed. This approach does not assume apriori knowledge of slow and fast variables for special coordinates that simplify the form of the nonlinear dynamics. Conventional approaches to analyze time-scale structure of nonlinear dynamics such as singular perturbation theory proceed from such specialized apriori knowledge which is
Dynamics of elastic nonlinear rotating composite beams with embedded actuators
NASA Astrophysics Data System (ADS)
Ghorashi, Mehrdaad
2009-08-01
A comprehensive study of the nonlinear dynamics of composite beams is presented. The study consists of static and dynamic solutions with and without active elements. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Numerical solutions for the steady state and transient responses have been obtained. It is shown that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. The effect of perturbing the steady state solution has also been calculated and the results are shown to be compatible with those of the accelerating beam analysis. Next, the coupled flap-lag rigid body dynamics of a rotating articulated beam with hinge offset and subjected to aerodynamic forces is formulated. The solution to this rigid-body problem is then used, together with the finite difference method, in order to produce the nonlinear elasto-dynamic solution of an accelerating articulated beam. Next, the static and dynamic responses of nonlinear composite beams with embedded Anisotropic Piezo-composite Actuators (APA) are presented. The effect of activating actuators at various directions on the steady state force and moments generated in a rotating composite beam has been presented. With similar results for the transient response, this analysis can be used in controlling the response of adaptive rotating beams.
Geometrically-Exact, Intrinsic Theory for Dynamics of Moving Composite Plates
Patil, Mayuresh
, a geometrically-exact, fully intrinsic theory for dynamics of curved and twisted composite beams has been helicopter rotor blades. Indeed, the geometrically nonlinear problem of dynamics of moving composite beams
On the dynamics of Airy beams in nonlinear media with nonlinear losses
Ruiz-Jiménez, Carlos; Porras, Miguel A
2015-01-01
We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward H\\"ankel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.
Two-dimensional nonlinear beam shaping Asia Shapira,1,
Arie, Ady
in the field of non- linear beam shaping and mode conversion. © 2012 Optical Society of America OCIS codes: 190.2620, 090.2890. Shaping a generated wavefront in nonlinear conversion adds functionality and opens exciting in linear optics is based on using CGH [10]. When a light beam is sent through a CGH, the far
Topological Synthesis of Compliant Mechanisms Using Nonlinear Beam Elements
Jinyong Joo; Sridhar Kota
2004-01-01
The article presents a methodology for generating topology of complaint mechanisms using nonlinear deformation theory. In an earlier work, (Joo, J., Kota, S., Kikuchi, N., (2000) Topological synthesis of compliant mechanisms using linear beam elements. Mechanics of Structures and Machines 28(4):245–280), we presented a topology synthesis methodology using linear beam elements. Using large deformation analysis, the article presents a methodology
Using Nonlinear RF Acceleration for FEL Beam Conditioning
Stupakov, G.; Huang, Z.; /SLAC
2005-12-14
We consider a new approach to condition an electron beam using nonlinear effects in the RF field. We demonstrate that such effects can generate a desirable--for the FEL interaction--radial variation of the particle's energy in the beam, and calculate the induced energy spread in the limit of weak field.
Beam loading by electrons in nonlinear plasma wakes
M. Tzoufras; W. Lu; F. S. Tsung; C. Huang; W. B. Mori; T. Katsouleas; J. Vieira; R. A. Fonseca; L. O. Silva
2009-01-01
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
Geometric manipulation of light : from nonlinear optics to invisibility cloaks
Hashemi, Hila
2012-01-01
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 ...
Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability
J. Michael Steele
1981-01-01
A limit theorem is established for a class of random processes (called here subadditive Euclidean functionals) which arise in problems of geometric probability. Particular examples include the length of shortest path through a random sample, the length of a rectilinear Steiner tree spanned by a sample, and the length of a minimal matching. Also, a uniform convergence theorem is proved
NASA Astrophysics Data System (ADS)
Akbarov, S. D.; Dzhamalov, Z. R.; Movsumov, E. A.
1992-12-01
The distribution of self-equilibrated normal and tangential stresses at the matrix-filler interface in composites with alternating periodically curved layers is investigated analytically in the case of uniaxial loading at infinity by uniformly distributed normal forces in the layer direction. The analysis is based on a piecewise homogeneous body model and employs three-dimensional elasticity equations in the geometrically nonlinear formulation. It is shown that the consideration of geometrical nonlinearity leads to a reduction of the self-equilibrated stresses in the case of tension and an increase of these stresses in the case of compression.
Geometric nonlinear analysis of microbeam under electrostatic loading
Murgude, Nikhil C.
2001-01-01
This study investigates the behavior of a microbeam subjected to electrostatic loading. Two devices, namely, a tungsten microtweezer and a clamped-clamped beam which is part of a micro-electromechanical system (MEMS), are used as the vehicles...
Geometric nonlinear analysis of microbeam under electrostatic loading
Murgude, Nikhil C.
2001-01-01
This study investigates the behavior of a microbeam subjected to electrostatic loading. Two devices, namely, a tungsten microtweezer and a clamped-clamped beam which is part of a micro-electromechanical system (MEMS), are used as the vehicles...
Design optimization of geometrically nonlinear truss structures considering cardinality constraints
Afonso C. C. Lemonge; Michelli M. Silva; Helio J. C. Barbosa
2011-01-01
The structural optimization problem of choosing the profile of each member belonging to a framed structure in order to minimize its weight while satisfying stress, displacement, stability, and other applicable constraints is often complicated by the requirement of considering non-linear structural behavior. The problem is further complicated if the members are to be chosen from a discrete set of commercially
MULTIPHASE WEAKLY NONLINEAR GEOMETRIC OPTICS FOR SCHRODINGER EQUATIONS
Dumas, Eric
in nonlinear optics, quantum superfluids, plasma physics or water waves, see e.g. [30] for a general overview experiments have shown the possibility of matter-wave mixing in BoseEinstein condensates [12]. A formal theoretical treatment, based on the GrossPitaevskii equation (i.e. a cubic NLS describing the condensate wave
MULTIPHASE WEAKLY NONLINEAR GEOMETRIC OPTICS FOR SCHRODINGER EQUATIONS
Sparber, Christof
in nonlinear optics, quantum superfluids, plasma physics or water waves, see e.g. [29] for a general overview experiments have shown the possibility of matter-wave mixing in BoseEinstein condensates [10]. A formal theoretical treatment, based on the GrossPitaevskii equation (i.e. a cubic NLS describing the condensate wave
A Geometrically Nonlinear Shear Deformation Theory for Composite Shells
Yu, Wenbin
-dimensional, generalized strains. The large rotation is represented by the general finite rotation of a frame embedded if the kinematical (strain-displacement) relations are nonlinear but the constitutive (stress-strain) relations are linear. This kind of theory allows large displacements and rotations with the restriction that strain
Emergence of Geometrical Optical Nonlinearities in Photonic Crystal Fiber Nanowires
Fabio Biancalana; Truong X. Tran; Sebastian Stark; Markus A. Schmidt; Philip St. J. Russell
2010-01-01
We demonstrate analytically and numerically that a subwavelength-core dielectric photonic nanowire embedded in a properly designed photonic crystal fiber cladding shows evidence of a previously unknown kind of nonlinearity (the magnitude of which is strongly dependent on the waveguide parameters) which acts on solitons so as to considerably reduce their Raman self-frequency shift. An explanation of the phenomenon in terms
Comparison of the geometrically nonlinear and linear theories of martensitic transformation
K. Bhattacharya
1993-01-01
Over the last few years, a continuum model based on finite or nonlinear thermoelasticity has been developed and successfully used to study crystalline solids that undergo a martensitic phase transformation. A geometrically linear version of this model was developed independently and has been widely used in the materials science literature. This paper presents the two theories and evaluates them by
Stability analysis using a geometrically nonlinear assumed strain solid shell element model
Chahngmin Cho; Hoon C. Park; Sung W. Lee
1998-01-01
A solid shell element model with six degrees of freedom per node is applied to buckling and postbuckling analysis of geometrically nonlinear shell structures. The present model allows changes in the thickness direction and does not require rotational angles or parameters for the description of the kinematics of deformation. The finite element model is constructed based on the assumed strain
Modal Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes
Eric Pesheck; Christophe Pierre; Steven W. Shaw
2002-01-01
A method for determining reduced-order models for rotating beams is presented. The approach is based on the construction of nonlinear normal modes that are defined in terms of invariant manifolds that exist for the system equations of motion. The beam considered is an idealized model for a rotor blade whose motions are dominated by transverse vibrations in the direction perpendicular
Geometrically derived anisotropy in cubically nonlinear dielectric composites
Tom G. Mackay; James Clerk
2003-01-01
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
Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
Li, Nianbei; Ren, Jie
2014-01-01
Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports. PMID:25169668
NASA Technical Reports Server (NTRS)
Mangalgiri, P. D.; Prabhakaran, R.
1986-01-01
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.
Emergence of geometrical optical nonlinearities in photonic crystal fiber nanowires
Biancalana, Fabio; Stark, Sebastian; Schmidt, Markus A; Russell, Philip St J
2010-01-01
We demonstrate analytically and numerically that a subwavelength-core dielectric photonic nanowire embedded in a properly designed photonic crystal fiber cladding shows evidence of a previously unknown kind of nonlinearity (the magnitude of which is strongly dependent on the waveguide parameters) which acts on solitons so as to considerably reduce their Raman self-frequency shift. An explanation of the phenomenon in terms of indirect pulse negative chirping and broadening is given by using the moment method. Our conclusions are supported by detailed numerical simulations.
Emergence of geometrical optical nonlinearities in photonic crystal fiber nanowires.
Biancalana, Fabio; Tran, Truong X; Stark, Sebastian; Schmidt, Markus A; Russell, Philip St J
2010-08-27
We demonstrate analytically and numerically that a subwavelength-core dielectric photonic nanowire embedded in a properly designed photonic crystal fiber cladding shows evidence of a previously unknown kind of nonlinearity (the magnitude of which is strongly dependent on the waveguide parameters) which acts on solitons so as to considerably reduce their Raman self-frequency shift. An explanation of the phenomenon in terms of indirect pulse negative chirping and broadening is given by using the moment method. Our conclusions are supported by detailed numerical simulations. PMID:20868164
Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion
NASA Astrophysics Data System (ADS)
McBride, A. T.; Javili, A.; Steinmann, P.; Bargmann, S.
2011-10-01
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.
Nonlinear Angle Beam Ultrasonic Evaluation of Adhesive Bonds
S. I. Rokhlin; L. Wang; A. Baltazar; V. A. Yakovlev; L. Adler
2003-01-01
We have developed an experimental method incorporating high frequency pulsed angle beam ultrasonic measurements under low frequency vibration of bonded structures utilizing parametric\\/nonlinear mixing between high and low frequencies. We have demonstrated that the effect of environmental degradation of adhesive bonds can be detected by this method. It is shown that good quality (undamaged) bonds do not exhibit dependence of
Heidari, Mohammad; Heidari, Ali; Homaei, Hadi
2014-01-01
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
Energy shedding during nonlinear self-focusing of optical beams.
Travis, C; Norris, G; McConnell, G; Oppo, G-L
2013-10-01
Self-focusing of intense laser beams and pulses of light in real nonlinear media is in general accompanied by material losses that require corrections to the conservative Nonlinear Schrödinger equations describing their propagation. Here we examine loss mechanisms that exist even in lossless media and are caused by shedding of energy away from the self-trapping beam making it to relax to an exact solution of lower energy. Using the conservative NLS equations with absorbing boundary conditions we show that energy shedding not only occurs during the initial reshaping process but also during oscillatory propagation induced by saturation of the nonlinear effect. For pulsed input we also show that, depending on the sign and magnitude of dispersion, pulse splitting, energy shedding, collapse or stable self-focusing may result. PMID:24104260
Nonlinear transient neutralization theory of ion beams with dissipation
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.
1975-01-01
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions. The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave. This periodic wave structure is damped out by intercomponent momentum transfer, i.e., after a few relaxation lengths a quasi-neutral beam results. The relaxation scale in space agrees with neutralization experiments of rarefied ion beams, if the collective momentum transfer between the electron and ion streams is assumed to be of the Buneman type.
Customizing the mass and geometric stiffness of plane beam elements by Fourier methods
Carlos A. Felippa
2001-01-01
Teaches by example the application of finite element templates in constructing high performance elements. The example discusses the improvement of the mass and geometric stiffness matrices of a Bernoulli-Euler plane beam. This process interweaves classical techniques (Fourier analysis and weighted orthogonal polynomials) with newer tools (finite element templates and computer algebra systems). Templates are parameterized algebraic forms that uniquely characterize
NASA Astrophysics Data System (ADS)
Lülf, Fritz Adrian; Tran, Duc-Minh; Matthies, Hermann G.; Ohayon, Roger
2015-02-01
For repeated transient solutions of geometrically nonlinear structures, the numerical effort often poses a major obstacle. Thus it may become necessary to introduce a reduced order model which accelerates the calculations considerably while taking into account the nonlinear effects of the full order model in order to maintain accuracy. This work yields an integrated method that allows for rapid, accurate and parameterisable transient solutions. It is applicable if the structure is discretised in time and in space and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced order model. Three approaches, each responding to one of the requirements of rapidity, accuracy and parameterisation, are united to form the integrated method. The polynomial formulation of the nonlinear terms renders the solution of the reduced order model autonomous from the finite element formulation and ensures a rapid solution. The update and augmentation of the reduced basis ensures the accuracy, because the simple introduction of a constant basis seems to be insufficient to account for the nonlinear behaviour. The interpolation of the reduced basis allows adapting the reduced order model to different external parameters. A Newmark-type algorithm provides the backbone of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method enables a rapid, accurate and parameterisable transient solution.
Pull-in instability of geometrically nonlinear micro-switches under electrostatic and Casimir forces
Xiao Li Jia; S. Kitipornchai
2011-01-01
This paper investigates the pull-in instability of micro-switches under the combined electrostatic and intermolecular forces\\u000a and axial residual stress, accounting for the force nonlinearity and geometric nonlinearity which stems from mid-plane stretching.\\u000a The micro-switch considered in the present study is made of either homogeneous material or non-homogeneous functionally graded\\u000a material with two material phases. Theoretical formulations are based on Euler–Bernoulli
NASA Technical Reports Server (NTRS)
Hasanyan, Davresh; Librescu, Liviu; Qin, Zhanming; Ambur, Damodar R.
2006-01-01
A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed, In this context. the first-order transversely shearable plate theory in conjunction with von-Karman geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic field disturbances within the plate, the assumptions proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e. the ones by Faraday, Ampere, Ohm, Maxwell and Lorentz), the modified Fourier's law of heat conduction and on the elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2- D one. The theory developed herein provides a foundation for the investigation, both analytical and numerical, of the interacting effects among the magnetic, thermal and elastic fields in multi-layered thin plates made of anisotropic materials.
A geometrical model for the Monte Carlo simulation of the TrueBeam linac.
Rodriguez, M; Sempau, J; Fogliata, A; Cozzi, L; Sauerwein, W; Brualla, L
2015-06-01
Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3??×??3 to 40??×??40 cm(2) at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for the 40??×??40 cm(2) field where the ansatz geometry was able to reproduce the measured dose more accurately. Our approach overcomes some of the limitations of using the Varian phase-space files. It makes it possible to: (i) adapt the initial beam parameters to match measured dose profiles; (ii) reduce the statistical uncertainty to arbitrarily low values; and (iii) assess systematic uncertainties (type B) by using different Monte Carlo codes. One limitation of using phase-space files that is retained in our model is the impossibility of performing accurate absolute dosimetry simulations because the geometrical description of the TrueBeam ionization chamber remains unknown. PMID:25984796
A geometrical model for the Monte Carlo simulation of the TrueBeam linac
NASA Astrophysics Data System (ADS)
Rodriguez, M.; Sempau, J.; Fogliata, A.; Cozzi, L.; Sauerwein, W.; Brualla, L.
2015-06-01
Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3??×??3 to 40??×??40 cm2 at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for the 40??×??40 cm2 field where the ansatz geometry was able to reproduce the measured dose more accurately. Our approach overcomes some of the limitations of using the Varian phase-space files. It makes it possible to: (i) adapt the initial beam parameters to match measured dose profiles; (ii) reduce the statistical uncertainty to arbitrarily low values; and (iii) assess systematic uncertainties (type B) by using different Monte Carlo codes. One limitation of using phase-space files that is retained in our model is the impossibility of performing accurate absolute dosimetry simulations because the geometrical description of the TrueBeam ionization chamber remains unknown.
Zhou, Junxiao; Liu, Yachao; Ke, Yougang; Luo, Hailu; Wen, Shuangchun
2015-07-01
We propose a novel method for the generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases. In our scheme, the Airy beam is generated by the dynamic phase with a spatial light modulator, and the vortex phase or the vector polarization is modulated by the geometric phase with a dielectric metasurface. The modulation of the geometric phase provides an extra degree of freedom to manipulate the phase and the polarization of Airy beams. This scheme can be extended to generate any other types of optical beams with desirable phase and polarization. PMID:26125400
Nonlinear transmission line based electron beam driver.
French, David M; Hoff, Brad W; Tang, Wilkin; Heidger, Susan; Allen-Flowers, Jordan; Shiffler, Don
2012-12-01
Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique. PMID:23277977
NASA Astrophysics Data System (ADS)
Bekhoucha, Ferhat; Rechak, Said; Duigou, Laëtitia; Cadou, Jean-Marc
2015-05-01
This paper deals with the computation of backbone curves bifurcated from a Hopf bifurcation point in the framework of nonlinear free vibrations of a rotating flexible beams. The intrinsic and geometrical equations of motion for anisotropic beams subjected to large displacements are used and transformed with Galerkin and harmonic balance methods to one quadratic algebraic equation involving one parameter, the pulsation. The latter is treated with the asymptotic numerical method using Padé approximants. An algorithm, equivalent to the Lyapunov-Schmidt reduction is proposed, to compute the bifurcated branches accurately from a Hopf bifurcation point, with singularity of co-rank 2, related to a conservative and gyroscopic dynamical system steady state, toward a nonlinear periodic state. Numerical tests dealing with clamped, isotropic and composite, rotating beams show the reliability of the proposed method reinforced by accurate results.
Non-geometrical effects on Gaussian beams transmitting through a thin dielectric slab
NASA Astrophysics Data System (ADS)
Li, Chun-Fang; Zhang, Yan; Chen, Xi; Zhu, Qi-Biao
2008-05-01
It is shown that a Gaussian light beam transmitting through a planar thin dielectric slab in the air undergoes four different effects, i.e. lateral Goos-Hänchen-like (GHL) displacement, angular deflection, width modification and longitudinal focal shift as compared with the results predicted by geometrical optics. According to the Taylor expansion of the exponent of transmission coefficient when expressed as an exponential form, the lateral GHL displacement and the angular deflection are the first-order effects and can be negative or positive. The width modification and the longitudinal focal shift are the second-order effects and can also be positive or negative. Owing to the waist-width dependent term, the non-geometrical effects of transmitted beam are not identical with the non-specular effects of reflected beam. The conditions for the validity of those effects are suggested and numerical simulations are also given.
Beam loading by electrons in nonlinear plasma wakesa)
NASA Astrophysics Data System (ADS)
Tzoufras, M.; Lu, W.; Tsung, F. S.; Huang, C.; Mori, W. B.; Katsouleas, T.; Vieira, J.; Fonseca, R. A.; Silva, L. O.
2009-05-01
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.
Nonlinear beam-dynamics calculations with an illustrative example
Whealton, J.H.; Murphy, B.D.; Raridon, R.J.; Rothe, K.E.; Becraft, W.R.; Owens, T.L. (Oak Ridge National Laboratory, P.O. Box 2009, Oak Ridge, Tennessee 37831 (United States))
1992-03-15
Nonlinear beam-dynamics calculations are described that account for space-charge and image-charge effects. The calculation technique is explained and, as an illustration, is applied to two elements in an intense beam-combining funnel: an rf rebuncher and an rf deflector. For the case of the rebuncher, the calculations make use of the cylindrical symmetry of the device. For the deflector, both two-dimensional and three-dimensional calculations are performed. Emittance growth is analyzed for both the rebuncher and the deflector. For the rebuncher, a technique is proposed that considerably reduces the emittance growth.
Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations
NASA Technical Reports Server (NTRS)
Tessler, Alexander; Sleight, David W.
2006-01-01
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.
Nonlinear evolution of the ion-ion beam instability
NASA Technical Reports Server (NTRS)
Pecseli, H. L.; Trulsen, J.
1982-01-01
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
Frequency conversion of Bessel light beams in nonlinear crystals
Belyi, V N; Kazak, N S [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus); Khilo, N A [Division of Optical problems in Informatics, National Academy of Sciences of Belarus, Minsk (Belarus)
2000-09-30
The properties of frequency conversion of Bessel light beams (BLBs) in nonlinear crystals are studied theoretically and experimentally. New possibilities and prospects of the development of methods for nonlinear optical frequency conversion using BLBs are discussed. The second harmonic generation (SHG) is studied under the conditions of critical and noncritical phase matching. The longitudinal and transverse phase matching is analysed in detail upon SHG and sum frequency generation in BLBs. The concept of azimuthal width of phase matching caused by the longitudinal and transverse wave detuning is introduced, and its value is calculated for collinear and {pi}-vector interactions. The regime of azimuthally matched interactions is selected, which is realised when the azimuthal phase matching width is small. A correlation of the azimuthal BLB components caused by these interactions is predicted. It is shown that azimuthally matched BLBs are characterised by a significant increase in the overlap integral and by nonlinear interactions that do not destroy their spatial structure. (invited paper)
Extreme nonlinear optical processes with beams carrying orbital angular momentum
NASA Astrophysics Data System (ADS)
Kern, C.; Zürch, M.; Hansinger, P.; Dreischuh, A.; Spielmann, Ch.
2014-03-01
Light beams carrying an isolated point singularity with a screw-type phase distribution are called an optical vortex (OV). The fact that in free space the Poynting vector of the beam gives the momentum flow leads to an orbital angular momentum (OAM) of the photons in such a singular beam, independent on the spin angular momentun1. There are many applications of optical OAM shown in literature that would benefit from the availability of optical vortex beams in all spectral regions. For example it was shown that transitions forbidden by selection rules in dipole approximation appear allowed when using photons with the additional degree of freedom of optical OAM2. However, the common techniques of producing new light frequencies by nonlinear optical processes seem problematic in conserving the optical vortex when the nonlinearity becomes large. We show that with the extremely nonlinear process of High Harmonic Generation (HHG) it is possible to transfer OVs from the near-infrared to the extreme ultraviolet (XUV)3 at wavelengths down to ~30 nm. The observed XUV light was examined spatially and spectrally. The spatial profile showed the expected singular behavior, a dark region in the center. A comparison of the far-field fringe pattern caused by a thin wire with corresponding simulations suggests that the XUV vortex beam carries a unit topological charge. A screw-like phase evolution around the profile was also verified by employing a Hartmann type measurement. The generated spectrum revealed that in all Harmonic orders an OV was present. The profile, however, looked the same in all orders, indicating identical topological charge, which runs counterintuitive to the assumption that the phase of exp(-il?) is multiplied by the harmonic order in a frequency up-conversion experiment.
NASA Technical Reports Server (NTRS)
Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.
1991-01-01
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.
Yang, Guang; Lin, Qingyu; Ding, Yu; Tian, Di; Duan, Yixiang
2015-01-01
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
NASA Astrophysics Data System (ADS)
Yang, Guang; Lin, Qingyu; Ding, Yu; Tian, Di; Duan, Yixiang
2015-01-01
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.
S. Panda; Manas Chandra Ray
2008-01-01
Summary This paper deals with the performance of the vertically reinforced 1–3 piezoelectric composite material as the distributed\\u000a actuator for controlling nonlinear deformations of smart functionally graded (FG) plates. A nonlinear semi-analytical model\\u000a based on von Karman type geometric nonlinearity has been derived for the FG plates integrated with a layer of this piezoelectric\\u000a composite acting as the distributed actuator of
Nonlinear combining of laser beams Pavel M. Lushnikov* and Natalia Vladimirova
Lushnikov, Pavel
, 2014 We propose to combine multiple laser beams into a single diffraction-limited beam by beam self-focusing by strong self-focusing in a waveguide with Kerr nonlinearity. The number of laser beams can be arbitrary eventually trigger a strong self-focusing event and produce a diffraction-limited beam carrying the critical
Transverse instabilities and pattern formation in two-beam-excited nonlinear optical
Bentley, Sean
higher intensity, whole-beam self-focusing of each beam begins to be observable, but interaction whole-beam self-focusing and small-scale filamenta- tion, and two-beam-excited self-diffraction spots instabilities that occur when two laser beams intersect in nonlinear optical liquids. Patterns that we observe
Riemann problem for kinematical conservation laws and geometrical features of nonlinear wavefronts
NASA Astrophysics Data System (ADS)
Baskar, S.; Prasad, Phoolan
2004-08-01
A pair of kinematical conservation laws (KCL) in a ray coordinate system ({xi},t) are the basic equations governing the evolution of a moving curve in two space dimensions. We first study elementary wave solutions and then the Riemann problem for KCL when the metric g, associated with the coordinate {xi} designating different rays, is an arbitrary function of the velocity of propagation m of the moving curve. We assume that m>1 (m is appropriately normalized), for which the system of KCL becomes hyperbolic. We interpret the images of the elementary wave solutions in the ({xi},t)-plane to the (x,y)-plane as elementary shapes of the moving curve (or a nonlinear wavefront when interpreted in a physical system) and then describe their geometrical properties. Solutions of the Riemann problem with different initial data give the shapes of the nonlinear wavefront with different combinations of elementary shapes. Finally, we study all possible interactions of elementary shapes.
NASA Astrophysics Data System (ADS)
Tran, Loc V.; Lee, Jaehong; Nguyen-Van, H.; Nguyen-Xuan, H.; Wahab, M. Abdel
2015-06-01
In this paper, we present an effectively numerical approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of laminated composite plates. The HSDT allows us to approximate displacement field that ensures by itself the realistic shear strain energy part without shear correction factors. IGA utilizing basis functions namely B-splines or non-uniform rational B-splines (NURBS) enables to satisfy easily the stringent continuity requirement of the HSDT model without any additional variables. The nonlinearity of the plates is formed in the total Lagrange approach based on the von-Karman strain assumptions. Numerous numerical validations for the isotropic, orthotropic, cross-ply and angle-ply laminated plates are provided to demonstrate the effectiveness of the proposed method.
Geredeli, Pelin G., E-mail: pguven@hacettepe.edu.tr [Hacettepe University (Turkey); Webster, Justin T., E-mail: websterj@math.oregonstate.edu [Oregon State University (United States)
2013-12-15
We analyze the convergence to equilibrium of solutions to the nonlinear Berger plate evolution equation in the presence of localized interior damping (also referred to as geometrically constrained damping). Utilizing the results in (Geredeli et al. in J. Differ. Equ. 254:1193–1229, 2013), we have that any trajectory converges to the set of stationary points N . Employing standard assumptions from the theory of nonlinear unstable dynamics on the set N , we obtain the rate of convergence to an equilibrium. The critical issue in the proof of convergence to equilibria is a unique continuation property (which we prove for the Berger evolution) that provides a gradient structure for the dynamics. We also consider the more involved von Karman evolution, and show that the same results hold assuming a unique continuation property for solutions, which is presently a challenging open problem.
Feng Xu; Kuan Fang Ren; Xiaoshu Cai
2006-01-01
The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate
NONLINEAR EVOLUTION OF BEAM-PLASMA INSTABILITY IN INHOMOGENEOUS MEDIUM
Ziebell, L. F.; Pavan, J. [Instituto de Fisica, UFRGS, Porto Alegre, RS (Brazil); Yoon, P. H. [IPST, University of Maryland, College Park (United States); Gaelzer, R. [Instituto de Fisica e Matematica, UFPel, Pelotas, RS (Brazil)
2011-01-20
The problem of electron-beam propagation in inhomogeneous solar wind is intimately related to the solar type II and/or type III radio bursts. Many scientists have addressed this issue in the past by means of quasi-linear theory, but in order to fully characterize the nonlinear dynamics, one must employ weak-turbulence theory. Available numerical solutions of the weak-turbulence theory either rely on only one nonlinear process (either decay or scattering), or when both nonlinear terms are included, the inhomogeneity effect is generally ignored. The present paper reports the full solution of weak-turbulence theory that includes both decay and scattering processes, and also incorporating the effects of density gradient. It is found that the quasi-linear effect sufficiently accounts for the primary Langmuir waves, but to properly characterize the back-scattered Langmuir wave, which is important for eventual radiation generation, it is found that both nonlinear decay and scattering processes make comparable contributions. Such a finding may be important in the quantitative analysis of the plasma emission process with application to solar type II and/or type III radio bursts.
Nonlinear Evolution of Beam-plasma Instability in Inhomogeneous Medium
NASA Astrophysics Data System (ADS)
Ziebell, L. F.; Yoon, P. H.; Pavan, J.; Gaelzer, R.
2011-01-01
The problem of electron-beam propagation in inhomogeneous solar wind is intimately related to the solar type II and/or type III radio bursts. Many scientists have addressed this issue in the past by means of quasi-linear theory, but in order to fully characterize the nonlinear dynamics, one must employ weak-turbulence theory. Available numerical solutions of the weak-turbulence theory either rely on only one nonlinear process (either decay or scattering), or when both nonlinear terms are included, the inhomogeneity effect is generally ignored. The present paper reports the full solution of weak-turbulence theory that includes both decay and scattering processes, and also incorporating the effects of density gradient. It is found that the quasi-linear effect sufficiently accounts for the primary Langmuir waves, but to properly characterize the back-scattered Langmuir wave, which is important for eventual radiation generation, it is found that both nonlinear decay and scattering processes make comparable contributions. Such a finding may be important in the quantitative analysis of the plasma emission process with application to solar type II and/or type III radio bursts.
Online optimization of storage ring nonlinear beam dynamics
Huang, Xiaobiao
2015-01-01
We propose to optimize the nonlinear beam dynamics of existing and future storage rings with direct online optimization techniques. This approach may have crucial importance for the implementation of diffraction limited storage rings. In this paper considerations and algorithms for the online optimization approach are discussed. We have applied this approach to experimentally improve the dynamic aperture of the SPEAR3 storage ring with the robust conjugate direction search method and the particle swarm optimization method. The dynamic aperture was improved by more than 5 mm within a short period of time. Experimental setup and results are presented.
Investigation of the Geometric Accuracy of Proton Beam Irradiation 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
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.
Generation of linear and nonlinear propagation of three-Airy beams.
Liang, Yi; Ye, Zhuoyi; Song, Daohong; Lou, Cibo; Zhang, Xinzheng; Xu, Jingjun; Chen, Zhigang
2013-01-28
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
Combination instabilities and non-linear vibratory interactions in beam systems
Cartmell, Matthew Phillip
As an extension of previously reported work on effects of internal resonance on non-linear vibration of beams, it has been shown that for blade-like beams excited parametrically by support motion in the plane of maximum ...
Practical geometric calibration for helical cone-beam industrial computed tomography.
Zhang, Feng; Yan, Bin; Li, Lei; Xi, Xiaoqi; Jiang, Hua
2014-01-01
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
C. E. S. Cesnik; D. G. Opoku; F. Nitzsche; T. Cheng
2004-01-01
An active aeroelastic and aeroacoustic analysis of helicopter rotor systems is presented in this paper. It is a tightly coupled computational aeroelastic code that interfaces a particle-wake panel method code with an active nonlinear mixed variational intrinsic beam element code. In addition, a Ffowcs-Williams–Hawkings equation-based acoustic component is incorporated to complete the numerical implementation. The theory behind each component is
C. E. S. Cesnik; D. G. Opoku; F. Nitzsche; T. Cheng
2004-01-01
An active aeroelastic and aeroacoustic analysis of helicopter rotor systems is presented in this paper. It is a tightly coupled computational aeroelastic code that interfaces a particle-wake panel method code with an active nonlinear mixed variational intrinsic beam element code. In addition, a Ffowcs-Williams-Hawkings equation-based acoustic component is incorporated to complete the numerical implementation. The theory behind each component is
Evaluation and Correction of the Non-linear Distortion of CEBAF Beam Position Monitors
M. Spata, T.L. Allison, K.E. Cole, J. Musson, J. Yan
2011-09-01
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.
NASA Astrophysics Data System (ADS)
Wang, Pai; Shim, Jongmin; Bertoldi, Katia
2013-07-01
We investigate the effects of geometric and material nonlinearities introduced by deformation on the linear dynamic response of two-dimensional phononic crystals. Our analysis not only shows that deformation can be effectively used to tune the band gaps and the directionality of the propagating waves, but also reveals how geometric and material nonlinearities contribute to the tunable response of phononic crystals. Our numerical study provides a better understanding of the tunable response of phononic crystals and opens avenues for the design of systems with optimized properties and enhanced tunability.
An Alternative Theory of Plasma Emission: a Nonlinear Beam Instability
NASA Astrophysics Data System (ADS)
Yoon, Peter H.
1997-11-01
Emission of electromagnetic radiation at or near the plasma frequency and/or its harmonic is known as the plasma emission in the literature. A good example is the type III solar radio bursts. These emissions occur when streams of energetic electron from the Sun first excite electrostatic (primary) Langmuir waves, which are then either backscattered off thermal ions, thus creating a secondary Langmuir wave component, or decay into a pair of secondary Langmuir and ion acoustic waves. In the standard theory, the actual emission of electromagnetic radiation takes place as a result of nonlinear wave-wave interaction process: In the case of harmonic emission, the primary and secondary Langmuir waves coalesce to produce radiation at twice the plasma frequency, while for the emission at the fundamental, the primary Langmuir waves and ion sound waves interact to produce radiation near the plasma frequency. In this presentation, an alternative theory is discussed, in which the emission of radiatio takes place as a result of excitation of long wavelength modes by a nonlinear beam instability, which are converted to radiative electromagnetic modes by a nonlinear mode conversion process. Unlike the standard theories, the new theory predicts high radiation growth rate.
Nonlinear response of a beam under distributed moving contact load
NASA Astrophysics Data System (ADS)
Kang, B.; Tan, C. A.
2006-03-01
In this paper, the nonlinear behavior of a one-dimensional model of the disc brake pad is examined. The contact normal force between the disc brake pad lining and rotor is represented by a second order polynomial of the relative displacement between the two elastic bodies. The frictional force due to the sliding motion of the rotor against the stationary pad is modeled as a distributed follower-type axial load with time-dependent terms. By Galerkin discretization, the equation governing the transverse motion of the beam model is reduced to a set of extended Duffing system with quasi-periodically modulated excitations. Retaining the first two vibration modes in the governing equations, frequency response curves are obtained by applying a two-dimensional spectral balance method. For the first time, it is predicted that nonlinearity resulting from the contact mechanics between the disc brake pad lining and rotor can lead to a possible irregular motion (chaotic vibration) of the pad in the neighborhood of simple and parametric resonance. This chaotic behavior is identified and quantitatively measured by examining the Poincaré maps, Fourier spectra, and Lyapunov exponents. It is also found that these chaotic motions emerge as a result of successive Hopf bifurcations characterized by the torus breakdown and torus doubling routes as the excitation frequency varies. Various aspects of the numerical difficulties in the solution of the nonlinear equations are also discussed.
NASA Technical Reports Server (NTRS)
Norwood, D. S.; Shuart, Mark J.; Herakovich, Carl T.
1991-01-01
An analytical study of interlaminar stresses in unsymmetrically laminated plates is presented. The study examines the linear elastic, large deflection response of square laminated composite plates subjected to uniform thermal loading. Both cross-ply and angle-ply, symmetric and unsymmetric, laminates are examined to evaluate the effects of mismatch between adjacent layers in elastic constants and coefficients of thermal expansion. A geometrically nonlinear kinematic description is used to predict the large out-of-plane (transverse) deflections. The nonlinear, three-dimensional boundary value problems are formulated from elasticity theory and approximate solutions are determined using the finite element method. A global/local analysis procedure is used to obtain improved free edge stress predictions. For the laminates and loading conditions considered, the results indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses. These deflections also reduce interlaminar normal stresses in some laminates and increase these stresses for others. The results indicate that as the out-of-plane deflections become large, the differences in interlaminar stress predictions between linear and nonlinear theory can become quite large.
The wave energy flux of high frequency diffracting beams in complex geometrical optics
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
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.
Nonlinear Potential Model of Space-Charge Electron Beams
NASA Astrophysics Data System (ADS)
Litz, Marc Stuart
1995-01-01
This body of work is new and comprises theoretical analysis, numerical simulation and experimental investigations of the vircator, a tunable, compact, simply constructed, high power reflexing electron device that is used as a microwave source. A 1D theoretical model is formulated that is based on a time-varying, nonlinear potential to better understand the sensitivities of individual electron trajectories to macroscopic parameters of the system. Self -consistent 2D (space) and 3D(velocity) numerical PIC simulations are used to find common dynamical behavior that links the individual test-particle trajectories examined in the 1D nonlinear model with the experimental measurements of the final state of the electron trajectories. The experiment designed and built for these studies is unique and contrasts with other virtual cathode electron beam sources because it operates at lower voltage, and longer pulse width than previous forms of the device. The anode-cathode (AK) gap spacing is externally tunable expediting parametric studies. In addition, it is repetitively pulsed, which permits discrimination between single-shot anomalies and repeatable variation that often occurs in pulsed power experimental devices. These attributes distinguish this experimental apparatus from previous experimental platforms. This novel, repetitively pulsed device has particular relevance to the industrial and medical applications of rf. The approach followed in the present studies is (1) to investigate the dynamic behavior of individual test -particles in a simplified 1D, nonlinear, time-varying, potential; (2) utilize a 2D, self-consistent, electromagnetic PIC code to generate single particle trajectories subject to the collective effects of the electron beam; and (3) measure macroscopic quantities of voltage, current, electromagnetic fields, and electron flux in an experimental platform. Results of the 3D experiments are compared to predictions of the 1D and 2D models. Electron flux calculated in the 1D nonlinear potential model and the 2D PIC simulations agree well with experimental measurements. Classes of orbit trajectories integrated in the 1D model are common to those calculated in the 2D PIC code. Comparison of frequency content calculated and measured also show favorable overlap. Experimental observations are supported by analytic and numerical modelling. Experimental pulsewidth limitations do not permit a data stream (time-series) sufficient to make a clear estimate of the fractal dimension of the system, though the sensitivity of particle trajectory to initial conditions is clear. The nonlinear equation contains parameter regimes that generate chaotic solutions, however the parameter regime in which the device operates is not chaotic, merely sensitive to initial conditions. Random initial conditions that occur as a result of beam thermalization and nonuniform electron-emission at the surface of the cathode are present in the experiment. These characteristics alone do not explain the experimentally observed fluctuations in power and frequency. The time -varying nonlinear potential exhibits classes of particle trajectories that follow trends in the experimental results, fluctuations in particle asymptotic states, and particle motion sensitive to the shape of the virtual cathode. (Abstract shortened by UMI.).
Light beams with general direction and polarization: global description and geometric phase
R. Nityananda; S. Sridhar
2012-12-05
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^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^2 X C^2, the Cartesian product of a sphere and a two dimensional complex vector space. A Hopf map (i.e mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S^2 X S^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^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^2 X S^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.
Multiscale Reduced Order Models for the Geometrically Nonlinear Response of Complex Structures
NASA Astrophysics Data System (ADS)
Perez, Ricardo Angel
The focus of this investigation includes three aspects. First, the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting "large" deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology, successfully validated in recent years on simpler panel structures, by developing a novel identification strategy of the reduced order model parameters, that enables the consideration of the large number of modes needed for complex structures, and by extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. These novel developments are successfully validated on the nonlinear static and dynamic responses of a 9-bay panel structure modeled within Nastran. In addition, a multi-scale approach based on Component Mode Synthesis methods is explored. Second, an assessment of the predictive capabilities of nonlinear reduced order models for the prediction of the large displacement and stress fields of panels that have a geometric discontinuity; a flat panel with a notch was used for this assessment. It is demonstrated that the reduced order models of both virgin and notched panels provide a close match of the displacement field obtained from full finite element analyses of the notched panel for moderately large static and dynamic responses. In regards to stresses, it is found that the notched panel reduced order model leads to a close prediction of the stress distribution obtained on the notched panel as computed by the finite element model. Two enrichment techniques, based on superposition of the notch effects on the virgin panel stress field, are proposed to permit a close prediction of the stress distribution of the notched panel from the reduced order model of the virgin one. A very good prediction of the full finite element results is achieved with both enrichments for static and dynamic responses. Finally, computational challenges associated with the solution of the reduced order model equations are discussed. Two alternatives to reduce the computational time for the solution of these problems are explored.
Asghari-Khiavi, Mehdi; Safinejad, Feryal
2010-03-01
The geometrical parameters and static electric properties of several metal porphyrin halides, including Fe(III) porphine chloride (FePCl), Fe(III) porphine bromide (FePBr), Fe(III) tetraphenylporphine chloride (FeTPPCl), aluminum phthalocyanine chloride (AlPcCl), gallium(III) phthalocyanine chloride (GaPcCl), and manganese(III) phthalocyanine chloride (MnPcCl), were investigated using density functional theory (DFT) methods. It was observed that FePBr and MnPcCl showed the highest total hyperpolarisabilities among the studied porphyrins. To investigate the effect of substituted phenyl groups on the nonlinear optical (NLO) responses of porphyrins, the optical properties of FeTPPCl and FePCl were compared using UBLYP/cc-pVDZ+LanL2DZ level of theory. Moreover, the polarised continuum model (PCM) was employed to study the influence of solvation on the optical properties of FePCl. PMID:19655180
Filamentation and supercontinuum generation by singular beams in self-focusing nonlinear media
Dreischuh, Alexander
Filamentation and supercontinuum generation by singular beams in self-focusing nonlinear media, including dark crosses and optical vortices, in self-focusing nonlinear media, resulting in filamentation beams, optical vortex, self-focusing, filamentation I. INTRODUCTION The study of waves with spatial
Nonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor S. Skupin,1
Skupin, Stefan
Nonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor S. Skupin,1 M. Saffman,2 stabilizes the propagation of vortex beams and higher order modes in the presence of a self-focusing solitonic structures in the pres- ence of a self-focusing nonlinearity. We start the theoretical development
Ibrahim Eren
2008-01-01
In this study, large deflection of cantilever beams of Ludwick type material subjected to a combined loading consisting of\\u000a a uniformly distributed load and one vertical concentrated load at the free end was investigated. In calculations, both material\\u000a and geometrical non-linearity have been considered. Horizontal and vertical deflections magnitudes were calculated throughout\\u000a Euler-Bernoulli curvature-moment relationship assuming different arc lengths. Vertical
Alexander G. Kyriakos
2004-07-09
The present paper is the continuity of the previous papers "Non-linear field theory" I and II. Here on the basis of the electromagnetic representation of Dirac's electron theory we consider the geometrical distribution of the electromagnetic fields of the electron-positron. This gives the posibility to obtain the explanation and solution of many fundamental problems of the QED.
A simple four-node solid shell element for geometric non-linear static and dynamic analysis
Brian Lee Kemp
1999-01-01
A simple four-node solid shell finite element is developed for geometric non-linear static and dynamic analysis. The solid shell formulation differs from the more common degenerate solid shell formulation. The degenerate solid shell formulation uses rotational angles to describe the kinematics of deformation and requires a constant element thickness during deformation. The solid shell formulation replaces both limitations by using
Sven Klinkel; Werner Wagner
2008-01-01
The paper is focused on a piezoelectric solid shell finite element formulation. A geometrically nonlinear theory allows large deformations and includes stability problems. The formulation is based on a variational principle of the Hu–Washizu type including six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has eight nodes with displacements and the electric
Paradox of a nonlinear beam splitter and its resolution
Belinsky, A. V., E-mail: belinsky@inbox.ru; Volkov, D. V.; Dmitriev, A. V.; Shulman, M. Kh. [Moscow State University (Russian Federation)
2013-11-15
A nonlinear beam splitter is shown to be an interesting object of investigation for the following reasons. First, the classical and quantum theories of its description give directly opposite behaviors of the phase fluctuations: according to the classical theory, the phase is unchanged; according to the quantum theory, the phase fluctuations increase or decrease, depending on the suppression or growth of amplitude fluctuations. The fundamental cause of these differences has been established. Second, the quantum fluctuations of the input mode can be separated into the amplitude and phase ones, so that the predominantly phase fluctuations are directed into one output mode, say, the reflected one, while the amplitude fluctuations are directed into the other (transmitted) mode.
Ronald C. Davidson; W. Wei-li Lee; Hong Qin; Edward Startsev
2001-11-08
This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.
A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation
NASA Technical Reports Server (NTRS)
Crivelli, Luis A.; Felippa, Carlos A.
1992-01-01
A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.
Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. II. Forced Motions
M. R. M. Crespo da Silva; C. C. Glynn
1978-01-01
The nonplanar, nonlinear, resonant forced oscillations of a fixed-free beam are analyzed by a perturbation technique with the objective of determining quantitative and qualitative information about the response. The analysis is based on the differential equations of motion developed in Part I of this paper which retain not only the nonlinear inertia but also nonlinear curvature effects. It is shown
Fast Calculations in Nonlinear Collective Models of Beam/Plasma Physics
Antonina N. Fedorova; Michael G. Zeitlin
2002-12-31
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).
Light beams with general direction and polarization: Global description and geometric phase
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
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.
A higher-order theory for geometrically nonlinear analysis of composite laminates
NASA Technical Reports Server (NTRS)
Reddy, J. N.; Liu, C. F.
1987-01-01
A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.
NASA Technical Reports Server (NTRS)
Stoll, Frederick
1993-01-01
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.
Geometric Nonlinear Analysis of Self-Anchored Cable-Stayed Suspension Bridges
Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang
2013-01-01
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
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1986-01-01
The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.
A nonlinear mathematical model for large deflection of incompressible saturated poroelastic beams
Xiao Yang; Chen Wang
2007-01-01
Nonlinear governing equations are established for large deflection of incompressible fluid saturated poroelastic beams under\\u000a constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams. Then, the nonlinear bending\\u000a of a saturated poroelastic cantilever beam with fixed end impermeable and free end permeable, subjected to a suddenly applied\\u000a constant concentrated transverse load at
Non-linear optical measurements using a scanned, Bessel beam
NASA Astrophysics Data System (ADS)
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-03-01
Oftentimes cells are removed from the body for disease diagnosis or cellular research. This typically requires fluorescent labeling followed by sorting with a flow cytometer; however, possible disruption of cellular function or even cell death due to the presence of the label can occur. This may be acceptable for ex vivo applications, but as cells are more frequently moving from the lab to the body, label-free methods of cell sorting are needed to eliminate these issues. This is especially true of the growing field of stem cell research where specialized cells are needed for treatments. Because differentiation processes are not completely efficient, cells must be sorted to eliminate any unwanted cells (i.e. un-differentiated or differentiated into an unwanted cell type). In order to perform label-free measurements, non-linear optics (NLO) have been increasingly utilized for single cell analysis because of their ability to not disrupt cellular function. An optical system was developed for the measurement of NLO in a microfluidic channel similar to a flow cytometer. In order to improve the excitation efficiency of NLO, a scanned Bessel beam was utilized to create a light-sheet across the channel. The system was tested by monitoring twophoton fluorescence from polystyrene microbeads of different sizes. Fluorescence intensity obtained from light-sheet measurements were significantly greater than measurements made using a static Gaussian beam. In addition, the increase in intensity from larger sized beads was more evident for the light-sheet system.
Propagation of Lorentz—Gaussian Beams in Strongly Nonlocal Nonlinear Media
NASA Astrophysics Data System (ADS)
Keshavarz, A.; Honarasa, G.
2014-02-01
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.
Satish N. R. Remala
2005-01-01
Nonlinear parametric response of a flexible cantilever beam is simulated. In the simulations, lateral response of the beam due to an imposed axial harmonic base displacement excitation is calculated. The response frequency is approximately half the input frequency. The transient simulations include the assumption of damping proportional to the square of the velocity along the beam. Velocity-squared damping is realistic
Twin beams, nonlinearity, and walk-off in optical parametric oscillators
Roberta Zambrini; Maxi San Miguel
2002-01-01
We study the quantum properties of the spatially tilted macroscopic signal beams in the transverse pattern formed in a degenerate optical parametric oscillator above threshold. We show that walk-off leads to an imbalance in the intensities and fluctuations of these beams when nonlinear multimode interactions are effective. Still, quantum correlations between the two beams are preserved, so that their intensity
NASA Astrophysics Data System (ADS)
Kuang, Zheng; Li, Jiangning; Edwardson, Stuart; Perrie, Walter; Liu, Dun; Dearden, Geoff
2015-07-01
We have demonstrated an original ultrafast laser beam shaping technique for material processing using a spatial light modulator (SLM). Complicated and time-consuming diffraction far-field phase hologram calculations based on Fourier transformations are avoided, while simple and direct geometric masks are used to shape the incident beam at diffraction near-field. Various beam intensity shapes, such as square, triangle, ring and star, are obtained and then reconstructed at the imaging plane of an f-theta lens. The size of the shaped beam is approximately 20 ?m, which is comparable to the beam waist at the focal plane. A polished stainless steel sample is machined by the shaped beam at the imaging plane. The shape of the ablation footprint well matches the beam shape.
Spatial Distributions Of Acoustic Parameters In Nonlinear Focused Beams Of Various Geometry
NASA Astrophysics Data System (ADS)
Bessonova, Olga V.; Khokhlova, Vera A.
2008-06-01
In this work, numerical simulations are performed and spatial distributions of specific parameters of nonlinear focused ultrasound beams of various geometry are compared. The numerical algorithm is based on the solution of the Khokhlov-Zabolotskaya (KZ) equation. Focused acoustic beams of periodic waves with an initially uniform amplitude distribution, typical for medical therapeutic transducers, and with Gaussian amplitude shading are considered. Numerical solutions are obtained and analyzed for nonlinear acoustic field in various regimes of linear, quasilinear, and nonlinear propagation when shock fronts are developed in the waveform close to the focus and while propagating to the focus of the beam.
Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium
Ianetz, D.; Kaganovskii, Yu.; Rosenbluh, M. [Jack and Pearl Resnick Institute for Advanced Technology, Department of Physics, Bar-Ilan University, Ramat-Gan 52900 (Israel); Wilson-Gordon, A. D. [Department of Chemistry, Bar-Ilan University, Ramat Gan 52900 (Israel)
2010-05-15
Propagation of an asymmetric Gaussian beam in a cubic-quintic absorbing medium is analyzed and compared with that of a symmetric beam in both lossless and lossy media. A 'collective variable approach' technique, based on trial functions, is used for solution of the general nonlinear Schroedinger equation. Using this variational approach, we investigate the self-focusing and breathing of an intense asymmetric Gaussian beam, taking into account both linear and nonlinear absorption. For a lossless medium, we define regions of oscillatory and diffractive beam propagation, for both symmetric and asymmetric beams. In particular, for an asymmetric beam, we find that there is no sharp boundary between the oscillatory self-focusing and oscillatory diffractive regimes of propagation. In the oscillatory region, we detect an interesting phenomenon -'beats' of the amplitude and perpendicular widths of the beam. For a lossy medium, significant differences between the amplitudes, widths, and phases of the symmetric and asymmetric beams have been predicted.
Nonlinear transient response of a thick composite beam with shape memory alloy layers
M. M. Ghomshei; N. Tabandeh; A. Ghazavi; F. Gordaninejad
2005-01-01
This study presents a nonlinear transient finite element model for the elastodynamic response of thick shape memory alloy (SMA) composite beams. A three-dimensional thick beam with a matrix material and embedded SMA ribbons or wires is investigated. To predict the behavior of the beam, a higher-order shear-deformation beam theory and the von-Karman strain field are employed. A one-dimensional constitutive model
NASA Astrophysics Data System (ADS)
Foucard, Louis; Kazuo Price, Jordan; Klug, William; Levine, Alex
2015-03-01
Extending previous studies on the affine-nonaffine transition of nematically ordered semiflexible networks, we investigate numerically the effect of geometric non-linearities on the mechanical response of anisotropic networks of elastic filaments. We find that the strong dependence of buckling susceptibility on segment length has a pronounced effect on the nonlinear elastic behavior of anisotropic networks; contrary to isotropic networks, highly ordered ones show an important softening of the shear modulus at nonlinear (finite) strains. We compute the spatial correlation of the Conti/McKintosh buckling order parameter and show that the particularity of the nonlinear response of nematic networks resides in the cooperativity of the buckling events. We also show that dependence of the shear modulus on the nematic order parameter can be predicted using the assumption of affine deformation at small shear, and in terms of a generalized floppy mode analysis of the nonaffine mechanics at larger deformation.
Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu
2006-07-10
The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles. PMID:16807610
Application of image relaying to nonlinear beam distortion measurements and profile shaping
Shimada, T.; Kurnit, N.A
1995-12-31
Image relaying of the defining aperture in a top-hat z-scan technique allows both accurate nonlinear index measurements as well as controllable reshaping (for example, flattening) of the beam profile at the image plane.
Patil, Mayuresh
equations. Nonlinear beam analysis is required when analyzing helicopter blades1 or high-aspect-ratio wings The nonlinear, intrinsic, mixed equations for the dynamics of a general (non-uniform, twisted, curved-sectional frame. k(x) = k1(x) k2(x) k3(x) is the initial twist/curvature of the beam, e1 = 1 0 0 T . The first two
Weight optimization for flexural reinforced concrete beams with static nonlinear response
T. T. Chung; T. C. Sun
1994-01-01
The weight optimization of reinforced concrete (RC) beams with material nonlinear response is formulated as a general nonlinear optimization problem. Incremental finite element procedures are used to integrate the structural response analysis and design sensitivity analysis in a consistent manner. In the finite element discretization, the concrete is modelled by plane stress elements and steel reinforcement is modelled by discrete
Nonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor
Skupin, S.; Krolikowski, W. [Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200 (Australia); Saffman, M. [Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706 (United States)
2007-06-29
We show that ballistic transport of optically excited atoms in an atomic vapor provides a nonlocal nonlinearity which stabilizes the propagation of vortex beams and higher order modes in the presence of a self-focusing nonlinearity. Numerical experiments demonstrate stable propagation of higher order nonlinear states (dipole, vortices, and rotating azimuthons) over a hundred diffraction lengths, before dissipation leads to decay of these structures.
A. V. Mamaev; M. Saffman; A. A. Zozulya
1996-01-01
We analyze the evolution of \\\\(1+1\\\\) dimensional dark stripe beams in bulk media with a photorefractive nonlinear response. These beams, including solitary wave solutions, are shown to be unstable with respect to symmetry breaking and formation of structure along the initially homogeneous coordinate. Experimental results show the complete sequence of events starting from self-focusing of the stripe, its bending due
Modeling of wireless remote shape control for beams using nonlinear photostrictive actuators
Dongchang Sun; Liyong Tong
2007-01-01
Photostrictive materials produce mechanical strain when irradiated by ultraviolet light, thus may be used in wireless remote control of smart microstructures. This paper presents an investigation into modelling and static shape control of beams with nonlinear photostrictive actuators. Governing equations of beams bonded with photostrictive actuator patches are derived to study the interaction between the photostrictive actuators and the host
Shen, Ming; Gao, Jinsong; Ge, Lijuan
2015-01-01
We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878
Shen, Ming; Gao, Jinsong; Ge, Lijuan
2015-01-01
We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878
NASA Astrophysics Data System (ADS)
Abd El Baky, Hussien
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.
Daniel G. Opoku; Fred Nitzsche
This paper describes the validation of a new code for predicting both aeroacoustic and aeroelastic behaviour of hingeless rotors. The structural component was based a non-linear beam element model considering small strains and finite rotations, which uses a mixed variational intrinsic formulation. The aerodynamic component was built on a low- order panel method incorporating a vortex particle free-wake model. The
Farr, J. B.; Schoenenberg, D. [Westdeutsches Protonentherapiezentrum Essen, Universitaetsklinikum-Essen, Hufelandstrasse 55, 45147 Essen (Germany); Dessy, F.; De Wilde, O.; Bietzer, O. [Ion Beam Applications, Chemin du Cyclotron, 3, 1348 Louvain-la-Neuve (Belgium)
2013-07-15
Purpose: The purpose of this investigation was to compare and contrast the measured fundamental properties of two new types of modulated proton scanning systems. This provides a basis for clinical expectations based on the scanned beam quality and a benchmark for computational models. Because the relatively small beam and fast scanning gave challenges to the characterization, a secondary purpose was to develop and apply new approaches where necessary to do so.Methods: The following performances of the proton scanning systems were investigated: beamlet alignment, static in-air beamlet size and shape, scanned in-air penumbra, scanned fluence map accuracy, geometric alignment of scanning system to isocenter, maximum field size, lateral and longitudinal field uniformity of a 1 l cubic uniform field, output stability over time, gantry angle invariance, monitoring system linearity, and reproducibility. A range of detectors was used: film, ionization chambers, lateral multielement and longitudinal multilayer ionization chambers, and a scintillation screen combined with a digital video camera. Characterization of the scanned fluence maps was performed with a software analysis tool.Results: The resulting measurements and analysis indicated that the two types of delivery systems performed within specification for those aspects investigated. The significant differences were observed between the two types of scanning systems where one type exhibits a smaller spot size and associated penumbra than the other. The differential is minimum at maximum energy and increases inversely with decreasing energy. Additionally, the large spot system showed an increase in dose precision to a static target with layer rescanning whereas the small spot system did not.Conclusions: The measured results from the two types of modulated scanning types of system were consistent with their designs under the conditions tested. The most significant difference between the types of system was their proton spot size and associated resolution, factors of magnetic optics, and vacuum length. The need and benefit of mutielement detectors and high-resolution sensors was also shown. The use of a fluence map analytical software tool was particularly effective in characterizing the dynamic proton energy-layer scanning.
Nonlinear beam-based vibration energy harvesters and load cells
Kluger, Jocelyn Maxine
2014-01-01
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 ...
NASA Technical Reports Server (NTRS)
Stricklin, J. A.; Haisler, W. E.; Von Riesemann, W. A.
1972-01-01
This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.
Vibrations in an elastic beam with nonlinear supports at both ends
NASA Astrophysics Data System (ADS)
Wang, Yi-Ren; Fang, Zhi-Wei
2015-03-01
Vibrations in an elastic beam supported by nonlinear supports at both ends under the influence of harmonic forces are analyzed in this study. It is hypothesized that the elastic Bernoulli-Euler beam is supported by cubic springs to simulate nonlinear boundary conditions. The dynamic behavior of the beam is described by using the Fourier expansion and the Bessel functions. The Hankel transform is then applied to obtain particular (nonhomogeneous) solutions. This study succeeds in describing the "jump" phenomenon (instantaneous transition of the system from one position to another) of the vibrating system at certain frequencies. Models based on linear boundary conditions are unable to capture this phenomenon. A larger modulus of elasticity in nonlinear supports increases the frequency of unstable vibrations in the first mode and also widens the frequency region of system instability. This influence is less prominent in the second mode, in which the largest amplitude is smaller than those observed in the first mode.
On the nonlinearity of the Langmuir turbulence excited by a weak electron beam-plasma interaction
Nariyuki, Y. [Department of Electrical Engineering and Information Science, Kochi National College of Technology, Kochi 783-8508 (Japan); Umeda, T. [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8601 (Japan)
2010-05-15
In the present study, we analyze the data sets produced by a one-dimensional Vlasov-Poisson simulation of the weak electron beam-plasma instability to clarify the nonlinearity of the Langmuir turbulence excited by the weak-beam interaction. The growth of wave number modes is analyzed by using the momentum equation of the whole electrons. The analysis shows that the primary Langmuir wave mode is almost linear, while the nonlinear terms play important roles in the growth of the lower harmonic mode and the secondary higher harmonic mode. After the linear growth saturates, while the wave power of the primary mode is much larger than the other modes, linear and nonlinear interactions occurring in both lower harmonic and secondary higher harmonic modes are more active than those in the primary mode. Nonlinearity in the system comes from the advection rather than the ponderomotive forces.
NASA Astrophysics Data System (ADS)
Cho, Yeong-Kwon; Kim, Kihong
2014-12-01
The propagation of optical vortex beams through disordered nonlinear photonic lattices is numerically studied. The vortex beams are generated by using a superposition of several Gaussian laser beams arranged in a radially-symmetric manner. The paraxial nonlinear Schrödinger equation describing the longitudinal propagation of the beam array through nonlinear triangular photonic lattices with two-dimensional disorder is solved numerically by using the split-step Fourier method. We find that due to the spatial disorder, the vortex beam is destabilized after propagating a finite distance and new vortex-antivortex pairs are nucleated at the positions of perfect destructive interference. We also find that in the presence of a self-focusing nonlinearity, the vortex-antivortex pair nucleation is suppressed and the vortex beam becomes more stable, while a self-defocusing nonlinearity enhances the vortex-antivortex pair nucleation.
Edward A. Startsev; Ronald C. Davidson; Hong Qin
2002-05-07
In this paper, a 3-D nonlinear perturbative particle simulation code (BEST) [H. Qin, R.C. Davidson and W.W. Lee, Physical Review Special Topics on Accelerators and Beams 3 (2000) 084401] is used to systematically study the stability properties of intense nonneutral charged particle beams with large temperature anisotropy (T{sub {perpendicular}b} >> T{sub {parallel}b}). The most unstable modes are identified, and their eigen frequencies, radial mode structure, and nonlinear dynamics are determined for axisymmetric perturbations with {partial_derivative}/{partial_derivative}{theta} = 0.
NASA Astrophysics Data System (ADS)
Nili Ahmadabadi, Z.; Khadem, S. E.
2014-09-01
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.
Production of uniform and well-confined beams by nonlinear optics
Blind, B.
1990-01-01
Particle beams with uniform and well-confined intensity distributions are desirable for medical treatments, food irradiation an ion implantation. Moreover, such beams are essential in the development of high-intensity accelerators to prevent target damage and optimize target efficiency. One accepted method for beam redistribution employs nonlinear beamline elements, in particular octupoles and to a lesser degree magnets of even higher odd multipolarity. The method is not limited to the production of uniform beam distributions. The development of this field is reviewed. Beam redistribution is explained and the degree of uniformity and confinement achievable under various conditions is discussed. A method for tuning the size of the irradiation area is presented. A possible alternative to the use of combined-function multipoles is given. The effect of beam jitter on the distribution is considered. Applications of the method are given as examples throughout.
Three-dimensional beam propagation analysis of nonlinear optical fibers and optical logic gates
Akira Niiyama; Masanori Koshiba
1998-01-01
A three-dimensional (3-D) beam propagation method is described for the analysis of nonlinear optical fibers, where the finite element and finite difference methods are, respectively, utilized for discretizing the fiber cross section and the propagation direction. For efficient evaluation of wide-angle beam propagation Pade approximation is applied to the differential operator along the propagation direction. In order to improve the
Random vibration of nonlinear beams by the new stochastic linearization technique
NASA Technical Reports Server (NTRS)
Fang, J.
1994-01-01
In this paper, the beam under general time dependent stationary random excitation is investigated, when exact solution is unavailable. Numerical simulations are carried out to compare its results with those yielded by the conventional linearization techniques. It is found that the modified version of the stochastic linearization technique yields considerably more accurate results for the mean square displacement of the beam than the conventional equivalent linearization technique, especially in the case of large nonlinearity.
Fardad, Shima; Mills, Matthew S; Zhang, Peng; Man, Weining; Chen, Zhigang; Christodoulides, D N
2013-09-15
We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions. PMID:24104820
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
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.
Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D
NASA Astrophysics Data System (ADS)
Shen, Wei; Fu, G. Y.; Tobias, Benjamin; Zeeland, Michael Van; Wang, Feng; Sheng, Zheng-Mao
2015-04-01
In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.
Nonlinear Models of Reinforced and Post-tensioned Concrete Beams
P. Fanning
2001-01-01
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
Nonlinear Potential Model of Space-Charge Electron Beams
Marc Stuart Litz
1995-01-01
This body of work is new and comprises theoretical analysis, numerical simulation and experimental investigations of the vircator, a tunable, compact, simply constructed, high power reflexing electron device that is used as a microwave source. A 1D theoretical model is formulated that is based on a time-varying, nonlinear potential to better understand the sensitivities of individual electron trajectories to macroscopic
Application of nonlinear finite strip technique to concrete deep beams
Mohammed Raoof
1995-01-01
The salient features of an alternative version of the nonlinear finite strip method for analysing reinforced concrete elements is presented. Unlike the conventional finite strip models which can only handle structures whose geometry does not change in one direction, the newly developed finite strip model can analyse certain structures whose geometry (although still fairly simple) can change along their length
Beam loading in the nonlinear regime of plasma-based acceleration
NASA Astrophysics Data System (ADS)
Tzoufras, Michail
2008-11-01
An analytical theory for the interaction of a negatively charged bunch with a nonlinear plasma wave is developed to make it possible to design efficient laser- and/or beam-driven accelerators that generate truly monoenergetic electron beams. This theory allows us to choose the charge, the shape and the placing of the beam so that the efficiency is maximized and the beam quality optimized. For intense drivers the nonlinear wake is described by the trajectory of the blowout radius and beam loading arises when the radial space-charge force of the beam acts back on the trajectory. Starting from the nonlinear theory by W. Lu et al. [1], an equation for the wakefield in the presence of an electron bunch is derived. The shape of the ion channel in an unloaded wake is determined and the modification of the wake due to the presence of flat-top electron bunches is studied. It is shown that the energy spread of an externally injected flat-top (or Gaussian) electron bunch can be kept low by choosing the correct charge per unit length and the analytical results are confirmed with PIC simulations. The bunch profile that leads to zero energy spread is found to be trapezoidal. The conversion efficiency from the fields of the bubble to the accelerating electrons is determined, and it is shown that for optimal bunches it approaches 100%. The differences between nonlinear and linear [2] theory are described and the advantages of operating in the nonlinear regime are discussed. [1] W. Lu et al., Phys. Rev. Lett. 96, 165002 (2006); Phys. Plasmas 13, 056709 (2006). [2] T. Katsouleas et al., Particle Accelerators, 1987, 22, pp. 81-99.
Nariyuki, Y. [Faculty of Human Development, University of Toyama, 3190, Toyama City, Toyama 930-8555 (Japan); Hada, T. [Department of Earth System Science and Technology, Kyushu University, 6-1, Kasuga City, Fukuoka 816-8580 (Japan); Tsubouchi, K. [Department of Earth and Planetary Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033 (Japan)
2012-08-15
In the present study, the dissipation processes of circularly polarized Alfven waves in solar wind plasmas including beam components are numerically discussed by using a 2-D hybrid simulation code. Numerical results suggest that the parent Alfven waves are rapidly dissipated due to the presence of the beam-induced obliquely propagating waves, such as kinetic Alfven waves. The nonlinear wave-wave coupling is directly evaluated by using the induction equation for the parent wave. It is also observed both in the 1-D and 2-D simulations that the presence of large amplitude Alfven waves strongly suppresses the beam instabilities.
NASA Astrophysics Data System (ADS)
Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Pang, Zhaoguang; Zhang, Shumin
2015-06-01
In this paper, using the rotating coordinates, we take the anomalous hollow Gaussian beam as an example to investigate the evolution of an ellipse-symmetric beam in strongly nonlocal nonlinear media. A set of analytical expressions are obtained and some numerical simulations are carried out to illustrate the relation between the evolution characteristics and the rotation angle. It is found that the evolution properties, such as the critical powers, beam widths, and intensity distributions in x and y directions, are all variational with the rotation angle.
Studies of Linear and Non-Linear Beam Transmission in Plasmas Driven with Multiple Laser Beams
NASA Astrophysics Data System (ADS)
Kirkwood, R. K.; Moody, J. D.; Niemann, C.; Cohen, B. I.; Williams, E. A.; Dorr, M. R.; Hittinger, J. A.; Meezan, N.; Berger, R. L.; Suter, L. J.; Divol, L.; Glenzer, S. H.; Landen, O. L.; Wurtele, J.; Charman, A. E.; Lindberg, R.; Fisch, N. J.; Malkin, V. M.
2003-10-01
Measurements of beam transmission in laser driven plasmas are essential for the understanding of the efficiency and symmetry of the drive in ICF and are also allowing development of multi-beam interactions for control of the temporal and spatial profiles of power deposition in laser experiments. Recent efforts in this area include 1) the deployment of the transmitted beam diagnositic (TBD) on the Omega laser to measure power transmission and beam spreading of the 527 nm beam, 2) the study of the effect of ion wave damping on energy transfer between two 351 nm beams in a flowing plasma produced by Omega [1], and 3) development of beam amplification and pulse compression by Raman scattering [2] using the Janus laser. We will describe experiments in which the transmission of a 351 nm beam is enhanced by resonant interaction with a second identical beam in a hot (> 1 keV) plasma with a Mach 1 flow, and the effect of varying the plasma composition from CH to Al (and hence the damping rate of the ion acoutic wave from 10studied at different laser intensities for comparison with wave saturation models. Separate experiments in which an ultra-short pulse 1124 nm beam interacts with a 1 ns pulse 1064 nm beam in low temperature plasma (< 100 eV) which has its density adjusted to match the resonance for simulating plasma waves will also be discussed, and evidence of amplification of the ultra-short pulse beam by the long pulse beam will be presented. Finally initial results from transmission measurements of a 527 nm beam in a hot, 2mm scale plasma will be discussed as available. [1] R. K. Kirkwood, et al., Phys. Rev. Lett. 89, 215003-1 (2002) [2] Malkin, et. al. Phys. Rev. Lett 82, 4448 (1999),
Geometrically nonlinear static and dynamic analysis of functionally graded skew plates
NASA Astrophysics Data System (ADS)
Upadhyay, A. K.; Shukla, K. K.
2013-08-01
The present paper deals with nonlinear static and dynamic behavior of functionally graded skew plates. The equations of motion are derived using higher order shear deformation theory in conjunction with von-Karman's nonlinear kinematics. The physical domain is mapped into computational domain using linear mapping and chain rule of differentiation. The spatial and temporal discretization is based on fast converging finite double Chebyshev series and Houbolt's method. Quadratic extrapolation technique is employed to linearize the governing nonlinear equations. The spatial and temporal convergence and validation studies have been carried out to establish the efficacy of the present solution methodology. In case of dynamic analysis, the results are obtained for uniform step, sine, half sine, triangular and exponential type of loadings. The effect of volume fraction index, skew angle and boundary conditions on nonlinear displacement and moment response are presented.
Simulations of the nonlinear Helmholtz equation: arrest of beam collapse,
Fibich, Gadi
.5940) Self-action ef- fects References and links 1. P. L. Kelley, "Self-Focusing of Optical Beams," Phys. Rev. Lett. 15, 1005 (1965). 2. G. A. Askar'yan, "Self-Focusing Effect," Sov. Phys. JETP 15, 1088 (1962). 3. Y. Shen, "Self-focusing: Experimental," Prog. Quantum Electron. 4, 1 (1975). 4. A. Barthelemy, S
Nonlinear natural frequencies of an elastically restrained tapered beam
M. Abdel-Jaber; A. A. Al-Qaisia; R. G. Beale
2008-01-01
This paper presents the results of an analysis of an elastically restrained tapered cantilever beam using the harmonic balance and the time transformation methods. The results of the analysis show that the frequencies obtained from a two-term harmonic balance analysis are the most accurate and that the frequencies of the first and second modes of vibration change from a hardening
ac electrokinetic micropumps: The effect of geometrical confinement, Faradaic current injection demonstrated that ac electrokinetic micropumps permit integrable, local, and fast pumping velocities mm-on-a-chip systems require micropumps and valves to manipulate small volumes of a liquid sample 1 . Often large
NON-LINEAR BEAM OSCILLATIONS EXCITED BY LATERAL FORCE AT COMBINATION RESONANCE
K. V. Avramov
2002-01-01
Non-linear oscillations of a beam subjected to a periodic force at a combination resonance are considered. Using the Galerkin method, a partial differential equation of oscillations is reduced to a system of ordinary differential equations with a small parameter. A system of three autonomous differential equations is derived, the multiple scales method being used. Qualitative properties of trajectories are analyzed.
Input-Output Linearisation of Nonlinear Systems with Ill-Defined Relative Degree: The Ball & Beam
Duffy, Ken
Input-Output Linearisation of Nonlinear Systems with Ill-Defined Relative Degree: The Ball & Beam systems with ill- defined relative degree. In SISO systems, lack of well- defined relative degree for the output to be directly coupled to the input. (In the MIMO case, relative degree may also be ill- defined
Nonlinear Thomson scattering of intense laser pulses from beams and plasmas
Eric Esarey; Sally K. Ride; Phillip Sprangle
1993-01-01
A comprehensive theory is developed to describe the nonlinear Thomson scattering of intense laser fields from beams and plasmas. This theory is valid for linearly or circularly polarized incident laser fields of arbitrary intensities and for electrons of arbitrary energies. Explicit expressions for the intensity distributions of the scattered radiation are calculated and numerically evaluated. The space-charge electrostatic potential, which
Nonlinear plasma waves excitation by intense ion beams in background plasma
Kaganovich, Igor
Nonlinear plasma waves excitation by intense ion beams in background plasma Igor D. Kaganovich, Edward A. Startsev, and Ronald C. Davidson Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 Received 2 February 2004; accepted 6 April 2004 Plasma neutralization of an intense
The cubic nonlinear theory of plasma-beam superheterodyne free electron laser of dopplertron type
V. V. Kulish; A. V. Lysenko; V. V. Koval
2008-01-01
The multiharmonical cubic nonlinear theory of plasma-beam superheterodyne free electron laser of dopplertron type is constructed. The unusual retarded electromagnetic wave is used as a pumping wave. Multi-harmonious interaction of waves is taken into consideration. Analysis of the levels and mechanisms of saturation is carried out. It is found that prospects of practical use of the considered systems for generation
Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams
Nikolas C. Logan and Ronald C. Davidson
2012-07-18
This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (TllT? < 1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in accelerated particle beams, including Harris-type electrostatic instabilities, known to limit the luminosity and minimum spot size attainable in experiments. The thermodynamic bound on the field perturbation energy of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an arbitrary initial distribution function, including the effects of intense self-fields, finite geometry and nonlinear processes. This paper also includes analytical estimates of the nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic bi-Maxwellian distributions.
High Current Electron Beam Emission Driven by a Nonlinear Transmission Line
NASA Astrophysics Data System (ADS)
French, David; Hoff, Brad; Heidger, Susan
2014-10-01
Simulations of an electron beam diode driven by a modulated voltage pulse provided by a nonlinear transmission line (NLTL) will be presented. Based on a previous low voltage experiment the new design operates at 250 kV and provides a multi-kA modulated electron beam based on the modulated drive signal from a ferrite based NLTL. The NLTL driver has been demonstrated experimentally and is tunable from 900-1400 MHz with pulse durations from 4-17 ns. Particle-In-Cell simulations in ICEPIC show the modulated voltage signal results in a modulated electron beam current emitted directly from the cathode in a few cm annular beam. Expected results and the experimental design for the electron beam diode and diagnostics will also be presented.
Nonlinear Interaction of a Powerful Oblique Wave Beam with the Ionosphere Layer F2.
NASA Astrophysics Data System (ADS)
Atamaniuk, Barbara; Rothkaehl, Hanna; Anatolevich Molotkov, Ivan; Popov, Alexei
2013-04-01
The presentation is devoted to modeling oblique sounding of the ionosphere layer F2 by powerful wave beams. Part of its energy propagates trough the ionospheric layer, the other part goes back along a downward trajectory. However, nonlinearity leads to further stratification of the ionospheric layer. A new feature, in comparison with the linear case, is appearing a narrow waveguide beneath the F2 layer maximum which traps a small part of the beam energy. • We study the relationship between these parts of the wave field in a simplified model of parabolic F2 layer, with nonlinearity caused by thermal plasma expulsion from the high field intensity region. • We model and analyze of the interaction of a powerful obliquely incident wave beam of decameter radio waves with the ionospheric layer F2. Oblique propagation of a powerful HF wave beam in the ionospheric F2 layer leads to additional plasma stratification, in particular to the formation of an artificial waveguide controlled by the beam intensity. We show that formation of the artificial waveguide is a nonlinear effect. The problem of efficient feeding the artificial waveguide depends on the ability to create in the F2 layer high values of the HF electric field compared with the characteristic "plasma fields". Analytical results are supplemented with numerical estimates of the effects. The proposed investigation can be used in Space Weather Services.
General nonlinear mechanics of an electron beam driven multimode plasma system
McCowan, R.B.
1986-01-01
The general nonlinear behavior of the beam driven multimode system is examined. The linearized dispersion for a beam plasma is reviewed, and the new features of linear theory needed to explain the behavior for the plasma with two oppositely directed beams are derived. The dispersion relation and an extension of van der Pol theory are used to develop nonlinear-amplitude rate equations for the plasma. Where quantitative comparison is possible, agreement between the model and the experimental behavior is within the expected ranges. Important qualitative features of the nonlinear multimode system, mode locking, and entrainment are observed in the model and in the experiment. An apparatus for experimental test of the model was built. The components of the system included a vacuum vessel, magnets to guide the electron beam and confine the plasma, and an electron gun to provide the electron beam. Diagnostics used in the experiment were also built and include probes, a microwave resonance shift cavity, and a retarding field energy analyzer. Data were collected and recorded by single channel superheterodyne receivers, spectrum analyzers, and a Data Precision D6000 - a digital waveform acquisition and analysis system. An Apple Macintosh computer is used to communicate with the D6000, and details of the communication between the D6000 and the Macintosh are presented.
Elasto-dynamics of multihulls in nonlinear beam seas-a multibody-BEM approach
NASA Astrophysics Data System (ADS)
Kral, R.; Kreuzer, E.; Schlegel, V.
2003-05-01
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.
White-Noise and Geometrical Optics Limits of Wigner-Moyal Equation for Wave Beams in Turbulent Media
NASA Astrophysics Data System (ADS)
Fannjiang, Albert C.
2005-03-01
Starting with the Wigner distribution formulation for beam wave propagation in Hölder 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 Itô 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.
NASA Astrophysics Data System (ADS)
Liu, Peipei; Sohn, Hoon; Park, Byeongjin
2015-06-01
Damage often causes a structural system to exhibit severe nonlinear behaviors, and the resulting nonlinear features are often much more sensitive to the damage than their linear counterparts. This study develops a laser nonlinear wave modulation spectroscopy (LNWMS) so that certain types of damage can be detected without any sensor placement. The proposed LNWMS utilizes a pulse laser to generate ultrasonic waves and a laser vibrometer for ultrasonic measurement. Under the broadband excitation of the pulse laser, a nonlinear source generates modulations at various frequency values due to interactions among various input frequency components. State space attractors are reconstructed from the ultrasonic responses measured by LNWMS, and a damage feature called Bhattacharyya distance (BD) is computed from the state space attractors to quantify the degree of damage-induced nonlinearity. By computing the BD values over the entire target surface using laser scanning, damage can be localized and visualized without relying on the baseline data obtained from the pristine condition of a target structure. The proposed technique has been successfully used for visualizing fatigue crack in an aluminum plate and delamination and debonding in a glass fiber reinforced polymer wind turbine blade.
Geometrically nonlinear free vibrations of simply supported isotropic thin circular plates
NASA Astrophysics Data System (ADS)
Haterbouch, M.; Benamar, R.
2005-02-01
Nonlinear free axisymmetric vibration of simply supported isotropic circular plates is investigated by using the energy method and a multimode approach. In-plane deformation is included in the formulation. Lagrange's equations are used to derive the governing equation of motion. Using the harmonic balance method, the equation of motion is converted into a nonlinear algebraic form. The numerical iterative method of solution adopted here is the so-called linearized updated mode method, which permits the authors to obtain accurate results for vibration amplitudes up to three times the plate thickness. The percentage of participation of each out-of-plane basic function to the deflection shape and to the bending stress at the plate centre and of each in-plane basic function to the membrane stress at the centre are calculated in order to determine the minimum number of in- and out-of-plane basic functions to be used in order to achieve a good accuracy of the model. The nonlinear frequency, the nonlinear fundamental mode shape and their associated nonlinear bending and membrane stresses are determined at large amplitudes of vibration. The numerical results obtained here are presented and compared with available published results, based on various approaches and with the single-mode solution. The limit of validity of the single-mode approach is also investigated.
G. M. Kulikov; S. V. Plotnikova
2007-01-01
This paper presents a family of geometrically exact assumed stress–strain four-node solid-shell elements with six displacement degrees of freedom per node based on the finite rotation first-order multilayered shell theory. The proposed formulation is based on the new objective non-linear strain–displacement relationships, which are invariant under arbitrarily large rigid-body motions. To improve a non-linear shell response, the modified assumed natural
Effect of Geometric Azimuthal Asymmetrics of PPM Stack on Electron Beam Characteristics
NASA Technical Reports Server (NTRS)
Kory, Carol L.
2000-01-01
A three-dimensional (3D) beam optics model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA. The model includes an electron beam with initial transverse velocity distribution focused by a periodic permanent magnet (PPM) stack. All components of the model are simulated in three dimensions allowing several azimuthally asymmetric traveling wave tube (TWT) characteristics to be investigated for the first time. These include C-magnets, shunts and magnet misalignment and their effects on electron beam behavior. The development of the model is presented and 3D TWT electron beam characteristics are compared in the absence of and under the influence of the azimuthally asymmetric characteristics described.
NASA Astrophysics Data System (ADS)
Sommer, S.; Stober, G.; Chau, J. L.; Latteck, R.
2014-11-01
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.
Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion
Arie, Ady
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
Gong, He; Zhang, Ming; Fan, Yubo; Kwok, Wai Leung; Leung, Ping Chung
2012-07-01
Precise quantification of femur strength and accurate assessment of hip fracture risk would help physicians to identify individuals with high risk and encourage them to take preventive interventions. A major contributing factor of hip fracture is the reduction of hip strength, determined by the bone quality. Bone mineral density (BMD) alone cannot determine bone strength accurately. In this paper, subject-specific quantitative computer tomography (QCT) image-based finite element analyses were conducted to identify the quantitative relationships between femoral strength and BMD, material distribution and geometric morphology. Sixty-six subjects with QCT data of hip region were selected from the MrOS cohorts in Hong Kong. Subject-specific nonlinear finite element models were developed to predict strengths of proximal femurs. The models took non-linear elasto-plasticity and heterogeneity of bone tissues into consideration and derived bone strengths with proper bone failure criteria. From finite element analysis (FEA), relationships between femoral strength and BMD, material distribution, and geometric parameters were determined. Results showed that FEA-predicted femoral strength was highly correlated with BMD, material distribution, height, weight, diameters of femoral head (HD), and femoral neck (ND), as well as the moment arm for femoral neck bending-offset (OFF). Through principal components analysis, three independent principal components (PCs) were extracted. PC1 was the component of bone material quality. PC2 included height, weight, HD, and ND. PC3 mainly represented OFF. Multivariate linear regression showed that the PCs were strongly predictive of the FEA-predicted strength. This study provided quantitative information regarding the contributing factors of proximal femur strength and showed that such a biomechanical approach may have clinical potential in noninvasive assessment of hip fracture risk. PMID:22258889
Luiz A. Duarte Filho; Armando M. Awruch
2004-01-01
An eight-node hexahedral isoparametric finite element with uniform reduced integration, which is free of volumetric and shear locking and has no spurious singular modes, is implemented in this work for geometrically nonlinear static and dynamic structural analysis. In the element formulation, one-point quadrature is used, so that the element tangent stiffness matrix is given explicitly and computational time is substantially
Feng, Zexin; Froese, Brittany D; Huang, Chih-Yu; Ma, Donglin; Liang, Rongguang
2015-07-10
We consider here creation of an unconventional flattop beam with a large depth of field by employing double freeform optical surfaces. The output beam is designed with continuous variations from the flattop to almost zero near the edges to resist the influence of diffraction on its propagation. We solve this challenging problem by naturally incorporating an optimal transport map computation scheme for unconventional boundary conditions with a simultaneous point-by-point double surface construction procedure. We demonstrate experimentally the generation of a long-range propagated triangular beam through a plano-freeform lens pair fabricated by a diamond-tuning machine. PMID:26193404
NASA Astrophysics Data System (ADS)
Sahmani, S.; Bahrami, M.; Ansari, R.
2014-12-01
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.
Rigid Element Concept for Geometric Nonlinear Analysis of Structures Involving Postbuckling Response
Y. B. Yang
In the incremental-iterative analysis of elastic nonlinear structures, great saving in computation can be achieved if distinction\\u000a is made between the predictor and corrector phases. The predictor relates to solution of the structural displacements for given load increments, which affects only the\\u000a number of iterations. For the sake of iteration, the equations used in the predictor need not be exact,
Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma
Wang Yunliang [International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum (Germany); Department of Physics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 (China); Shukla, P. K. [International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum (Germany); Department of Mechanical and Aerospace Engineering and Center for Energy Research, University of California San Diego, La Jolla, California 92093 (United States); School of Chemistry and Physics, KwaZulu-Natal University, Durban 4000 (South Africa); Eliasson, B. [International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum (Germany)
2013-01-15
We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schroedinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.
Results of including geometric nonlinearities in an aeroelastic model of an F/A-18
NASA Technical Reports Server (NTRS)
Buttrill, Carey S.
1989-01-01
An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.
Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres
NASA Astrophysics Data System (ADS)
Zhang, Likun; Marston, Philip L.
2011-09-01
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.
NASA Astrophysics Data System (ADS)
Egorov, E. N.; Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E.
2013-11-01
Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.
Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionisation
Vlasov, R A [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus); Khasanov, O Kh; Smirnova, T V [Institute of Solid-State and Semiconductor Physics, National Academy of Sciences of Belarus, Minsk (Belarus)
2005-10-31
The dynamics of a high-power femtosecond tubular pulsed beam in a dielectric medium is numerically analysed upon optically induced ionisation. It is found that the balance between nonlinearities of opposite sign and different magnitude in the case of multiphoton ionisation favours the establishment of a quasi-soliton regime of radiation propagation over a distance exceeding several diffraction lengths. The use of these beams enables attaining high-density light fields and generate high-density plasmas. (interaction of laser radiation with matter. laser plasma)
Egorov, E. N., E-mail: evgeniy.n.egorov@gmail.com; Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E. [Chernyshevsky Saratov State University (Russian Federation)] [Chernyshevsky Saratov State University (Russian Federation)
2013-11-15
Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.
Analytical theory for the propagation of laser beams in nonlinear media
Tatarinova, Larisa L.; Garcia, Martin E. [Theoretische Physik, Universitaet Kassel, FB 18, Heinrich-Plett-Strasse 40, 34132 Kassel (Germany)
2007-10-15
The propagation of a laser beam of intensity I in a nonlinear medium with a refractive index n(I) of arbitrary form is studied. In particular, the influence of the functional form n=n(I) on self-focusing and self-trapping is investigated. Starting from the propagation equations and using symmetry considerations and the Bogoliubov renormalization group approach, we derive a general equation relating the self-focusing distance, the intensity, and n(I). For different polynomial dependences of n(I) on I, we construct analytical solutions for the spatial intensity profile I(r) for an initially collimated Gaussian beam inside the medium. We also explicitly analyze the case of nonlinear self-focusing accompanied by multiphoton ionization. For particular (already studied) cases, we considerably improve the accuracy of the results with respect to previous semianalytical studies and obtain very good agreement with recent numerical simulations.
Nonlinear Saturation of Cyclotron Maser Instability Associated with Energetic Ring-Beam Electrons
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
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.
Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets.
Panagiotopoulos, P; Papazoglou, D G; Couairon, A; Tzortzakis, S
2013-01-01
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
Two and three-dimensional geometrical nonlinear finite elements for analysis of adhesive joints
Raul H. Andruet; David A. Dillard; Siegfried M. Holzer
2001-01-01
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
Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies
NASA Astrophysics Data System (ADS)
Chang, Jing; Gao, Yixian; Li, Yong
2015-05-01
Consider the one dimensional nonlinear beam equation utt + uxxxx + mu + u3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.
NASA Astrophysics Data System (ADS)
Creaghan, Stephen G.
1992-12-01
This research was directed toward the investigation of nonlinear large displacements and moderate rotations of composite beam structures considering a finite element potential energy approach incorporating through the thickness shear strain as an analytical function. This approach was compared to large rotation theories. Test cases were run to evaluate numerical algorithms Riks method and displacement imposed techniques were employed. The limitations and advantages of both methods were considered. Loading arrangements included concentrated forces as well as moments.
Numerical simulation of nonlinear beam-plasma interaction for the application to solar radio burst
T. Takakura
1981-01-01
The Takakura (1977, 1979) semi-analytical method is used in numerical simulations of nonlinear scattering of axially-symmetric plasma waves into both plasma and radio waves, where the initial electron beam has a finite length and one-dimensional velocity distribution power law. The ratio between plasma wave and thermal electron energy densities is of the order of 10 to the -6th, which may
Nonlinear dust-plasma interactions of a cross-beam system in interplanetary space
Jammalamadaka, S.; Araneda, J.; McKenzie, J. F.; Gruenwaldt, H. [Max-Planck Institut fuer Aeronomie, Max-Planckstr. 2, D-37191 Katlenburg-Lindau (Germany)
1998-10-21
Dust plasma interaction has been considered. The present work is an extension of the paper of Mann and McKenzie [Mann and McKenzie, 1997]. Using the cross-beam configuration we investigate the dust plasma interaction taking into account the inhomogeneity of density. The dust interacts in our case with an inhomogeneous collisionless multi-ion plasma. Linear and nonlinear behaviour of the system has been examined and its impact on the dust dynamics is pointed out.
A nonlinear-optical method for combining high power laser beams
Jay S. Chivian; C. A. Glosson; W. D. Cotten; C. D. Cantrell III; S. F. Dimarco
1989-01-01
The overall program goal was to investigate concepts for laser-controlled optics based on near-resonance non-linear dispersion in gases, and to demonstrate a laser-induced grating capable of high power laser beam combining. The theoretical work extended the previous year's effort in giving a more detailed view of those aspects which might prevent observation of a grating, and led to optimization of
Nonlinear Dynamics of Relativistic Electron Beam with Virtual Cathode in External Magnetic Field
A. E. Hramov; A. A. Koronovskii; S. A. Kurkin; I. S. Rempen
The proposed report contains the results of numerical investigation of non-stationary non-linear dynamics and pattern forming processes in weakly relativistic electron beam with the virtual cathode. We used a 2D model where the dynamics of the electrons in interaction space was described with the help of particle-in-cell method and for calculation of self-consistent field the numerical integration of 2D Poisson
Robert A. Fisher; Leroy E. Wilson
1989-01-01
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
2D Corotational Beam Formulation by Louie L. Yaw
Yaw, Louis L.
words: geometrically nonlinear analysis, 2d corotational beam, variationally consistent, load control in terms of beam elements. As a frame structure is loaded the entire frame deforms from its original1 2D Corotational Beam Formulation by Louie L. Yaw Walla Walla University November 30, 2009 key
Stimulated Raman Scattering and Nonlinear Focusing of High-Power Laser Beams Propagating in Water
Hafizi, B; Penano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-01-01
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.
Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water.
Hafizi, B; Palastro, J P; Peñano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-04-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown, and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. The phenomenon of gain-focusing discussed here for propagation in water is expected to be of general occurrence applicable to any medium supporting nonlinear focusing and stimulated Raman scattering. PMID:25831383
A geometrically exact finite beam element formulation for thin film adhesion and debonding
to study the peeling behavior of a gecko spatula. It is shown that the beam model is capable of capturing methods, gecko adhesion, van der Waals interaction 1 Introduction The adhesion, debonding, and peeling and coatings, adhesive tapes, liquid films, and adhesive pads of insects and lizards like the gecko spatula pad
NASA Astrophysics Data System (ADS)
Akbari, M. R.; Ganji, D. D.; Rostami, A. K.; Nimafar, M.
2015-03-01
In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji's method (AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method (Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration ( A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure. Therefore, AGM can be considered as a significant progress in nonlinear sciences.
Geometrically nonlinear axisymmetric response of thin circular plate under piezoelectric actuation
NASA Astrophysics Data System (ADS)
Kapuria, Santosh; Dumir, P. C.
2005-06-01
The objective of this study is to present an approximate analytical one-term Galerkin solution for the problem of nonlinear deflection, thermal buckling and natural frequencies of a three-layer thin circular plate made of an isotropic elastic core with piezoelectric layers bonded to its faces. The analysis is restricted to axisymmetric moderately large deflection of the plate subjected to a thermal load, radial edge load or edge displacement and actuated by applying an electric potential across a piezoelectric layer. The accuracy of this solution is assessed by comparison with the numerical series solution using collocation. The direct piezoelectric effect is neglected in the governing equations. The piezoelectric layers are assumed to be very thin and having Young's modulus and density much smaller than those of the elastic core. Hence, their stiffness and inertia are neglected. The rotational and inplane inertia and the shear deformation are neglected in the Von Karman type classical thin plate theory used in the analysis. Comparison with the collocation solution establishes that the Galerkin solution yields quite accurate results for the problems considered.
HAMMERAND,DANIEL C.; KAPANIA,RAKESH K.
2000-05-01
A triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads. The nonlinear deformation process is computed using an incremental/iterative approach with the Newton-Raphson Method used to find the incremental displacements in each step. The presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation-independent mechanical loads, deformation-dependent pressure loads, and thermal loads. Unlike elastic structures that have a single critical load value associated with a given snapping of buckling instability phenomenon, viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times. Both creep buckling and snap-through examples are presented here. In some cases, viscoelastic results are also obtained using the quasielastic method in which load-history effects are ignored, and time-varying viscoelastic properties are simply used in a series of elastic problems. The presented numerical examples demonstrate the capability and accuracy of the formulation.
Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads
Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209
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
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.
Hojjat Rezaei DA; Mahmoud Kadkhodaei; Hassan Nahvi
2012-01-01
Nonlinear free vibration and damping of a clamped–clamped composite beam containing shape memory alloy wires with different prestrains embedded in the midsurface are investigated. The constitutive relations of shape memory alloy are considered in the large deflection response of the elastic Euler–Bernoulli beam, and Hamilton’s principle is used to derive differential equation of the beam motion with extensible midplane. Considering
Kulish, V. V.; Lysenko, A. V.; Koval, V. V. [Sumy State University (Ukraine)
2010-12-15
A multiharmonic cubic-nonlinear theory of a plasma-beam superheterodyne free-electron laser of the dopplertron type is constructed. A retarded electromagnetic wave propagating in the magnetized plasma-beam system toward the electron beam is used for pumping. The multiharmonic interaction of waves which plays an important role is taken into account. Saturation levels and mechanisms are analyzed. The promising application of such systems for generating high-power electromagnetic radiation in the millimeter wavelength range is demonstrated.
V. V. Kulish; A. V. Lysenko; V. V. Koval
2010-01-01
A multiharmonic cubic-nonlinear theory of a plasma-beam superheterodyne free-electron laser of the dopplertron type is constructed.\\u000a A retarded electromagnetic wave propagating in the magnetized plasma-beam system toward the electron beam is used for pumping.\\u000a The multiharmonic interaction of waves which plays an important role is taken into account. Saturation levels and mechanisms\\u000a are analyzed. The promising application of such systems
NASA Astrophysics Data System (ADS)
Kulish, V. V.; Lysenko, A. V.; Koval, V. V.
2010-12-01
A multiharmonic cubic-nonlinear theory of a plasma-beam superheterodyne free-electron laser of the dopplertron type is constructed. A retarded electromagnetic wave propagating in the magnetized plasma-beam system toward the electron beam is used for pumping. The multiharmonic interaction of waves which plays an important role is taken into account. Saturation levels and mechanisms are analyzed. The promising application of such systems for generating high-power electromagnetic radiation in the millimeter wavelength range is demonstrated.
NASA Astrophysics Data System (ADS)
Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline
2001-12-01
Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.
Sepehri Javan, N; Adli, F
2013-10-01
Nonlinear dynamics of an intense circularly polarized laser beam interacting with a hot magnetized plasma is investigated. Using a relativistic fluid model, a modified nonlinear Schrödinger equation is derived based on a quasineutral approximation, which is valid for hot plasma. Using a three-dimensional model, spatial-temporal development of the laser pulse is investigated. The occurrence of some nonlinear phenomena such as self-focusing, self-modulation, light trapping, and filamentation of the laser pulse is discussed. Also the effect of polarization and external magnetic field on the nonlinear evolution of these phenomena is studied. PMID:24229288
NASA Astrophysics Data System (ADS)
Sonnad, Kiran G.; Cary, John R.
2015-04-01
A procedure to obtain a near equilibrium phase space distribution function has been derived for beams with space charge effects in a generalized periodic focusing transport channel. The method utilizes the Lie transform perturbation theory to canonically transform to slowly oscillating phase space coordinates. The procedure results in transforming the periodic focusing system to a constant focusing one, where equilibrium distributions can be found. Transforming back to the original phase space coordinates yields an equilibrium distribution function corresponding to a constant focusing system along with perturbations resulting from the periodicity in the focusing. Examples used here include linear and nonlinear alternating gradient focusing systems. It is shown that the nonlinear focusing components can be chosen such that the system is close to integrability. The equilibrium distribution functions are numerically calculated, and their properties associated with the corresponding focusing system are discussed.
Nonlinear theory of electron neutralization waves in ions beams with dissipation
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.
1974-01-01
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.
Two-beam nonlinear Kerr effect to stabilize laser frequency with sub-Doppler resolution.
Martins, Weliton Soares; Cavalcante, Hugo L D de S; Passerat de Silans, Thierry; Oriá, Marcos; Chevrollier, Martine
2012-07-20
Avoiding laser frequency drifts is a key issue in many atomic physics experiments. Several techniques have been developed to lock the laser frequency using sub-Doppler dispersive atomic lineshapes as error signals in a feedback loop. We propose here a two-beam technique that uses nonlinear properties of an atomic vapor around sharp resonances to produce sub-Doppler dispersivelike lineshapes that can be used as error signals. Our simple and robust technique has the advantage of not needing either modulation or magnetic fields. PMID:22858948
Nonlinear Elastic J-Integral Measurements in Mode I Using a Tapered Double Cantilever Beam Geometry
NASA Technical Reports Server (NTRS)
Macon, David J.
2006-01-01
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.
Fisher, R.A.; Wilson, L.E.
1989-01-01
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.
Non-Linear Optical Flow Cytometry Using a Scanned, Bessel Beam Light-Sheet
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-01-01
Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers. PMID:26021750
Model for nonlinear evolution of localized ion ring beam in magnetoplasma
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
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.
High power microwave beam steering based on gyromagnetic nonlinear transmission lines
NASA Astrophysics Data System (ADS)
Romanchenko, I. V.; Rostov, V. V.; Gunin, A. V.; Konev, V. Yu.
2015-06-01
We demonstrate electronically controlled beam steering by high power RF pulses produced by two gyromagnetic nonlinear transmission lines (NLTLs) connected to a one high voltage driver. Each NLTL is capable of producing several ns RF pulses with peak power from 50 to 700 MW (6% standard deviation) at frequencies from 0.5 to 1.7 GHz (1% standard deviation) with 100 Hz repetition rate. Using a helix antenna allows irradiating of RF pulses with almost circular polarization and 350 MW maximum peak power, which corresponds to 350 kV effective potential of radiation. At the installation of two identical channels, we demonstrate the possibility of beam steering within ±15° in the horizontal plane by coherent RF pulses with circular polarization at 1.0 GHz center frequency. Fourfold increase in the power flux density for in-phase irradiation of RF pulses is confirmed by comparison with one-channel operation.
NASA Astrophysics Data System (ADS)
Davidson, Ronald
2008-11-01
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.
Beam quality from self and ionization induced trapping in the nonlinear LWFA regime
NASA Astrophysics Data System (ADS)
Davidson, Asher; Lu, Wei; Joshi, Chan; Silva, Luis; Martins, Joana; Fonseca, Ricardo; Mori, Warren
2011-10-01
In plasma based accelerators (LWFA and PWFA), the methods of injecting high quality electron bunches into the accelerating wakefield is of utmost importance for various applications. Understanding how injection occurs in both self and controlled scenarios is therefore important. We present results from high fidelity OSIRIS simulations on the beam quality that can be obtained from self and ionized induced trapping in the nonlinear LWFA regime. We compare trapping thresholds from the simulations to analytical expressions. We also quantify how the beam quality of 1.5-5 GeV beams can be improved through angle and energy selection as well as quantify the slice energy spread and emittance. We also study the effect of ion motion and the axial density profile. Preliminary results on inputting beams from OSIRS into the FEL code GENESIS will be presented. This work was supported by UC Lab Fees Research Award No. 09-LR-05-118764-DOUW, DOE grants DOE DE-FC02-07ER41500 and DE-FG02-92ER40727 and by NSF grants NSF PHY-0904039 and NSF PHY-0936266. The simulations were performed on Jaguar under an INCITE award.
NASA Astrophysics Data System (ADS)
Matney, Andrew
This paper addresses some aspects of the development of fully coupled thermal-structural reduced order modeling of planned hypersonic vehicles. A general framework for the construction of the structural and thermal basis is presented and demonstrated on a representative panel considered in prior investigations. The thermal reduced order model is first developed using basis functions derived from appropriate conduction eigenvalue problems. The modal amplitudes are the solution of the governing equation, which is nonlinear due to the presence of radiation and temperature dependent capacitance and conductance matrices, and the predicted displacement field is validated using published data. A structural reduced order model was developed by first selecting normal modes of the system and then constructing associated dual modes for the capturing of nonlinear inplane displacements. This isothermal model was validated by comparison with full finite element results (Nastran) in static and dynamic loading environments. The coupling of this nonlinear structural reduced order model with the thermal reduced order model is next considered. Displacement-induced thermal modes are constructed in order to account for the effect that structural deflections will have on the thermal problem. This coupling also requires the enrichment of the structural basis to model the elastic deformations that may be produced consistently with the thermal reduced order model. The validation of the combined structural-thermal reduced order model is carried out with pure mechanical loads, pure thermal loads, and combined mechanical-thermal excitations. Such comparisons are performed here on static solutions with temperature increases up to 2200F and pressures up to 3 psi for which the maximum displacements are of the order of 3 thicknesses. The reduced order model predicted results agree well with the full order finite element predictions in all of these various cases. A fully coupled analysis was performed in which the solution of the structural-thermal-aerodynamic reduced order model was carried out for 300 seconds and validated against a full order model. Finally, a reduced order model of a thin, aluminum beam is extended to include linear variations with local temperature of the elasticity tensor and coefficients of thermal expansion.
Vibration of vehicle-pavement coupled system based on a Timoshenko beam on a nonlinear foundation
NASA Astrophysics Data System (ADS)
Ding, Hu; Yang, Yan; Chen, Li-Qun; Yang, Shao-Pu
2014-12-01
This paper focuses on the coupled nonlinear vibration of vehicle-pavement system. The pavement is modeled as a Timoshenko beam resting on a six-parameter foundation. The vehicle is simplified as a spring-mass-damper oscillator. For the first time, the dynamic response of vehicle-pavement coupled system is studied by modeling the pavement as a Timoshenko beam resting on a nonlinear foundation. Consequently, the shear effects and the rotational inertia of the pavement are included in the modeling process. The pavement model is assumed to be a linear-plus-cubic Pasternak-type foundation. Furthermore, the convergent Galerkin truncation is used to obtain approximate solutions to the coupled vibratory response of the vehicle-pavement coupled system. The dynamic responses of the vehicle-pavement system with the asphalt pavement on soft soil foundation are investigated via the numerical examples. The numerical results show that the calculation for the coupled vibratory response needs high-order modes. Moreover, the coupling effects between the pavement and the vehicle are numerically examined by using the convergent modal truncation. The physical parameters of the vehicle-pavement system such as the shear modulus are compared for determining their influences on the coupled vibratory response.
Control of high power laser in nonlinear media by lens-focusing and beam self-focusing
NASA Astrophysics Data System (ADS)
Liu, Hui; Fu, Xiquan; Hou, Yanchao; Deng, Jianqin
2010-11-01
In this paper, we firstly preliminary analyzed how to control the collapse position of beam when intensity and beam waist have been varied by the laser self-focusing in nonlinear media and lens-focusing. We obtain the relations of the focusing position with input power and focal length of lens. The length of focusing is inversely proportional to the input power and directly proportional to focal length of lens. Secondly, Based on the nonlinear propagation equation and split-step Fourier method, we investigate how to control the focal distance and beam quality of high-power laser at focusing spot in nonlinear media. We can control the focusing spot at any position by changed power and lens. The numerical simulations is good consistent with theoretical analysis.
NASA Astrophysics Data System (ADS)
Yang, Xinmai; Cleveland, Robin O.
2005-01-01
A time-domain numerical code (the so-called Texas code) that solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation has been extended from an axis-symmetric coordinate system to a three-dimensional (3D) Cartesian coordinate system. The code accounts for diffraction (in the parabolic approximation), nonlinearity and absorption and dispersion associated with thermoviscous and relaxation processes. The 3D time domain code was shown to be in agreement with benchmark solutions for circular and rectangular sources, focused and unfocused beams, and linear and nonlinear propagation. The 3D code was used to model the nonlinear propagation of diagnostic ultrasound pulses through tissue. The prediction of the second-harmonic field was sensitive to the choice of frequency-dependent absorption: a frequency squared f2 dependence produced a second-harmonic field which peaked closer to the transducer and had a lower amplitude than that computed for an f1.1 dependence. In comparing spatial maps of the harmonics we found that the second harmonic had dramatically reduced amplitude in the near field and also lower amplitude side lobes in the focal region than the fundamental. These findings were consistent for both uniform and apodized sources and could be contributing factors in the improved imaging reported with clinical scanners using tissue harmonic imaging. .
Sepehri Javan, N.; Adli, F. [Department of Physics, Faculty of Sciences, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil 56199-11367 (Iran, Islamic Republic of)] [Department of Physics, Faculty of Sciences, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil 56199-11367 (Iran, Islamic Republic of)
2013-06-15
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.
NASA Astrophysics Data System (ADS)
He, Qingbo; Xu, Yanyan; Lu, Siliang; Dai, Daoyi
2014-04-01
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.
NASA Astrophysics Data System (ADS)
Sasmal, Saptarshi; Kalidoss, S.
2015-05-01
In the present study, investigations on fiber-reinforced plastic (FRP) plated-reinforced concrete (RC) beam are carried out. Numerical investigations are performed by using a nonlinear finite element analysis by incorporating cracking and crushing of concrete. The numerical models developed in the present study are validated with the results obtained from the experiment under monotonic load using the servo-hydraulic actuator in displacement control mode. Further, the validated numerical models are used to evaluate the influence of different parameters. It is found from the investigations that increase in the elastic modulus of adhesive layer and CFRP laminate increases the interfacial stresses whereas increase in laminate modulus decreases the displacement and reinforcement strain of the beam. It is also observed that increase in the adhesive layer can largely reduce the interfacial stresses, whereas increase in laminate thickness increases it. However, increase in laminate thickness decreases the displacement and reinforcement strain of the beam significantly. It is mention worthy that increase in laminate length reduces the interfacial stresses, whereas CFRP width change does not affect the interfacial stresses. The study will be useful for the design and practicing engineers for arriving at the FRP-based strengthening schemes for RC structures judiciously.
NASA Technical Reports Server (NTRS)
Crespo Da Silva, M. R. M.; Hodges, D. H.
1986-01-01
The dynamic response and aeroelastic stability of rotating beams such as helicopter blades is investigated analytically. The Hamilton principle is used to formulate the equations of motion for extensional and inextensional beams with precone angles and variable pitch angles, taking higher-order nonlinearities into account. The derivation of the equations and their approximate solution by a Galerkin procedure are explained in detail, and numerical results of equilibrium solutions and stability analyses are presented graphically.
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
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.
Potrebko, Peter S.; McCurdy, Boyd M. C.; Butler, James B.; El-Gubtan, Adel S.; Nugent, Zoann [Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 (Canada) and Division of Medical Physics, CancerCare Manitoba, 675 McDermot Avenue, Winnipeg, Manitoba R3E 0V9 (Canada); Division of Medical Physics, CancerCare Manitoba, 675 McDermot Avenue, Winnipeg, Manitoba R3E 0V9 (Canada); Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada) and Department of Radiology, University of Manitoba, Winnipeg, Manitoba R3A 1R9 (Canada); Department of Radiation Oncology, CancerCare Manitoba, 675 McDermot Avenue, Winnipeg, Manitoba R3E 0V9 (Canada) and Department of Radiology, University of Manitoba, Winnipeg, Manitoba R3A 1R9 (Canada); Department of Epidemiology, CancerCare Manitoba, 675 McDermot Avenue, Winnipeg, Manitoba R3E 0V9 (Canada)
2007-10-15
A fast, geometric beam angle optimization (BAO) algorithm for clinical intensity-modulated radiation therapy (IMRT) was implemented on ten localized prostate cancer patients on the Radiation Therapy Oncology Group (RTOG) 0126 protocol. The BAO algorithm computed the beam intersection volume (BIV) within the rectum and bladder using five and seven equiangular-spaced beams as a function of starting gantry angle for comparison to the V 75 Gy and V 70 Gy. A mathematical theory was presented to explain the correlation of BIV with dose and dose-volume metrics. The class solution 'W' pattern in the rectal V 75 Gy and V 70 Gy as a function of starting gantry angle using five equiangular-spaced beams (with two separate minima centered near 20 deg. and 50 deg. ) was reproduced by the 5 BIV within the rectum. A strong correlation was found between the rectal 5 BIV and the rectal V 75 Gy and V 70 Gy as a function of starting gantry angle. The BAO algorithm predicted the location of the two dosimetric minima in rectal V 75 Gy and V 70 Gy (optimal starting gantry angles) to within 5 deg. . It was demonstrated that the BIV geometric variations for seven equiangular-spaced beams were too small to translate into a strong dosimetric effect in the rectal V 75 Gy and V 70 Gy. The relatively flat distribution with starting gantry angle of the bladder V 75 Gy and V 70 Gy was reproduced by the bladder five and seven BIV for each patient. A geometric BAO method based on BIV has the advantage over dosimetric BAO methods of simplicity and rapid computation time. This algorithm can be used as a standalone optimization method or act as a rapid calculation filter to reduce the search space for a dosimetric BAO method. Given the clinically infeasible computation times of many dosimetric beam orientation optimization algorithms, this robust geometric BIV algorithm has the potential to facilitate beam angle selection for prostate IMRT in clinical practice.
NASA Astrophysics Data System (ADS)
Levin, V. A.; Zubov, L. M.; Zingerman, K. M.
2015-04-01
The plane problem on large deformations of the flexure of a composite rectangular beam consisting of two layers, one of which is preliminarily deformed, has been solved. An exact analytical solution of this problem is derived for the case when the beam is made of a compressible nonlinearly elastic material, the mechanical properties of which are described by the John potential. When stating and solving the problem, the theory of imposing large deformations is used. Based on the calculations, the influence of the prestressed layer on a strong flexure of a composite beam is determined.
NASA Astrophysics Data System (ADS)
Buks, Eyal
2009-03-01
A driven nonlinear system operating close to bifurcation, namely, close to transition between different stability zones, is extremely sensitive to external perturbations. This behavior can be exploited for amplifying small signals, and also for noise reduction (squeezing). We experimentally demonstrate these effects using two classes of systems, namely, nanomechanical resonators in the form of doubly clamped beams, and electromagnetic resonators made of superconducting striplines. While a bifurcation between monostable and bistable zones is employed for the first class of resonators, a bifurcation between monostable and astable zones is employed for the second one. In both cases we observe extremely high gain and very strong noise squeezing as we approach bifurcation. While the Duffing-like nonlinearity of the mechanical beams is well understood, the piecewise-linear behavior exhibited by the superconducting stripline resonators is yet not fully accountable. We provide theoretical evidence to support our hypothesis that the underlying mechanism responsible for the observed piecewise-linear behavior is thermal instability in a narrow stripline section (a microbridge), which is integrated into the resonator. A simple theoretical model predicts a rich variety of dynamical effects, including self-sustained oscillations, stochastic resonance, and intermittency between different steadystate and limit-cycle solutions. These effects are experimentally observed by tuning the system close to the zone of astability, where no steadystate response exists. A comparison with theory yields partial agreement. Moreover, in more recent experiments we study a new configuration in which the microbridge is replaced by a superconducting interference device (SQUID) in the form of a loop containing two microbridges. Our preliminary experimental results show that self-sustained oscillations occur also in this configuration. Moreover, the frequency and lineshape of these oscillations exhibit periodicity as a function of externally applied magnetic flux. Further work is needed to theoretically account for the observed behavior.
Jimmy Haedir; Xiao-Ling Zhao; Raphael H. Grzebieta; Michael R. Bambach
2011-01-01
External bonding of fibre reinforced polymer (FRP) composites has emerged as a popular technique for strengthening steel structures in recent years. In this study, the non-linear behaviour of circular hollow steel beams bonded with thin carbon FRP sheets was investigated theoretically by including the effect of the amount of CFRP reinforcement, fibre configuration, fibre and adhesive volume fractions and material
Nonlinear vibration of a post-buckled beam subjected to external and parametric excitations
NASA Astrophysics Data System (ADS)
El-Bassiouny, A. F.
2006-07-01
An analytical investigation of the nonlinear vibration of a post-buckled beam subjected to harmonic excitations is presented. The system can be modelled as a nonlinear oscillator with parametric and external excitations having frequencies ? 1 and ? 2. The method of multiple scales is used to determine to second order the amplitude and phase-modulation equations. Attention is focused on subharmonic resonances (? 1 cong 2? 0, ? 2 cong 2? 0 ; ? 1 cong 3? 0, ? 2 cong 3? 0 ; ? 1 cong 4? 0, ? 2 cong 4? 0 ; ? 1 cong 5? 0 and ? 1 cong 6? 0) where ? 0 is the natural frequency. Steady-state amplitude for each case is plotted as a function of a detuning parameter showing the influences of the several parameters. Stability is performed on figures by solid and broken lines. There exist multivalued solutions which increase or decrease by the variation of some parameters. The response amplitude is not affected by increasing and decreasing the parameters F1 and ? 3 for the cases of subharmonics of order one-half and one-third. The solution loses stability on increasing the parameters ? 4, ? 5 and F1 in the case of subharmonic resonance of order one-fifth and also for decreasing the parameters ? and ? 4 in the case of subharmonic resonance of order one-sixth.
Nonlinear dynamic response of submarine pipelines in contact with the ocean floor
Chung
1986-01-01
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
Karaton, Muhammet
2014-01-01
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
Analysis of the nonlinear dynamics of a horizontal drillstring Americo Cunha Jr1,2
Boyer, Edmond
, which is used to drill the soil in oil prospecting. During its operation, this column presents a three is a long column under rotation, composed by a sequence of connected drill-pipes and auxiliary equipment, drillstring dynamics, nonlinear beam theory, geometric nonlinearity 1 Introduction Oil prospecting uses
Pili, Giorgio; Grimaldi, Luca; Fidanza, Christian; Florio, Elena T. [Department of Medical Physics, 'A. Perrino' Hospital, Brindisi (Italy); Petruzzelli, Maria F. [Department of Radiation Oncology, 'A. Perrino' Hospital, Brindisi (Italy); D'Errico, Maria P. [Department of Laboratory Medicine, 'A. Perrino' Hospital, Brindisi (Italy); De Tommaso, Cristina; Tramacere, Francesco [Department of Radiation Oncology, 'A. Perrino' Hospital, Brindisi (Italy); Musaio, Francesca [Department of Medical Physics, 'A. Perrino' Hospital, Brindisi (Italy); Castagna, Roberta; Francavilla, Maria C. [Department of Radiation Oncology, 'A. Perrino' Hospital, Brindisi (Italy); Gianicolo, Emilio A.L. [National Research Council-Clinical Physiology Institute, Pisa-Lecce (Italy); Portaluri, Maurizio, E-mail: portaluri@hotmail.com [Department of Radiation Oncology, 'A. Perrino' Hospital, Brindisi (Italy); National Research Council-Clinical Physiology Institute, Pisa-Lecce (Italy)
2011-11-01
Purpose: To evaluate the probability of late cardiac mortality resulting from left breast irradiation planned with tangential fields and to compare this probability between the wedged beam and field-in-field (FIF) techniques and to investigate whether some geometric/dosimetric indicators can be determined to estimate the cardiac mortality probability before treatment begins. Methods and Materials: For 30 patients, differential dose-volume histograms were calculated for the wedged beam and FIF plans, and the corresponding cardiac mortality probabilities were determined using the relative seriality model. As a comparative index of the dose distribution uniformity, the planning target volume (PTV) percentages involved in 97-103% of prescribed dose were determined for the two techniques. Three geometric parameters were measured for each patient: the maximal length, indicates how much the heart contours were displaced toward the PTV, the angle subtended at the center of the computed tomography slice by the PTV contour, and the thorax width/thickness ratio. Results: Evaluating the differential dose-volume histograms showed that the gain in uniformity between the two techniques was about 1.5. With the FIF technique, the mean dose sparing for the heart, the left anterior descending coronary artery, and the lung was 15% (2.5 Gy vs. 2.2 Gy), 21% (11.3 Gy vs. 9.0 Gy), and 42% (8.0 Gy vs. 4.6 Gy) respectively, compared with the wedged beam technique. Also, the cardiac mortality probability decreased by 40% (from 0.9% to 0.5%). Three geometric parameters, the maximal length, angle subtended at the center of the computed tomography slice by the PTV contour, and thorax width/thickness ratio, were the determining factors (p = .06 for FIF, and p = .10 for wedged beam) for evaluating the cardiac mortality probability. Conclusion: The FIF technique seemed to yield a lower cardiac mortality probability than the conventional wedged beam technique. However, although our study demonstrated that FIF technique improved the dose coverage of the PTV, the restricted number of patients enrolled and the short follow-up did not allow us to evaluate and compare the breast cancer survival rates of the patients.
NASA Astrophysics Data System (ADS)
Fenili, André; Balthazar, José M.; Francisco, Cayo Prado Fernandes; da Fonseca Brasil, Reyolando Manoel Lopes Rebello
2014-12-01
We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.
Nonlinear-optical method for combining high-power laser beams. Report for 1 April 1988-30 April 1989
J. S. Chivian; C. A. Glosson; W. D. Cotten; C. D. Cantrell; S. F. DiMarco
1989-01-01
The overall program goal was to investigate concepts for laser-controlled optics based on near-resonance nonlinear dispersion in gases, and to demonstrate a laser-induced grating capable of high-power laser-beam combining. The theoretical work extended the previous year's effort in giving a more detailed view of those aspects that might prevent observation of a grating, and led to optimization of experimental parameters.
NASA Technical Reports Server (NTRS)
Moyer, E. T., Jr.
1984-01-01
The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system. It is also shown that while the fundamental response is contained in a first mode envelope, the fluctuations caused by the higher order modes must be resolved.
NASA Astrophysics Data System (ADS)
Gao, Q. D.; Budny, R. V.
2015-03-01
By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (V?) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.
Vivi Rottschäfer; Tasso J. Kaper
2003-01-01
We establish the existence and local uniqueness of two classes of multi-bump, self-similar, blowup solutions for the cubic nonlinear Schrödinger equation close to the critical dimension d = 2. Our results for one class of orbits build on the earlier discovery of these orbits via numerical simulation and via asymptotic analysis, providing a proof of their existence. The second class
Paris-Sud XI, Université de
nano-mechanical systems (MEMS and NEMS) are of current interest due to their broad field of scientific in micro/nano mechanics, which can even be extended to the quantum-limited nano-mechanical device [18 parametric am- plification [21, 22], and parametric drive [23]. In partic- ular, non-linear dampings [24
NASA Astrophysics Data System (ADS)
Zeng, Juan; Garg, Anurag; Kovacs, Andrew; Bajaj, Anil K.; Peroulis, Dimitrios
2015-05-01
Anchor supports in MEMS beams are often far from the ideally assumed built-in or step-up conditions. Practical fabrication processes often result in non-vertical anchoring supports (referred to as inclined supports in the following text) which significantly influence the post-release performance of the beam. This paper brings attention to the presence of the inclined supports in surface micromachined fixed–fixed beams and models the mechanical and electromechanical effects of inclined supports for the first time. Specifically, we calculate and validate the effects of residual stress and loading on the post-release beam behavior including their nonlinear large-displacement characteristics. In addition the model accounts for non-flat beam profiles caused by residual stress and/or a non-flat sacrificial layer profile. Inclined supports are modeled as cantilever beams connected to a horizontal beam. The Euler–Bernoulli equations for all beams are simultaneously solved to calculate the axial stress of the horizontal beam and the axial, translational, and rotational compliance of the supports. Nonlinear effects due to stretching and residual stress are also included. The calculated beam displacements agree with FEM models to within 1.1% in both the linear and nonlinear regimes. Furthermore, experimentally-obtained displacements of six fabricated beams with inclined supports agree to within 5.2% with the presented model.
Two kinds of C 0-type elements for buckling analysis of thin-walled curved beams
N. Hu; B. Hu; B. Yan; H. Fukunaga; H. Sekine
1999-01-01
This paper deals with the spatial buckling analysis of curved beams. First, a second-order expansion for the finite rigid-rotations in nonlinear strain expressions is derived and employed to produce the geometric stiffness matrix. This second-order accurate geometric stiffness matrix can ensure that all significant instability modes can be predicted. Furthermore, Timoshenko's and Vlasov's beam theories are combined to develop two
1 Reshaping the trajectory and spectrum 2 of nonlinear Airy beams
Chen, Zhigang
on the initial spectral distribution under a self-focusing (or 15 defocusing) nonlinearity. © 2012 Optical, 24 especially under the action of a self-focusing nonlinearity 25 [10,11]. Formation of accelerating dramatically during nonlinear propagation leading to po- 39 sitive (or negative) spectral defects under a self-focusing
Giuseppe Saccomandi; Raffaele Vitolo
2014-08-26
Using the theory of $1+1$ hyperbolic systems we put in perspective the mathematical and geometrical structure of the celebrated circularly polarized waves solutions for isotropic hyperelastic materials determined by Carroll in Acta Mechanica 3 (1967) 167--181. We show that a natural generalization of this class of solutions yields an infinite family of \\emph{linear} solutions for the equations of isotropic elastodynamics. Moreover, we determine a huge class of hyperbolic partial differential equations having the same property of the shear wave system. Restricting the attention to the usual first order asymptotic approximation of the equations determining transverse waves we provide the complete integration of this system using generalized symmetries.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
A model for the nonlinear mechanism responsible for cochlear amplification.
Fessel, Kimberly; Holmes, Mark H
2014-12-01
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
NASA Astrophysics Data System (ADS)
Cottrill, Larissa A.; Lasinski, B. F.; Lund, S. M.; Tabak, M.; Town, R. P. J.
2007-11-01
A crucial issue surrounding the feasibility of fast ignition is the ability to efficiently couple energy from an incident short-pulse laser to a high-density, pre-compressed fuel core. Energy transfer will involve the generation and transport of a relativistic electron beam, which may be subject to a number of instabilities that act to inhibit energy transport. The initial linear and later nonlinear growth phases of these instabilities will evolve differently depending on a number of issues such as the initial beam distribution and collisional effects. Analytical calculations will be presented in the collisionless and collisional limits to demonstrate differences in instability growth in the linear growth phase for advanced distributions such as the relativistic Maxwellian and waterbag, as well as a distribution extracted from explicit PIC simulations of the laser-plasma interaction. Simulations from the LSP code will also be shown to highlight beam transport issues in the nonlinear saturated state. This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract W-7405-ENG-48.
Rigid mechanics and its role in nonlinear structural analysis
Y. B. YANG
In the nonlinear analysis of elastic structures, the displacement increments generated at each incremental step can be decomposed into two components as the rigid displacements and natural deformations. Based on the updated Lagrangian (UL) formulation, the geometric stiffness matrix (kg) is derived for a 3D rigid beam element from the virtual work equation using a rigid displacement field. Further, by
V. N. Lugovoi; A. A. Manenkov
2009-01-01
This chapter presents a review of the theory of the multi-focus structure (MFS) and moving nonlinear foci (MNLF) models of\\u000a self-focusing. It also reviews some experimental results on self-focusing of nanosecond-duration-pulses that support these\\u000a models. Some experimental and simulation results of studies of femtosecond self-focusing in air are discussed. It is concluded\\u000a that the main features of MFS-MNLF models can
A. Cot; J. Sempau; D. Pareto; S. Bullich; J. Pavia; F. Calvino; D. Ros
2002-01-01
The quantitative analysis of single-photon emission computed tomography data requires an accurate determination of the collimator point spread function (PSF). The aim of this paper is to characterize fan-beam collimators' PSFs by using Monte Carlo simulation. Given a particular collimator configuration, a detailed hexagonal hole array was generated and information describing its geometry was stored in a lookup table. When
NASA Astrophysics Data System (ADS)
Dantu, Subbarao; Uma, R.
2000-10-01
The nonlinear Schrodinger equation in cylindrical geometry with saturating nonlinearity like the ponderomotive or relativistic nonlinearity in a plasma is analysed with the help of Symmetry Group Analysis. The symmetry group of the equation is deduced and a fiber-preserving subgroup of linear transformations are identified that leave such a nonlinear Schrodinger equation invariant. The MACSYMA-based Lie algebra of the symmetry group is realized to the extent possible. The theory results in an ordinary differential equation apart from a dictated beam profile. The resulting ordinary differential equation for self-focusing is compared with similar equations obtained from other existing theories of self-focusing in cylindrical geometry like the modified paraxial theory based on harmonic-oscillator basis, the moments theory and the variational theory . New types of solutions are identified and the limitations of the different methods are indicated.Acknowledgements: Financial assistance of CSIR(India)(Research Project,03(0815)/97/ EMR-II) for this work is acknowledged.
Analysis of the propagation of flat-topped beam in nonlinear optical fiber
NASA Astrophysics Data System (ADS)
Avila, Duber A.; Torres, Cesar O.
2013-11-01
In this paper we study wave propagation type Flat Topped through nonlinear optical fibers using as mathematical tool nonlinear equation schrödinger. In this paper we propose to perform a mathematical expansion of a Flat Topped pulse and express it as a combination of Gaussian functions where it is necessary to solve the dynamic equation numerically using the method of Split Step Fourier.
New integrable nonlocal nonlinear Schrodinger systems from geometric curve flows in SO(2N)/U(N)
Ahmed M. G. Ahmed; Stephen C. Anco
2014-08-29
A class of integrable nonlocal nonlinear Schrodinger systems with a unitary invariant bi-Hamiltonian formulation is derived by applying a general moving frame method to non-stretching curve flows in the symmetric space SO(2n)/U(n). The systems involve a real scalar variable coupled to a pair of complex vectors variables which arise as Hasimoto variables defined by a parallel frame along the curves, where the equivalence group of the frame contains the factor U(1) x SU(2). The curve flow equations corresponding to these systems are shown to be non-stretching variants of Schrodinger maps. The same method can be applied to other symmetric spaces in which curves admit a parallel frame with a similar unitary equivalence group.
Fabio BIONDINI
SUMMARY The paper presents a three-dimensional finite beam element for damage evaluation and seismic analysis of concrete structures. The proposed formulation takes both mechanical and geometrical non-linearity into account. The measure of the seismic structural performance is based on a set of damage indices defined at different scales. The accuracy of the finite beam element is proven with reference to
Bayro-Corrochano, E J
2001-01-01
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
Nonlinear acoustic effect of high-current electron beam at radiation rebuilding of metal target
A. I. Kalinichenko; G. F. Popovl; V. A. Deryuga; A. G. Ponomarev; V. V. Uvarov
1996-01-01
The acoustic emission caused by high-current electron beam in massive polycrystalline metallic samples is studied. Under experiment conditions the bulk expansion of metal due to melting makes the main contribution into total volume increase under radiation heating, and determines the acoustic pulse amplitude. The latter increases with decreasing of crystalline grain dimensions in the region of the beam-target interaction. Size
Low sidelobe limited diffraction beams in the nonlinear regime Sverre Holm and Fabrice Prieur
Sahay, Sundeep
with as a Bessel function of order n, Jn where is the transverse coordinate, and the transverse wavenumber of the Bessel beam. There is a solution for each order, n, of the Bessel function, but since the n=0 beam has
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
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.
Moolla, S. [University of KwaZulu-Natal, Durban 4000 (South Africa); Bharuthram, R. [University of the Western Cape, Modderdam Road, Belville 7535 (South Africa); Singh, S. V.; Lakhina, G. S.; Reddy, R. V. [Indian Institute of Geomagnetism, New Panvel (W), Navi Mumbai 410218 (India)
2010-02-15
Observations from the Fast Auroral SnapshoT (FAST) satellite indicate that the parallel and perpendicular (to the Earth's magnetic field) electric field structures exhibit a spiky appearance. In this study, a magnetized plasma system consisting of protons, electrons, and a cold oxygen ion beam is considered. Both background electrons and protons are treated as hot species with Boltzmann density distributions. The dynamics of the oxygen ion beam is governed by the fluid equations. Effect of charge separation is studied on nonlinear fluctuations arising from a coupling of ion cyclotron and ion-acoustic waves. A scan of parameter space reveals a range of solutions for the parallel electric field from sinusoidal to sawtooth to highly spiky waveforms. The inclusion of charge separation effects tends to in most cases increase the frequency of oscillation of the nonlinear structures. In the case of a weakly magnetized plasma, the amplitude of the oscillations are found to be constant while they are modulated for a strongly magnetized plasma. The findings are compared with satellite observations.
NASA Technical Reports Server (NTRS)
Kvaternik, R. G.; Kaza, K. R. V.
1976-01-01
The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.
Shi-rong Li; Hou-de Su; Chang-jun Cheng
2009-01-01
Free vibration of statically thermal postbuckled functionally graded material (FGM) beams with surface-bonded piezoelectric\\u000a layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on\\u000a the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric\\u000a layers subject to thermo-electromechanical loadings are formulated. It is assumed that the
NASA Astrophysics Data System (ADS)
Kucherov, Arkadii N.; Makashev, N. K.; Ustinov, E. V.
1995-02-01
An algorithm is proposed for the approximation of the parameters of a beam in which a quadratic polynomial, expressed in terms of coordinates transverse to the beam axis, is used to describe the phase front profile. The coefficients in this polynomial are related to the spatial moments of the intensity distribution and to their derivatives with respect to a coordinate along the beam axis. A system of approximate ordinary differential equations for the moments is derived for a convective gasdynamic thermal self-interaction. The use of this system of equations reduces significantly the computer time needed to analyse beam perturbations. The approximation quality is checked by comparing the results of rigorous and approximate calculations.
Focal-Plane Imaging of Crossed Beams in Nonlinear Optics Experiments
NASA Technical Reports Server (NTRS)
Bivolaru, Daniel; Herring, G. C.
2007-01-01
An application of focal-plane imaging that can be used as a real time diagnostic of beam crossing in various optical techniques is reported. We discuss two specific versions and demonstrate the capability of maximizing system performance with an example in a combined dual-pump coherent anti-Stokes Raman scattering interferometric Rayleigh scattering experiment (CARS-IRS). We find that this imaging diagnostic significantly reduces beam alignment time and loss of CARS-IRS signals due to inadvertent misalignments.
NASA Astrophysics Data System (ADS)
Rashidian Vaziri, M. R.; Hajiesmaeilbaigi, F.; Maleki, M. H.
2013-03-01
Knowing the Gaussian beam parameters, such as its radius of curvature and spot size during propagation in nonlinear Kerr media, is of paramount importance in describing the observable far-field diffraction ring patterns as well as in design and stability analysis of Kerr-lens mode-locked resonators. Specifically, the sign of the beam radius of curvature after exiting these media has been proposed to be of assistance in recognizing their optical nonlinearity sign through determining the type of diffraction ring pattern in the far field. In order to be able to trace the evolution of the beam parameters in the Gaussian beam formalism, we have used the common aberration-free theory. We have shown that the nonlinear propagation problem of a fundamental Gaussian beam in a Kerr medium with an intensity-dependent index of refraction can be handled by assuming a ducting index profile along the propagation direction. Knowing the familiar ABCD matrix of a duct, the evolution of the mentioned beam parameters can be traced during propagation using the ABCD law in Gaussian beam theory. We have validated our ducting model by comparing its results with the outcomes of one widely used and accepted model which has been known to yield consistent results when electronic optical nonlinearity prevails. We have shown that when thermal optical nonlinearity is dominant, as in diffraction ring observation experiments, our ducting model yields sensible results and should be used. Our model predicts that when the sign of the thermal nonlinearity and the beam radius of curvature on the entrance plane of the medium are positive, the sign of the beam radius of curvature on the exit plane may have either sign, depending on the medium thickness used in the experiment. Hence, two types of diffraction ring pattern may be obtained using the same medium with two different thicknesses and this may cast doubt on the validity of the methods proposing the detection of the optical nonlinearity signs by observing these patterns. We have proposed a simple procedure for experimentally obtaining the two different types of diffraction pattern from the same medium.
arXiv:cond-mat/0503130v228Aug2006 1 Nonlinear Damping in Nanomechanical Beam
Buks, Eyal
into nonlinear regime and the response is mea- sured by a displacement detector. For data analysis we introduce noise squeezing [12], and enhanced sensitivity mass detection [13] can be implemented by applying modest in the linear regime may be difficult when a displacement detector with high sensitivity is not available. Thus
Skryabin, Dmitry
in self-focusing saturable and quadratic nonlinear media. Varying parameters, we demonstrate transitions stripe into a set of filaments in the self-focusing case 3 , while a vortex chain forms from a dark,13 . The present paper deals with 2D propagation of electro- magnetic waves in self-focusing saturable
Numerical Modeling of Nonlinear Coupling between Lines/Beams with Multiple Floating Bodies
Yang, Chan K.
2010-07-14
/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...
T. Peschel; U. Peschel; F. Lederer
1994-01-01
By using a modal approach, the distributed coupling of two inhomogeneous, transient waves with opposite angles of incidence into nonlinear waveguides is studied. We show that cross modulation and the coherent interaction via a dynamic grating, nonlinearily induced by the excited counterpropagating leaky waves, provide a longitudinal feedback. This feedback is the necessary prerequisite for bistability to occur. We show
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
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.
NASA Astrophysics Data System (ADS)
Ali Shan, S.; El-Tantawy, S. A.; Moslem, W. M.
2013-08-01
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.
Unconventional finite element method for nonlinear analysis of beams and plates
Kim, Wooram
2009-05-15
-Bernoulli Beam Theory????????.. 3 1.1.1 Kinematics of EBT??????????????? 4 1.1.2 Equilibriums of EBT??????????????. 4 1.1.3 Constitutive Relations and Resultants of EBT????.. 6 1.2 Review of Timoshenko Beam Theory (TBT) ??????... 7 1.2.1 Kinematics... of TBT??????????????? 7 1.2.2 Equilibriums of TBT??????...???????.. 8 1.2.3 Constitutive Relations and Resultants of TBT????.. 10 1.3. Review of Classical Plate Theory (CPT) ????????. 11 1.3.1 Kinematics of CPT??????????????? 12 1...
Kheifets, S.
1983-01-01
A perturbation method which allows one to find the distribution function and the beam size for a broad class of storage ring nonlinear problems is described in Part I of this work. In present note I apply this method to a particular problem. Namely, I want to evaluate an enhancement of the vertical beam size of a bunch due to the presence of the ring of nonlinear magnetic fields. The main part of the work deals with sextupole magnets. Formula for the beam size in the presence of octupole fields are also developed to the first order in the octupole strength, although octupole magnets are not widely used in present storage ring designs. This calculation is done mainly because the octupole field has the same symmetry as the beam-beam force for the head-on collision. This will give us the opportunity to compare the conduct of the bunch due to this two types of nonlinear kicks. The general terms of the applicability of the Green's function method is discussed in the first part of this work.
Calculation of non-linear vibration of rotating beams by using tetrahedral and solid finite elements
J. J. Jiang; C. L. Hsiao; A. A. Shabana
1991-01-01
A development is presented of the non-linear dynamic equations that govern the motion of the tetrahedral and solid finite elements that undergo large displacements. The development presented is exemplified by using the four-node, 12-degree-of-freedom tetrahedral element and the eight-node, 24-degree-of-freedom solid element. It is shown that the element shape functions used in this investigation can be used to describe large
Esfandyari-Kalejahi, A. [Faculty of Science, Department of Physics, Azerbaijan University of Tarbiat Moallem, 51745-406 Tabriz (Iran, Islamic Republic of); Kourakis, I. [Center for Plasma Physics (CPP), Department of Physics and Astronomy, Queen's University Belfast, BT7 1 NN Northern Ireland (United Kingdom); Institut fuer Theoretische Physik IV, Fakultaet fuer Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany); Shukla, P. K. [Institut fuer Theoretische Physik IV, Fakultaet fuer Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
2008-02-15
The nonlinear propagation of finite amplitude ion acoustic solitary waves in a plasma consisting of adiabatic warm ions, nonisothermal electrons, and a weakly relativistic electron beam is studied via a two-fluid model. A multiple scales technique is employed to investigate the nonlinear regime. The existence of the electron beam gives rise to four linear ion acoustic modes, which propagate at different phase speeds. The numerical analysis shows that the propagation speed of two of these modes may become complex-valued (i.e., waves cannot occur) under conditions which depend on values of the beam-to-background-electron density ratio {alpha}, the ion-to-free-electron temperature ratio {sigma}, and the electron beam velocity v{sub 0}; the remaining two modes remain real in all cases. The basic set of fluid equations are reduced to a Schamel-type equation and a linear inhomogeneous equation for the first and second-order potential perturbations, respectively. Stationary solutions of the coupled equations are derived using a renormalization method. Higher-order nonlinearity is thus shown to modify the solitary wave amplitude and may also deform its shape, even possibly transforming a simple pulse into a W-type curve for one of the modes. The dependence of the excitation amplitude and of the higher-order nonlinearity potential correction on the parameters {alpha}, {sigma}, and v{sub 0} is numerically investigated.
Karuna Batra; Sugata Mitra; D. Subbarao; R. P. Sharma; R. Uma
2005-01-01
The task for the present study is to make an investigation of self-similarity in a self-focusing laser beam both theoretically and numerically using graphical user interface based interactive computer simulation model in MATLAB (matrix laboratory) software in the presence of saturating ponderomotive force based and relativistic electron quiver based plasma nonlinearities. The corresponding eigenvalue problem is solved analytically using the
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines
NASA Astrophysics Data System (ADS)
Franchetti, G.; Schmidt, F.
2015-06-01
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom).
Wei, Jingsong, E-mail: weijingsong@siom.ac.cn [Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China); Yan, Hui [Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China); University of Chinese Academy of Sciences, Beijing 100049 (China)
2014-08-14
Self-focusing is a well-researched phenomenon. Nanoscale spots can be achieved through self-focusing, which is an alternative method for achieving high-density data storage, high-resolution light imaging, and maskless nanolithography. Several research groups have observed that self-focusing spots can be reduced to nanoscale levels via incident laser power manipulation. Self-focusing spots can be analyzed by solving the nonlinear Schrödinger equation and the finite difference time domain method. However, both procedures are complex and time-consuming. In the present work, a multi-layer thin-lens self-focusing model that considers diffraction effects and changes of refractive index along the radial and film thickness directions is proposed to analyze the self-focusing behavior and traveling process of light beams intuitively. The self-focusing behaviors of As{sub 2}S{sub 3} are simulated, and results show that a nanoscale self-focusing spot with a radius of about 0.12??m can be formed at the bottom of nonlinear sample when the incident laser power exceeds 4.25?mW. Our findings are basically consistent with experimental reports and provide a good method for analyzing and understanding the self-focusing process. An appropriate application schematic design is also provided.
NASA Astrophysics Data System (ADS)
Wei, Jingsong; Yan, Hui
2014-08-01
Self-focusing is a well-researched phenomenon. Nanoscale spots can be achieved through self-focusing, which is an alternative method for achieving high-density data storage, high-resolution light imaging, and maskless nanolithography. Several research groups have observed that self-focusing spots can be reduced to nanoscale levels via incident laser power manipulation. Self-focusing spots can be analyzed by solving the nonlinear Schrödinger equation and the finite difference time domain method. However, both procedures are complex and time-consuming. In the present work, a multi-layer thin-lens self-focusing model that considers diffraction effects and changes of refractive index along the radial and film thickness directions is proposed to analyze the self-focusing behavior and traveling process of light beams intuitively. The self-focusing behaviors of As2S3 are simulated, and results show that a nanoscale self-focusing spot with a radius of about 0.12 ?m can be formed at the bottom of nonlinear sample when the incident laser power exceeds 4.25 mW. Our findings are basically consistent with experimental reports and provide a good method for analyzing and understanding the self-focusing process. An appropriate application schematic design is also provided.
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines.
Franchetti, G; Schmidt, F
2015-06-12
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom). PMID:26196806
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
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.
Problems in nonlinear dynamics
Char-Ming Chin
1993-01-01
Three types of problems in nonlinear dynamics are studied. First, we use a complex-variable invariant-manifold approach to determine the nonlinear normal modes of weakly nonlinear discrete systems with one-to-one and three-to-one internal resonances. Cubic geometric nonlinearities are considered. The system under investigation possesses similar nonlinear normal modes for the case of one-to-one internal resonance and nonsimilar nonlinear normal modes for
Buckling and longterm dynamics of a nonlinear model for the extensible beam
Ivana Bochicchio; Elena Vuk
2011-02-07
This work is focused on the longtime behavior of a non linear evolution problem describing the vibrations of an extensible elastic homogeneous beam resting on a viscoelastic foundation with stiffness k>0 and positive damping constant. Buckling of solutions occurs as the axial load exceeds the first critical value, \\beta_c, which turns out to increase piecewise-linearly with k. Under hinged boundary conditions and for a general axial load P, the existence of a global attractor, along with its characterization, is proved by exploiting a previous result on the extensible viscoelastic beam. As P<\\beta_c, the stability of the straight position is shown for all values of k. But, unlike the case with null stiffness, the exponential decay of the related energy is proved if P<\\bar\\beta(k), where \\bar\\beta(k) < \\beta_c(k) and the equality holds only for small values of k.
Complex light: dynamic phase transitions of a light beam in a nonlinear nonlocal disordered medium.
Conti, Claudio
2005-12-01
The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and nonlocal random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a dynamic phase transition. A connection with the random matrices approach for explaining the vibrational spectra of an ensemble of solitons is pointed out. General arguments based on a Brownian dynamics model are validated by the numerical simulation of a stochastic partial differential equation system. The results are also relevant for Bose condensed gases and plasma physics. PMID:16486091
NASA Technical Reports Server (NTRS)
Manning, Robert M.
2012-01-01
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.
The nonlinear saturation of beam-driven instabilities: Irregular bursting in the DIII-D tokamak
Heidbrink, W.W.; Danielson, J.R. (Department of Physics, University of California, Irvine, California 92717 (United States))
1994-12-01
Intense fast-ion populations created by neutral-beam injection into a tokamak can destabilize fishbone modes and other instabilities. Regular, periodic bursts of fishbones often occur but, when another magnetohydrodynamic (MHD) mode is also unstable, the burst cycle is irregular. The complexity of the burst cycle over a long time scale correlates with the purity of the Fourier spectrum during a single burst (a short time scale). The data are consistent with a simple predator--prey model in which the second MHD mode introduces periodic perturbations into the evolution equations.
Arbind, Archana
2012-10-19
+ @ w @x Qx + @ w @x Nxx @w @x wq dx Q2 w(xa; t) Q5 w(xb; t) (5.7b) 0 = Z xb xa I1 x @2u @t2 + I2 x @2 x @t2 + xQx + @ x @x Mxx dx Q3 x(xa; t) Q6 x(xb; t) (5.7 c) where Qi are the generalized forces... for the Timoshenko beam theory and can be given as Q1 = [ Nxx]xa ; Q4 = [Nxx]xb Q2 = Qx Nxx @w @x xa ; Q5 = Qx +Nxx @w @x xb Q3 = [ Mxx]xa ; Q6 = [Mxx]xb (5.8) The weak forms (5.7a){(5.7 c) can be expressed in terms of the displacements (u;w...
Normal dynamic scaling in the class of the nonlinear molecular-beam-epitaxy equation
NASA Astrophysics Data System (ADS)
Aarão Reis, F. D. A.
2013-08-01
The scaling of local height fluctuations is studied numerically in lattice growth models of the class of the nonlinear stochastic equation of Villain-Lai-Das Sarma (VLDS) in substrate dimensions d=1 and 2. In d=1, the average local slopes of the conserved restricted solid-on-solid (CRSOS) models converge to a finite value in the long-time limit, with power-law corrections in time whose exponents are close to 0.1. Other VLDS models in d=1, such as that of Das Sarma and Tamborenea, show a divergence of local slopes up to 106 monolayers, typical of anomalous roughening, but a comparison of roughness distributions shows that they scale as the linear fourth-order growth equation in those time scales. Normal scaling is also obtained in a modified VLDS equation with instability suppression, in contrast to recent numerical works. In d=2, a CRSOS model and a model with lateral aggregation of diffusing particles show normal scaling of the local slopes, also with small correction exponents. These results consistently show that the VLDS class has normal dynamic scaling in d=1 and 2, in agreement with the theoretical predictions of Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.94.166103 94, 166103 (2005), and they show that the apparently anomalous features observed in previous works are effects of large scaling correction terms or crossover effects.
Yin, Yaling; Lv, Xinjie; Zhao, Lina; Cao, Jingxiao; Yuan, Ye; Zhang, Chao; Leng, Hanyang; Xie, Zhenda; Xu, Ping; Zhao, Gang; Zhu, Shining
2011-03-14
We experimentally demonstrate a compact, all-solid-state 532 nm semi-Gaussian laser beam (SGB) source based on a 1064 nm laser and a transversely varying periodically-poled LiTaO3 (TPPLT) crystal as the laser beam shaper as well as the nonlinear frequency converter. We have used the designed TPPLT crystal to obtain a neat 532nm SGB with the quality of QSGB=1:17.5 by a single-pass second harmonic generation. The dependence of the generated SGB quality on the designed TPPLT parameter and the potential applications of the neat SGB are also discussed. PMID:21445167
Geometric Additions +Logarithms = Geometric Multiplication
NSDL National Science Digital Library
Mathematicians often argue that anything which can be represented numerically or algebraically can also be represented geometrically. This is perhaps true even to the extent that simple numeric calculations can be demonstrated geometrically. This example illustrates one such geometric process of addition. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.
Nonlinear-optical method for combining high-power laser beams. Report for 1 April 1988-30 April 1989
Chivian, J.S.; Glosson, C.A.; Cotten, W.D.; Cantrell, C.D.; DiMarco, S.F.
1989-04-28
The overall program goal was to investigate concepts for laser-controlled optics based on near-resonance nonlinear dispersion in gases, and to demonstrate a laser-induced grating capable of high-power laser-beam combining. The theoretical work extended the previous year's effort in giving a more detailed view of those aspects that might prevent observation of a grating, and led to optimization of experimental parameters. Modifications and improvements were made to the experimental apparatus. No grating was observed over a wide range of experimental conditions, although the apparatus was capable of such demonstration had a grating existed. The most likely cause of trouble appears to be the complexity of the SF{sub 6} medium chosen for demonstration. As an apparatus check, a medium (e.g, vanadium dioxide) can be used in which it is known that a grating can be demonstrated. Measurements were extended on the effect of noble gas admixtures into SF{sub 6} on the absorption of 16.26-micrometer radiation; helium suppresses absorption, argon and xenon enhance absorption. It would be worthwhile to continue these studies in light of information to be gained regarding the effect of collisions on absorption spectra in molecular species.
NSDL National Science Digital Library
2012-09-18
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).
ALI TUNA ALPER; J. Arnbak
1980-01-01
The use of a flexible transmit multiple-beam antenna (MBA) connected to a nonlinear satellite repeater is investigated as a means of adaptive resource allocation in a common-user communications network comprising different types and deployments of earth terminals. Such a general-purpose network is typically encountered in hybrid systems architectures supporting international command and control functions, e.g., in defense alliances or in
J. Sussmann; Guoqing Tang
1991-01-01
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
Steady-State Thermal Self-Focusing of Laser Beams
Anatolii P. Sukhorukov; S. Ya Fel'd; A. M. Khachatryan; É. N. Shumilov
1972-01-01
Some aspects of the theory of thermal self-focusing of cw laser beams are considered. A geometrical-optics ray equation is derived for a nonlinear absorbing medium. This ray equation is used to construct the aberration pattern in thermal self-focusing. The structure of the focal region is also analyzed. A detailed discussion is given of the behavior of the field at the
STEADY-STATE THERMAL SELF-FOCUSING OF LASER BEAMS
Anatolii P Sukhorukov; S Ya Feld; A M Khachatryan; É N Shumilov
1972-01-01
Some aspects of the theory of thermal self-focusing of cw laser beams are considered. A geometrical-optics ray equation is derived for a nonlinear absorbing medium. This ray equation is used to construct the aberration pattern in thermal self-focusing. The structure of the focal region is also analyzed. A detailed discussion is given of the behavior of the field at the
Nonlinear models Nonlinear Regression
Penny, Will
Nonlinear models Will Penny Nonlinear Regression Nonlinear Regression Priors Energies Posterior Metropolis-Hasting Proposal density References Nonlinear models Will Penny Bayesian Inference Course, WTCN, UCL, March 2013 #12;Nonlinear models Will Penny Nonlinear Regression Nonlinear Regression Priors
NASA Technical Reports Server (NTRS)
Muravyov, Alexander A.
1999-01-01
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.
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
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.
Jafari Bahman, F.; Maraghechi, B. [Department of Physics, Amirkabir University of Technology, Post Code 15916-34311 Tehran (Iran, Islamic Republic of)
2013-02-15
Efficiency enhancement in free-electron laser is studied by three-dimensional and nonlinear simulation using tapered helical wiggler magnetic field or tapered ion-channel density. In order to reduce the saturation length, prebunched electron beam is used. A set of nonlinear and coupled differential equations are derived that provides the self-consistent description of the evolution of both an ensemble of electrons and the electromagnetic radiation. These equations are solved numerically to show that the combined effect of tapering and prebunching results in significant enhancement of power and considerable reduction of the saturation length. To have a deeper insight into the problem, an analytical treatment is also presented that uses the small signal theory to derive a modified pendulum equation.
Lajimi, Seyed Amir Mousavi
2014-01-01
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.
Kim, Hyung Jin; /Fermilab
2011-12-01
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.
Geometric source separation: merging convolutive source separation with geometric beamforming
Lucas C. Parra; Christopher V. Alvino
2002-01-01
Convolutive blind source separation and adaptive beamforming have a similar goal—extracting a source of interest (or multiple sources) while reducing undesired interferences. A benefit of source separation is that it overcomes the conventional cross-talk or leakage problem of adaptive beamforming. Beam- forming on the other hand exploits geometric information which is often readily available but not utilized in blind algorithms.
Energy Dissipation when Internal Wave Beams Reflect from a Slope
NASA Astrophysics Data System (ADS)
Rodenborn, Bruce; Kiefer, Daniel; Zhang, Hepeng; Swinney, Harry L.
2015-03-01
Internal wave reflection from a uniform sloping boundary is often analyzed using linear or a weakly nonlinear inviscid theory. Under these assumptions for a linearly stratified fluid, Thorpe and Tabaei et al. derived predictions for the boundary angle where second harmonic generation should be most intense. We previously conducted experiments and simulations that found the angle that maximizes second harmonic generation is given instead by an empirical geometric relationship between the wave beam and boundary angles. In the previous study, we used integrated kinetic energy as a measure of beam intensity. We compare these results with a method using energy flux. We also study the energy flux into and out of a surface above the reflection region Eout /Ein and find high rates of energy dissipation O(90%). The rates remain high even for weakly nonlinear wave beams and with the viscosity reduced by an order of magnitude. S. A. Thorpe, J. Fluid Mech., 178, 279-302 (1987)
Hussien Abd El Baky
2008-01-01
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
Cha’o-Kuang Chen; H. Y. Lai; Chin-Chia Liu
2009-01-01
Analyzing the dynamic response of electrostatic devices is problematic due to the complexity of the interactions between the\\u000a electrostatic coupling effect, the fringing field effect and the nonlinear electrostatic force. To resolve this problem, this\\u000a study presents an efficient computational scheme in which the nonlinear governing equation of the electrostatic device is\\u000a obtained in accordance with Hamilton’s principle and is
Bright beam deflection by steering beams with mixed phase dislocations
Dreischuh, Alexander
and orientation of the dislocation. Keywords: Nonlinear optics, singular optics, photorefractive optics, self-focusing, the opportunities for implementation of beams with complex phase structure to steer beams in self-focusing nonlinear, the ability of beams containing mixed phase dislocation to steer light beams in self-focusing photorefractive
NSDL National Science Digital Library
Mr. Hoskins
2005-11-21
We will be learning the names and properties (# of sides, vertices, parallel sides, etc.) of several different geometric shapes. By now, everybody should know how many sides a square has and be able to recognize a circle. But, do you know how many vertices a parallelogram has, or how many sides to a rhombus? After completing the following exercies, you should be able to answer those questions and many ...
Eric Chisolm
2012-05-27
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.
Nonlinear computer-generated holograms.
Shapira, Asia; Juwiler, Irit; Arie, Ady
2011-08-01
We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering. PMID:21808390
Aronovich, Daniel; Bartal, Guy
2013-02-15
The performance of an optical hyperlens made of metal-dielectric layers can be improved by incorporating self-focusing nonlinearity in the dielectric layers. Using a modified beam propagation method in cylindrical coordinates, we show increased bandwidth and better propagation length, which can improve the spatial and temporal resolution of the device. PMID:23455086
Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Muravyov, Alexander A.
2000-01-01
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.
I. V. Dzedolik; V. P. Zakharov; V. V. Kulish
1988-01-01
A one-dimensionally limited, transversely homogeneous model of an artificial magnetodielectric is used to obtain a system of self-consistent nonlinear truncated equations for the parametrically resonant interaction of electromagnetic waves in an REB plasma. All the various types of transverse, periodically reversing electromagnetic pump and signal fields are taken into account, and the polarization, dispersion, impedance, and phase characteristics of the
NASA Astrophysics Data System (ADS)
Dai, Xiaoyu; Xiang, Yuanjiang; Wen, Shuangchun; Fan, Dianyuan
2010-08-01
Through using the standard split-step Fourier method, it is found that the transverse modulation instability (MI)can develop when beams copropagate in the positive- and the negative-index region of the metamaterials (MMs) respectively and it is equivalent with the temporal MI in the case of two pulses copropagate in the anomalous and normal dispersion regions of the optical fibers respectively, which is meaning that bright and dark electromagnetic spatial solitons may generate simultaneously. Furthermore, it is confirmed that the bright and dark electromagnetic spatial solitons may even generate simultaneously when beams copropagate in MM, which is a new way to generate spatial soliton pair for there is only leading to the generation of bright or dark spatial solitons in conventional material when two beams copropagate.
Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft
NASA Astrophysics Data System (ADS)
Patil, Mayuresh Jayawant
The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.
Griffin, L V; Gibeling, J C; Gibson, V A; Martin, R B; Stover, S M
1997-02-01
Experiments and analyses were performed to determine the cause of a nonlinear force-deflection response observed in four-point flexural fatigue of beams of cortical bone machined from the mid-diaphysis of the equine third metacarpus. Observable grooves which formed on the beam surface at supports and load noses were found to be the primary cause of the nonlinearity. An additional geometric nonlinearity at large deflections revealed by finite element modeling may be minimized by using the smallest diameter supports and load noses recommended in ASTM 790. However, frictional constraint of the beams at the load noses and supports can occur at low load levels and should be avoided by using roller-bearing supports and load noses, or some equivalent method. PMID:9001939
Hoffstaetter, Georg
can describe as image currents or as surface charge due to the transverse component of the bunchs analytical approaches to determining the fac- tors kx;y make drastic approximations to the BPM geome- try, we with approximately 100 beam position monitors (BPMs) dis- tributed around the storage ring. Each BPM consists of four
Volkov, S N; Koroteev, Nikolai I; Makarov, Vladimir A [Department of Physics, M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
1998-09-30
A theoretical investigation is made of second- harmonic generation in the interior of an isotropic and gyrotropic medium on a fourth-order optical nonlinearity. It is shown that a correct description of this experimentally detected effect requires taking into account the spatially finite nature of the fundamental-frequency wave, giving rise to a small longitudinal (directed along the beam axis) component of the electric field. Quadrature formulas are derived for the transverse distribution of the second harmonic field and for the total power of the harmonic. A detailed study is made of the special cases of tight focusing of the pump (fundamental-frequency) wave at the centre of a long medium and of exact phase matching. In these cases the quadrature expressions can be reduced to an analytic form. A study is reported of the characteristic features of the transverse profile of the second-harmonic intensity and of the dependence of the harmonic power on the state of polarisation of the pump wave. (nonlinear optical phenomena)
BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint
Wang, Q.; Sprague, M.; Jonkman, J.; Johnson, N.
2015-01-01
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.
Nonlinear feedback in robot arm control
T. J. Tarn; A. K. Bejczy; A. Isidori; Y. Chen
1984-01-01
Nonlinear feedback control is proposed for implementation of an advanced dynamic control strategy for robot arms. Using differential geometric system theory we obtained necessary and sufficient conditions for the existence of a nonlinear feedback control for a general nonlinear system to be externally linearized and simultaneously output decoupled. An algorithm is given for the construction of the required nonlinear feedback.
Youichi Sakawa
1992-01-01
An intermediate frequency (f_{ci } < f < f_{ce}) electrostatic instability has been observed in an electron beam produced, cylindrical plasma column. We have identified this instability as a new instability, the Modified Simon-Hoh instability (MSHI), which has an instability mechanism similar to the Simon-Hoh instability (SHI). This instability can occur in a cylindrical collisionless plasma if a radial DC
Effect of mass capture on the propogation of transverse waves in rotating beams
NASA Astrophysics Data System (ADS)
Hwang, K. H.; Shabana, A. A.
1995-09-01
The dispersive nature of the impact-induced transvers waves in mechanical systems with variable kinematic structure is examined in this investigation. The non-linear equations of motion of the rotatinf beam that account for the geometric stiffening are first derived using the principle of virtual work in dynamics. The effect of the geometric stiffening on the dynamics of the beam is first examined in order to determine the conditions under which the linearization of the dynamic equations of the beam is valid. In particular, the effect of the centrifugal geometric stiffening due to the distributed inertia of the beam is compared with the effect of the centrifugal geometric stiffening due to the inertia of a mass concentrated at the end of the beam. Using the results of this preliminary study, a simple model for the rotating beam is derived and used in the analysis of the impact0induced transverse waves. The jump discontinuity in the system velocities as the result of impact is predicted using the generalized impulse momentum equations that involove the restitution conditions. The effect of the mass capture on the phase and the group velocities of the dispersive transverse waves is demonstrated using the simple model that consists of a rotatinf beam impacted transversely by a rigid mass. The results obtained in this investigation indicate that the change in the system topology has more significant effects on the wave velocities of low frequency transverse waves as compared to high frequency waves. Furthermore, the change in these velocities is more significant in rotating beams as compared to non-rotating beams. A dimensionless rotation wave number is defined and is used to measure the significance of the effect of the angular velocity on the velocity of wave propagation.
NSDL National Science Digital Library
This learning resources comprise a healthy introduction to the physics of beams. The site, from the American Physical Society and Michigan State University's Beam Theory and Dynamical Systems Group, contains a brochure providing a basic introduction to the study of beams and their applications. Sections include Accelerators of the World, Spectrometers, Scientific and Medical Applications, Non-linear Dynamics, and more.
Omid Sepahi; Mohammad Reza Forouzan; Parviz Malekzadeh
2010-01-01
Based on the geometrically nonlinear theory of extensible elastic rods, the governing equations for post-buckling of variable\\u000a cross-section cantilever beams subjected to a concentrated axial load at its free end and a non-uniformly distributed axial\\u000a load are formulated. The Differential Quadrature Method (DQM) as a simple and computationally efficient numerical method is\\u000a used to obtain the critical buckling load. The
Jian-Xin Gu; Siu-Lai Chan
2005-01-01
This paper describes a consistent formulation of a tangent stiffness matrix for the geometrically nonlinear analysis of the space beam–column elements allowing for axial–flexural, lateral–torsional and axial–torsional buckling. In the proposed formulation, three deformation matrices are derived for moderately large rotations in practical three-dimensional space frames subjected to axial force and moments. These matrices are functions of the element deformations
NASA Astrophysics Data System (ADS)
Granmayeh Rad, A.; Madanipour, K.; Koohian, A.; Taheri, N.
2012-09-01
In this paper, a visual rapid technique is presented for the sign identification of nonlinear refractive index of colloidal nanoparticles based on non-scanning Moiré deflectometry technique. In this method two lasers are used, one as a pump laser beam which causes thermal nonlinear effects in the sample and the second one is used as a probe beam laser which allows us to monitor these effects by Moiré deflectometry technique. The gradient of the nonlinear refractive index produced by the interaction of the pump laser, generates a cylindrical lens in the sample. The concave and convex lenses are produced as a result of negative and positive nonlinear refractive index respectively. Geometrical and experimental investigations show the Moiré fringes are deflected in two different directions by these lenses. By observing the shape of deflected moirÃ© fringes, we can determine the sign of nonlinear refractive index and there will be no need for calibration or complicated calculations. This technique was applied for identification of nonlinear refractive index of Au and Tio_2 colloidal nanoparticles, under 47 mW second harmonic of Nd:YAG laser illumination. The sign of nonlinear refractive index of colloidal Au and Tio_2 nanoparticles were observed to be negative and positive respectively.
NASA Astrophysics Data System (ADS)
Leadenham, Stephen; Erturk, Alper
2014-04-01
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.
Ground control pointing and geometric transformation of satellite imagery
G. J. DAVISON
1986-01-01
LANDSAT imagery has been corrected for Earth curvature and rotation, satellite attitude errors and sensor non-linearities, it still contains significant geometric distortions with the centre of the scene only located to an accuracy of a few kilometres. For some applications these errors are unimportant but an increasing number of users need geometrically transformed imagery either for direct comparison with maps
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.
1984-01-01
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.
Beam-beam interaction in P-P colliding accelerators
Parzen, G.
1982-08-01
One model for beam growth due to the beam-beam interaction in P-P colliding accelerators is that it is due to the presence of non-linear forces generated by the fields produced by the beam plus some radomizing effect like noise, or a tune modulation. According to this model, to limit beam-beam effects, one should try to limit the size of the non-linear forces and the sources of noise or tune modulation. This model can also be used to compare the severity of beam-beam effects in two situations by comparing the size of the non-linear forces. In this paper, this approach will be used to study three problems: to compare the effects of beam-beam non-linear resonances in the ISR with those in ISABELLE; to estimate the strength of a spectrometer magnet that may be placed at one of the beam crossing points, without appreciably increasing the beam-beam effects; and to compare the beam-beam interaction for colliding beam accelerators with different crossing-angles and different ..beta../sub x/ and ..beta../sub y/ at the crossing points.
Constrained ballistics and geometrical optics
Epstein, Marcelo
2014-01-01
The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the initially unconstrained formulation. Although the resulting equations are not, in principle, obtained from a variational statement, it is shown that the trajectories coincide with those of geometrical optics in a medium with a suitably chosen refractive index, as prescribed by Fermat's principle of least time. This fact gives rise to an intriguing mechano-optical analogy. The trajectories are further studied and discussed.
Transition from linear- to nonlinear-focusing regime in filamentation
Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin
2014-01-01
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
Transition from linear- to nonlinear-focusing regime in filamentation.
Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin
2014-01-01
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
Nonlinear aerostatic stability analysis of suspension bridges
Virote Boonyapinyo; Yingsak Lauhatanon; Panitan Lukkunaprasit
2006-01-01
Nonlinear aerostatic stability analysis of long-span suspension bridges is studied by including directly the three combined effects of: (1) nonlinear three-component displacement-dependent wind loads, (2) geometric nonlinearity, and (3) material nonlinearity. The nonlinear three-component displacement-dependent wind loads are included through the static aerodynamic coefficients as a function of angle of attack. The various structural bucklings, such as flexural buckling, torsional
Analysis of nonlinear self-focusing phenomenon in high-power laser system based on ray-tracing
NASA Astrophysics Data System (ADS)
Wang, Weiwei; Li, Xiaotong; Cen, Zhaofeng; Zhang, Luwei
2014-11-01
In high power laser systems, nonlinear effect, one of the key factors of beam wavefront aberration and even irreversible damage to system, has always been one of the top considerations of researchers for decades. A hybrid ray-tracing method for both linear media and nonlinear media based on geometric optics is presented in this paper and realized by programming. In a simple optic system with KDP crystal, an obvious decline of beam quality is observed in high laser power density conditions and a method taking component intervals as compensation of beam quality is proved feasible. Considering the complexity of traditional modeling method based on surfaces, a modeling method based on components is established. Hopefully, the conclusions and flaws of this paper can shed light on relevant work and further research.
On geometric factors for neutral particle analyzers
Stagner, L.; Heidbrink, W. W. [University of California-Irvine, Irvine, California 92697-4575 (United States)
2014-11-15
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.
On geometric factors for neutral particle analyzers.
Stagner, L; Heidbrink, W W
2014-11-01
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
HIERARCHICAL GEOMETRIC APPROXIMATIONS
North Carolina at Chapel Hill, University of
HIERARCHICAL GEOMETRIC APPROXIMATIONS TR-050 1994 Amitabh Varshney Department of Computer Science;HIERARCHICAL GEOMETRIC APPROXIMATIONS by Amitabh Varshney A Dissertation submitted to the faculty Advisor Reader Reader Reader #12;@1994 Amitabh Varshney ALL RIGHTS RESERVED #12;AMITABH VARSHNEY
Topological defects, geometric phases, and the angular momentum of light
S C Tiwari
2007-04-02
Recent reports on the intriguing features of vector vortex bearing beams are analyzed using geometric phases in optics. It is argued that the spin redirection phase induced circular birefringence is the origin of topological phase singularities arising in the inhomogeneous polarization patterns. A unified picture of recent results is presented based on this proposition. Angular momentum shift within the light beam (OAM) has exact equivalence with the angular momentum holonomy associated with the geometric phase consistent with our conjecture.
Hybrid Matrix Geometric Algebra
Garret Sobczyk; Gordon Erlebacher
2004-01-01
\\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
N. Rashevsky
1956-01-01
The twentieth century has witnessed a geometrization of physics, that is, a reduction of the basic concepts of physics to\\u000a geometric concepts. The topological approach to biology, recently proposed and to some extent developed by the author, is\\u000a a small step in the direction of geometrization of biology, but is unable to achieve the main purpose of such a geometrization
ArithmeticGeometric Progression
Feret, Jérôme
VMCAI'05 The ArithmeticGeometric Progression Abstract Domain Jérôme Feret École Normale Supérieure; Overview 1. Introduction 2. Case study 3. Arithmeticgeometric progressions 4. Benchmarks 5. Conclusiongeometric progressions 4. Benchmarks 5. Conclusion Jérôme Feret, LIENS 13 January, 2005 #12; Arithmetic
Bloch-sphere representation of three-vertex geometric phases
Tamate, Shuhei; Ogawa, Kazuhisa; Kitano, Masao [Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510 (Japan)
2011-11-15
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.
NASA Technical Reports Server (NTRS)
Gray, Carl E., Jr.
1988-01-01
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.
Deforming geometric transitions
NASA Astrophysics Data System (ADS)
Rossi, Michele
2015-04-01
After a quick review of the wild structure of the complex moduli space of Calabi-Yau 3-folds and the role of geometric transitions in this context (the Calabi-Yau web) the concept of deformation equivalence for geometric transitions is introduced to understand the arrows of the Gross-Reid Calabi-Yau web as deformation-equivalence classes of geometric transitions. Then the focus will be on some results and suitable examples to understand under which conditions it is possible to get simple geometric transitions, which are almost the only well-understood geometric transitions both in mathematics and in physics.
Geometric Gyrokinetic Theory for Edge Plasma
Qin, H; Cohen, R H; Nevins, W M; Xu, X Q
2007-01-18
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.
A study on the dynamics of rotating beams with functionally graded properties
NASA Astrophysics Data System (ADS)
Piovan, M. T.; Sampaio, R.
2009-10-01
The constant needs of the industry impel the engineering community in seeking of new concepts and new strategies in order to improve the structural response of structures as well as to enhance the endurance of materials. This is particularly true in the case of rotating blades that are subjected to severe environmental conditions such as high temperatures as well as mechanical conditions such as high rotating accelerations, centrifugal forces, geometric stiffening, among others. It is well known that flexible beams become stiffer when subjected to high speed rotations, because of the axial-bending coupling associated to the large displacements of the beam cross-section. This is called geometric stiffening effect and it was analyzed over the last decades in many beam applications from blade problems to drill-string modeling. In this paper a rotating nonlinear beam model accounting for arbitrary axial deformations is developed. The beam is made of functionally graded materials (FGM). This model is also employed to analyze other simplified models based on isotropic materials or composite materials, that are particular cases of the present formulation. The assumption of steady-state values of centrifugal loads is evaluated. It has to be said that there is a lack of information about modeling of beams made of functionally graded materials and this paper is intended to be a contribution on the subject.
An efficient geometric image distortion correction method for a biplanar planar gradient coil
Haiying Liu
2000-01-01
Since the spatial field non-linearity of gradient coils translates into image geometric distortion in MRI, in many applications,\\u000a such as cardiac function analysis and interventional MR-based device tracking\\/guidance, where the precise geometric information\\u000a is needed, the presence of geometric image distortion can not be simply ignored. To address the concern for geometric image\\u000a distortion, we have developed and validated a
Geometric integrators for ODEs
Robert I. McLachlan; G. Reinout W. Quispel
2006-01-01
Geometric integration is the numerical integration of a differential equation, while preserving one or more of its 'geometric' properties exactly, i.e. to within round-off error. Many of these geometric properties are of crucial importance in physical applications: preservation of energy, momentum, angular momentum, phase-space volume, symmetries, time-reversal symmetry, symplectic structure and dissipation are examples. In this paper we present a
Geometric continuum regularization of quantum field theory
Halpern, M.B. (California Univ., Berkeley, CA (USA). Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
MECHANICS AND NONLINEAR CONTROL: MAKING UNDERWATER VEHICLES
Leonard, Naomi
MECHANICS AND NONLINEAR CONTROL: MAKING UNDERWATER VEHICLES RIDE AND GLIDE Naomi Ehrich Leonard \\Lambda \\Lambda Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544 naomi@princeton.edu Abstract: Methods from geometric mechanics and dynamical systems theory make
Geometric Dimensioning Sentence Structure.
ERIC Educational Resources Information Center
McCuistion, Patrick J.
1991-01-01
Explanations of geometric dimensioning symbols are provided to assist in the comprehension of the implied basic sentence structure of modern geometric dimensioning and tolerance. The proper identification and interpretation of the substantive language within several exemplary engineering drawings, otherwise called feature control frames, is…
Geometric Shapes in Architecture
NSDL National Science Digital Library
Fox, Lauretta J.
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.
Geometrization of Quantum Mechanics
J. F. Carinena; J. Clemente-Gallardo; G. Marmo
2007-03-23
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.
Harrington, J. Patrick
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
Geometrical Optics In A Laser Laboratory
NASA Astrophysics Data System (ADS)
Hopkins, Robert E.
1981-12-01
About four years ago I joined the University of Rochester Laboratory for Laser Energetics; being apprehensive that my extensive experience in classical geometrical optics would be of little use to a laser fusion program. The Laboratory was in the early phase of building the 24 beam OMEGA laser system and it soon became evident that once again basic geometrical optics could make significant contributions to a modern new development. In this talk I will describe some of the basic optical concepts encountered during the engineering phase of building a large laser system. The optical concepts are not new but often forgotten. It illustrates again that geometrical optics takes one far down the road to solving optical problems and is used in almost every new advance in science and engineering.
Hierarchies of Geometric Entanglement
Blasone, M; De Siena, S; Illuminati, F
2007-01-01
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...
Geometrical Monte Carlo simulation of atmospheric turbulence
NASA Astrophysics Data System (ADS)
Yuksel, Demet; Yuksel, Heba
2013-09-01
Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes intensity scintillation and beam wander from propagation through turbulent eddies of varying sizes and refractive index. This can severely impair the operation of target designation and Free-Space Optical (FSO) communications systems. In addition, experimenting on an FSO communication system is rather tedious and difficult. The interferences of plentiful elements affect the result and cause the experimental outcomes to have bigger error variance margins than they are supposed to have. Especially when we go into the stronger turbulence regimes the simulation and analysis of the turbulence induced beams require delicate attention. We propose a new geometrical model to assess the phase shift of a laser beam propagating through turbulence. The atmosphere along the laser beam propagation path will be modeled as a spatial distribution of spherical bubbles with refractive index discontinuity calculated from a Gaussian distribution with the mean value being the index of air. For each statistical representation of the atmosphere, the path of rays will be analyzed using geometrical optics. These Monte Carlo techniques will assess the phase shift as a summation of the phases that arrive at the same point at the receiver. Accordingly, there would be dark and bright spots at the receiver that give an idea regarding the intensity pattern without having to solve the wave equation. The Monte Carlo analysis will be compared with the predictions of wave theory.
NASA Technical Reports Server (NTRS)
Aston, Graeme (Inventor)
1984-01-01
A system is described that combines geometrical and electrostatic focusing to provide high ion extraction efficiency and good focusing of an accelerated ion beam. The apparatus includes a pair of curved extraction grids (16, 18) with multiple pairs of aligned holes positioned to direct a group of beamlets (20) along converging paths. The extraction grids are closely spaced and maintained at a moderate potential to efficiently extract beamlets of ions and allow them to combine into a single beam (14). An accelerator electrode device (22) downstream from the extraction grids, is at a much lower potential than the grids to accelerate the combined beam.
Morphing of Geometric Composites via Residual Swelling
Matteo Pezzulla; Steven A. Shillig; Paola Nardinocchi; Douglas P. Holmes
2015-05-30
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth--like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques.
AJ Geometric Formulas Calculator
NSDL National Science Digital Library
Jimmy Raymond
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.
Geometric ghosts and unitarity
Ne'eman, Y.
1980-09-01
A review is given of the geometrical identification of the renormalization ghosts and the resulting derivation of Unitarity equations (BRST) for various gauges: Yang-Mills, Kalb-Ramond, and Soft-Group-Manifold.
Geometric intrinsic symmetries
Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl; Szulerecka, A.; Pedrak, A. [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)] [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Geometric Algebras and Extensors
NASA Astrophysics Data System (ADS)
Fernández, V. V.; Moya, A. M.; Rodrigues, W. A.
This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field. In this first paper we introduce the key algebraic tools for the development of our program, namely the euclidean geometrical algebra of multivectors Cl(V,G_{E}) and the theory of its deformations leading to metric geometric algebras Cl(V,G) and some special types of extensors. Those tools permit obtaining, the remarkable golden formula relating calculations in Cl(V,G) with easier ones in Cl(V,G_{E}) (e.g., a noticeable relation between the Hodge star operators associated to G and G_{E}). Several useful examples are worked in details fo the purpose of transmitting the "tricks of the trade".
Prospects for Geometric Complexity Theory Prospects for Geometric Complexity Theory
Bürgisser, Peter
Prospects for Geometric Complexity Theory Prospects for Geometric Complexity Theory Peter B¨urgisser University of Paderborn 27th IEEE Conference on Computational Complexity Porto, June 28, 2012 #12;Prospects for Geometric Complexity Theory Two major problems Two major problems #12;Prospects for Geometric Complexity
Nonlinear Analysis ( ) Contents lists available at SciVerse ScienceDirect
Radulescu, Vicentiu
of quasiconformal mappings, non-Newtonian fluids, image processing, differential geometry, geometric function theory, partial differential equations, calculus of variations, non-linear potential theory, the theory
Input Pulse Response in Nonlinear Transmission Line
Ian M. Rittersdorf; David M. French; Michael Johnson; Y. Y. Lau; Ronald M. Gilgenbach; Donald Shiffler; Brad Hoff; John Luginsland
2010-01-01
Nonlinear transmission lines have been demonstrated to be an effective technique for generating high power ultrawideband or mesoband radiation without the need for a vacuum system, electron beam, or magnet. Experiments have been performed at UM on a discrete element nonlinear transmission line that uses ferrite inductors as the nonlinear element. Pulse sharpening of multi-kA input pulses has been observed
Nonlinear Optics and Applications
NASA Technical Reports Server (NTRS)
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
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.
Confined energy distribution for charged particle beams
Jason, Andrew J. (Los Alamos, NM); Blind, Barbara (Los Alamos, NM)
1990-01-01
A charged particle beam is formed to a relatively larger area beam which is well-contained and has a beam area which relatively uniformly deposits energy over a beam target. Linear optics receive an accelerator beam and output a first beam with a first waist defined by a relatively small size in a first dimension normal to a second dimension. Nonlinear optics, such as an octupole magnet, are located about the first waist and output a second beam having a phase-space distribution which folds the beam edges along the second dimension toward the beam core to develop a well-contained beam and a relatively uniform particle intensity across the beam core. The beam may then be expanded along the second dimension to form the uniform ribbon beam at a selected distance from the nonlinear optics. Alternately, the beam may be passed through a second set of nonlinear optics to fold the beam edges in the first dimension. The beam may then be uniformly expanded along the first and second dimensions to form a well-contained, two-dimensional beam for illuminating a two-dimensional target with a relatively uniform energy deposition.
Geometrical stiffness and sensitivity matrices for optimization of semi-rigid steel frameworks
L. Xu
1992-01-01
A geometrical stiffness matrix for a flexibly-connected member is developed for the analysis and design of semirigid framed structures when geometrical non-linearity (P — ? effects and other second-order effects) must be considered. A “fixity factor” defining the rigidity of a connection relative to the attached member is introduced to model different types of member connectivity. The sensitivities of the
Variational Analysis of the Coupling Between a Geometrically Exact Cosserat Rod and an Elastic
Nabben, Reinhard
Variational Analysis of the Coupling Between a Geometrically Exact Cosserat Rod and an Elastic coupling of a geometrically exact Cosserat rod to a nonlinearly elastic continuum. In this setting, appro- priate coupling conditions have to connect a one-dimensional model with director variables to a three
Geometric Surface and Brain Warping via Geodesic Minimizing Lipschitz Extensions
Paris-Sud XI, Université de
in this area have developed and/or have their favorite brain warping technique.4 A few representative works canGeometric Surface and Brain Warping via Geodesic Minimizing Lipschitz Extensions Facundo M´emoli1, and in particular the nonlinear registration of brain imaging data, is presented in this paper. The basic concept
Nonlinear cyclotron harmonic absorption
Seol, Jae Chun [National Fusion Research Institute, Yuseong, Daejeon 555-333 (Korea, Republic of); Hegna, C. C.; Callen, J. D. [Department of Engineering Physics, University of Wisconsin, Madison, Wisconsin 53706-1609 (United States)
2009-05-15
Nonlinear oscillations of particle's energy occur when a particle stays in a resonance zone. In this work, we found that collisionless heating of particles occurs when they pass the microwave beam at first, second, and third harmonic resonances. It is found that the net energy gain of particles from the microwaves is inversely proportional to the wave frequency. It is also found that the net energy gain is dependent on the microwave beam width. The energy gain of particles from a single pass through a resonance zone has been formulated analytically. A numerical calculation has been performed and the results are in good agreement with the analytic calculation. Both analytic and numerical calculations show a strong frequency dependence and a beam width dependence of nonlinear cyclotron resonance heating.
Thermodynamic Geometric Stability of Quarkonia states
Stefano Bellucci; Vinod Chandra; Bhupendra Nath Tiwari
2010-10-21
We compute exact thermodynamic geometric properties of the non-abelian quarkonium bound states from the consideration of one-loop strong coupling. From the general statistical principle, the intrinsic geometric nature of strongly coupled QCD is analyzed for the Columbic, rising and Regge rotating regimes. Without any approximation, we have obtained the non-linear mass effect for the Bloch-Nordsieck rotating strongly coupled quarkonia. For a range of physical parameters, we show in each cases that there exists a well-defined, non-degenerate, curved, intrinsic Riemannian manifold. As the gluons become softer and softer, we find in the limit of the Bloch-Nordsieck resummation that the strong coupling obtained from the Sudhakov form factor possesses exact local and global thermodynamic properties of the underlying mesons, kaons and $D_s$ particles.
Determination of nonlinear refractive indices by external self-focusing
B. Meier; A. Penzkofer
1989-01-01
The nonlinear refractive index of benzene is determined by measuring the reduction of the beam divergence of picosecond ruby laser pulses when passing through a benzene sample. Time-integrated spatial beam profiles give an effective refractive index while time-resolved beam profiles measured with a streak camera allow the determination of the temporal evolution of the nonlinear refractive index.
NASA Astrophysics Data System (ADS)
Tahani, Masoud; Askari, Amir R.
2014-09-01
In spite of the fact that pull-in instability of electrically actuated nano/micro-beams has been investigated by many researchers to date, no explicit formula has been presented yet which can predict pull-in voltage based on a geometrically non-linear and distributed parameter model. The objective of present paper is to introduce a simple and accurate formula to predict this value for a fully clamped electrostatically actuated nano/micro-beam. To this end, a non-linear Euler-Bernoulli beam model is employed, which accounts for the axial residual stress, geometric non-linearity of mid-plane stretching, distributed electrostatic force and the van der Waals (vdW) attraction. The non-linear boundary value governing equation of equilibrium is non-dimensionalized and solved iteratively through single-term Galerkin based reduced order model (ROM). The solutions are validated thorough direct comparison with experimental and other existing results reported in previous studies. Pull-in instability under electrical and vdW loads are also investigated using universal graphs. Based on the results of these graphs, non-dimensional pull-in and vdW parameters, which are defined in the text, vary linearly versus the other dimensionless parameters of the problem. Using this fact, some linear equations are presented to predict pull-in voltage, the maximum allowable length, the so-called detachment length, and the minimum allowable gap for a nano/micro-system. These linear equations are also reduced to a couple of universal pull-in formulas for systems with small initial gap. The accuracy of the universal pull-in formulas are also validated by comparing its results with available experimental and some previous geometric linear and closed-form findings published in the literature.
I. V. Dzedolik; V. P. Zakharov; V. V. Kulish
1988-01-01
A self-consistent nonlinear theory is used to carry out a physical analysis of three-wave parametric resonance occurring during the interaction of REBs in periodically reversing electromagnetic fields. H-ubitron and Dopplertron amplification models are considered. Polarization effects, saturation during the achievement of asymptoptic and explosive regimes, and the generation mechanism of an additional H-ubiutron field are investigated. It is shown that
NASA Astrophysics Data System (ADS)
Dzedolik, I. V.; Zakharov, V. P.; Kulish, V. V.
1988-06-01
A self-consistent nonlinear theory is used to carry out a physical analysis of three-wave parametric resonance occurring during the interaction of REBs in periodically reversing electromagnetic fields. H-ubitron and Dopplertron amplification models are considered. Polarization effects, saturation during the achievement of asymptoptic and explosive regimes, and the generation mechanism of an additional H-ubiutron field are investigated. It is shown that high values of interaction efficiency can be achieved in models with an optimal electrostatic support.
Characteristics of Laser Beams Propagating in a Homogeneous Medium
Ching-Yen Ho
Characteristics of laser beams propagating in a homogeneous medium were investigated in this paper. The wavelength, refractive index, and beam waist radius specify the divergence angles of laser beams. Based on the viewpoints of geometrical and physical optics the properties of optics field near and far from beam waist are evidently different. The main aim of this study was to
Shakedown Analysis of Curved Beams
F. Tin Lol
1984-01-01
Shakedown analysis of fixed-ended elastoplastic curved beams is presented. Both nonlinear and piecewise linearized yield conditions are considered. It is shown that the former assumption requires the solution of a nonlinear programming problem, while the latter assumption leads to a linear programming problem. Although these formulations cover both cases when either incremental collapse or alternating plasticity governs the shakedown limit
Structured pursuits for geometric super-resolution
Stéphane Mallat; Guoshen Yu
2009-01-01
Abstract—Super-resolution image zooming,is possible when,the image,has,some,geometric,regularity. We introduce,a general class of non-linear inverse estimators, which combines linear estimators,with mixing,weights,in a frame,providing,a sparse representation. Mixing weights are computed,with a block decom- position, which minimizes a Tikhonov energy penalized by an l, norm,of the mixing,weights. A fast orthogonal,matching,pursuit algorithm,computes,the mixing,weights. Adaptive,directional image,interpolations,are calculated,with,mixing,weights,in a wavelet frame.
Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings
NASA Astrophysics Data System (ADS)
Dakel, Mzaki; Baguet, Sébastien; Dufour, Régis
2014-05-01
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.
L. Heisserman
1994-01-01
Boundary solid grammars use design rules that express complex geometric conditions and operations using a logical reasoning mechanism, allowing one to construct powerful rules and describe appropriate grammars for the generation of solid models for a variety of design domains. The formalism I present in this article is not sufficient for all engineering and architectural domains (e.g., polyhedral solids are
ERIC Educational Resources Information Center
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
Geometric Algorithms primitive operations
Sedgewick, Robert
algebra and check. · Idea 2: check if the endpoints of one line segment are on differe1 Geometric Algorithms primitive operations convex hull closest pair voronoi diagram References://www.ics.uci.edu/~eppstein/geom.html airflow around an aircraft wing #12;3 primitive operations convex hull closest pair voronoi diagram #12
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
Geometric Series via Probability
ERIC Educational Resources Information Center
Tesman, Barry
2012-01-01
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…
Attributes of Geometric Shapes
NSDL National Science Digital Library
Michael Banek
2012-06-18
This resource is a fun and engaging activity that will allow the students to identify and name shapes by their attributes. The students will move around and construct various geometric figures in order to build a solid understanding of the figures.
Frank Hülsemann; Markus Kowarschik; Marcus Mohr; Ulrich Rüde
Multigrid methods are among the fastest numerical algorithms for the solution of large sparse systems of linear equations. While these algorithms exhibit asymptotically optimal computational complexity, their efficient parallelisation is hampered by the poor computation-to-communication ratio on the coarse grids. Our contribution discusses parallelisation techniques for geometric multigrid methods. It covers both theoretical approaches as well as practical implementation issues
Pragmatic geometric model evaluation
NASA Astrophysics Data System (ADS)
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to calculate basically two model variations that can be seen as geometric extremes of all available input data. This does not lead to a probability distribution for the spatial position of geometric elements but it defines zones of major (or minor resp.) geometric variations due to data uncertainty. Both model evaluations are then analyzed together to give ranges of possible model outcomes in metric units.
Acoustic nonlinearity in fluorinert FC-43
Pantea, Cristian [Los Alamos National Laboratory; Sinha, Dipen N [Los Alamos National Laboratory; Osterhoudt, Curtis F [Los Alamos National Laboratory; Mombourquette, Paul C [Los Alamos National Laboratory
2009-01-01
Fluorinert FC-43 nonlinearity was investigated using two approaches: (i) a finite amplitude method with harmonic production; and (ii) a nonlinear frequency mixing in the fluid with consequent beam profile measurement of the difference frequency. The finite amplitude method provides information on the coefficient of nonlinearity, {beta}, through the amplitudes of the fundamental and the second harmonic, at a certain transmitter-receiver distance. A calibrated hydrophone was used as a receiver, in order to obtain direct pressure measurements of the acoustic waves in the fluid. The role of transmitter-receiver distance in {beta} determination is investigated. In the second approach, a single transducer is used to provide two high-frequency beams. The collinear high-frequency beams mix nonlinearly in the fluid resulting in a difference frequency beam and higher order harmonics of the primaries. The difference frequency beam profite is investigated at lengths beyond the mixing distance. The experimental data are compured with the KZK theory.
GEOMETRIC STIFFNESS AND STABILITY OF RIGID BODY MODES
H. El-Absy; A. A. Shabana
1997-01-01
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
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-01-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Crystal-Like geometric modeling
Landreneau, Eric Benjamin
2006-08-16
Crystals are natural phenomena that exhibit high degrees of order, symmetry, and recursion. They naturally form interesting and inspiring geometric shapes. This thesis provides geometric modeling techniques for creating shapes with crystallike...
Beam-beam interaction working group summary
Siemann, R.H.
1995-03-01
The limit in hadron colliders is understood phenomenologically. The beam-beam interaction produces nonlinear resonances and makes the transverse tunes amplitude dependent. Tune spreads result from the latter, and as long as these tune spreads do not overlap low order resonances, the lifetime and performance is acceptable. Experience is that tenth and sometimes twelfth order resonances must be avoided, and the hadron collider limit corresponds roughly to the space available between resonances of that and lower order when operating near the coupling resonance. The beam-beam interaction in e{sup +}e{sup {minus}} colliders is not understood well. This affects the performance of existing colliders and could lead to surprises in new ones. For example. a substantial amount of operator tuning is usually required to reach the performance limit given above, and this tuning has to be repeated after each major shutdown. The usual interpretation is that colliding beam performance is sensitive to small lattice errors, and these are being reduced during tuning. It is natural to ask what these errors are, how can a lattice be characterized to minimize tuning time, and what aspects of a lattice should receive particular attention when a new collider is being designed. The answers to this type of question are not known, and developing ideas for calculations, simulations and experiments that could illuminate the details of the beam-beam interaction was the primary working group activity.
Geometrical Wake of a Smooth Flat Collimator
Stupakov, G.V.; /SLAC
2011-09-09
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.
Geometric Solids and Their Properties
NSDL National Science Digital Library
Illuminations; National Council of Teachers of Mathematics (NCTM)
2000-01-01
Explore geometric solids and their properties with these interactive tools, beginning with an introduction to the faces of basic polyhedra; counting the number of faces, edges, and corners (vertices) in various solids; discovering Euler's Formula; constructing physical models of geometric solids; and identifying which geometric solids can be made from given nets.
The classical geometrization electromagnetism
C. A. Duarte
2015-02-11
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.
CAM - Geometric systems integration
NASA Astrophysics Data System (ADS)
Dunlap, G. C.
The integration of geometric and nongeometric information for efficient use of CAM is examined. Requirements for engineering drawings requested by management are noted to involve large volumes of nongeometric data to define the materials and quantity variables which impinge on the required design, so that the actual design may be the last and smaller step in the CAM process. Geometric classification and coding are noted to offer an alpha/numeric identifier for integrating the engineering design, manufacturing, and quality assurance functions. An example is provided of a turbine gear part coding in terms of polycode and monocode displays, showing a possible covering of more than 10 trillion features. Software is stressed as the key to integration of company-wide data.
Global Tracking Control Structures for Nonlinear Singularly Perturbed
Valasek, John
Global Tracking Control Structures for Nonlinear Singularly Perturbed Aircraft Systems Anshu Literature Review Geometric Singular Perturbation Theory Mathematical Development & Stability Analysis: Two-Time Scale Systems/ Singularly Perturbed Systems Examples: mechanical oscillators, airplanes
Nonlinear dynamics of harmonically excited circular cylindrical shells containing fluid flow
K. Karagiozis; M. Amabili; M. P. Païdoussis
2010-01-01
In the present study, the geometrically nonlinear vibrations of circular cylindrical shells, subjected to internal fluid flow and to a radial harmonic excitation in the spectral neighbourhood of one of the lowest frequency modes, are investigated for different flow velocities. The shell is modelled by Donnell's nonlinear shell theory, retaining in-plane inertia and geometric imperfections; the fluid is modelled as
Jacques Carette; Mustafa Elsheikh; Spencer Smith
2011-01-01
We present the design and implementation of a generative geometric kernel. The kernel generator is generic, type-safe, parametrized by many design-level choices and extensible. The resulting code has minimal traces of the design abstractions. We achieve genericity through a layered design deriving concepts from affine geometry, linear algebra and abstract algebra. We achieve parametrization and type-safety by using OCaml's module
Geometrical deuteron stripping revisited
Neoh, Y. S.; Yap, S. L. [Plasma Research Technology Center, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2014-03-05
We investigate the reality of the idea of geometrical deuteron stripping originally envisioned by Serber. By taking into account of realistic deuteron wavefunction, nuclear density, and nucleon stopping mean free path, we are able to estimate inclusive deuteron stripping cross section for deuteron energy up to before pion production. Our semiclassical model contains only one global parameter constant for all nuclei which can be approximated by Woods-Saxon or any other spherically symmetric density distribution.
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr. (Principal Investigator)
1996-01-01
The goal of this research project is to develop assumed-stress hybrid elements with rotational degrees of freedom for analyzing composite structures. During the first year of the three-year activity, the effort was directed to further assess the AQ4 shell element and its extensions to buckling and free vibration problems. In addition, the development of a compatible 2-node beam element was to be accomplished. The extensions and new developments were implemented in the Computational Structural Mechanics Testbed COMET. An assessment was performed to verify the implementation and to assess the performance of these elements in terms of accuracy. During the second and third years, extensions to geometrically nonlinear problems were developed and tested. This effort involved working with the nonlinear solution strategy as well as the nonlinear formulation for the elements. This research has resulted in the development and implementation of two additional element processors (ES22 for the beam element and ES24 for the shell elements) in COMET. The software was developed using a SUN workstation and has been ported to the NASA Langley Convex named blackbird. Both element processors are now part of the baseline version of COMET.
Identification of nonlinear boundary effects using nonlinear normal modes
Hamid Ahmadian; Arash Zamani
2009-01-01
Local nonlinear effects due to micro-slip\\/slap introduced in boundaries of structures have dominant influence on their lower modal model. This paper studies these effects by experimentally observing the behavior of a clamped–free beam structure with local nonlinearities due to micro-slip at the clamped end. The structure is excited near one of its resonance frequencies and recorded responses are employed to
Overview of the APT high-energy beam transport and beam expanders
Shafer, R.E.; Blind, B.; Gray, E.R. [and others
1997-08-01
The APT high energy beam transport (HEBT) and beam expanders convey the 1700-MeV, 100-mA cw proton beam from the linac to the tritium target/blanket assembly, or a tuning beam stop. The HEBT includes extensive beam diagnostics, collimators, and beam jitter correction, to monitor and control the 170-MW beam prior to expansion. A zero-degree beamline conveys the beam to the beam stop, and an achromatic bend conveys the beam to the tritium production target. Nonlinear beam expanders make use of higher-order multipole magnets and dithering dipoles to expand the beam to a uniform-density, 16-cm wide by 160-cm high rectangular profile on the tritium-production target. The overall optics design will be reviewed, and beam simulations will be presented.
Geometric phase in Bohmian mechanics
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
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.
Bound states of nonlinear Schr¨ odinger equations with a periodic nonlinear microstructure
G. Fibich; Y. Sivan
We consider nonlinear bound states of the nonlinear Schr¨ odinger equation i@z( z,x) = @2x (1 + m(Nx))| | p 1, in the presence of a nonlinear periodic microstructure m(Nx). This equation models the propagation of laser beams in a medium whose nonlinear refractive index is modulated in the transverse direction, and also arises in the study of Bose-Einstein Condensation
NASA Technical Reports Server (NTRS)
Cantrell, John H.; Yost, William T.
1990-01-01
The effects of material structure on the nonlinearity parameters are reviewed. Problems discussed include definition of nonlinearity parameters, square-law nonlinearity and collinear beam-mixing, structure dependence of the nonlinearity parameters, negative nonlinearity parameters, and implications for materials characterization.
Stabilization of LCD devices via geometric alteration.
Jeon, Il; Yoon, MinSung; Lee, Je-Hoon
2013-02-20
Glass bending in LCD displays is an inherent problem that has challenged many engineers. As a solution to this problem, we propose a methodology that can tackle the root of the phenomenon in terms of linear elastic beam theory. Using this hypothesis, we devised a background theory and a solution. In this paper, we present a glass panel to which geometrical changes, such as furrow, groove, and curb have been applied. These geometrical changes are applied to the nonactive area of the glass panel. To confirm the validity of our approach, we conducted simulation tests as well as hands-on experiments to observe the thermo-mechanical behavior of the device under various conditions. The simulation results using the Ansys simulator show that the proposed technique can reduce the deformation level of panel bending by 40%. In the experiment using a bare cell with polarizer films attached and with performing the high temperature reliability test, the deformation level of panel bending is reduced by half compared to the reference glass panel without any geometric alteration. PMID:23434997
Auto calibration of a cone-beam-CT
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
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.
Rotordynamic instability: nonlinear modeling and analysis
Cooper, Charles Ira
1998-01-01
A basic rotordynamic model is developed for an crographics. unbalanced rotor connected to a shaft modeled as a continuous beam. This model examines the effects of nonlinear dynamics strictly related to the rotor and shaft. The model dynamics include...
Discontinuous Buckling of Wide Beams and Metabeams
Corentin Coulais; Johannes T. B. Overvelde; Luuk A. Lubbers; Katia Bertoldi; Martin van Hecke
2015-04-20
We uncover how nonlinearities dramatically influence the buckling of elastic beams by means of experiments, simulations and theory. We show that sufficiently wide, ordinary elastic beams exhibit discontinuous buckling, an unstable form of buckling where the post-buckling stiffness is negative. We develop a 1D model that matches our data and identify nonlinearity as the main cause for negative stiffness. Finally, we create nonlinear metamaterials that allow us to rationally design the (negative) post-buckling stiffness of metabeams, independently of beam thickness, and demonstrate discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally.
Geometric Brownian Motion Consider the geometric Brownian motion process
Lyuu, Yuh-Dauh
Geometric Brownian Motion Â· Consider the geometric Brownian motion process Y (t) eX(t) Â X(t) is a (Âµ, ) Brownian motion. Â· As Y/X = Y and 2 Y/X2 = Y , Ito's formula (51) on p. 453 implies dY Y = Âµ-Dauh Lyuu, National Taiwan University Page 459 Product of Geometric Brownian Motion Processes Â· Let d
NASA Astrophysics Data System (ADS)
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
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
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
Coherence delay augmented laser beam homogenizer
Rasmussen, P.; Bernhardt, A.
1993-06-29
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.
Technology Transfer Automated Retrieval System (TEKTRAN)
This work examines the application of a geometric-optical canopy reflectance model to provide measures of woody shrub abundance in desert grasslands at the landscape scale. The approach is through inversion of the non-linear simple geometric model (SGM) against 631 nm multi-angle reflectance data fr...
NASA Astrophysics Data System (ADS)
Sracic, Michael W.; Allen, Matthew S.
2014-06-01
The authors recently presented a new nonlinear system identification method, here dubbed the NL-LTP method, in which the system of interest is forced harmonically so that it responds in a stable periodic orbit, and then it is perturbed slightly and its response is recorded as it returns to the orbit. Under mild assumptions the response about the periodic orbit can be approximated using a linear time periodic system model, which can be identified from the measurements using techniques that are akin to linear modal analysis. While the prior work focused on simulated measurements from single degree-of-freedom systems, this work presents several tools that are needed in order to use this approach on multi-degree-of-freedom systems and focuses on applying the method to experimental hardware. The proposed system identification methodology is unique in that it identifies both the order of the nonlinear system and a mathematical model for the nonlinear restoring forces without assuming the mathematical form for the nonlinearities a priori. Towards these ends, this work explains how to extract the underlying nonlinear system model, or nonlinear restoring force versus displacement relationships, from the time periodic model that governs deviations of the system from its periodic orbit, and presents various metrics that can be used to determine which terms in the model are meaningful. These new tools are used to apply the identification method to a continuous, multi-degree-of-freedom structure with a discrete geometric nonlinearity, using both simulated and experimental measurements. The experimental hardware consists of a cantilever beam with a nonlinear spring attached to its tip, which is driven in a periodic limit cycle by an electromagnetic shaker.
Nonlinear transient analysis via energy minimization
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Knight, N. F., Jr.
1978-01-01
The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose.
Generalized nonlinear models of suspension bridges
NASA Astrophysics Data System (ADS)
Malik, Josef
2006-12-01
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.
Geometric and topological approaches to significance testing in wavelet analysis
NASA Astrophysics Data System (ADS)
Schulte, J. A.; Duffy, C.; Najjar, R. G.
2015-03-01
Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, i.e., contiguous regions of significant wavelet power coefficients with respect to some noise model. This geometric significance test was found to produce results similar to an existing areawise significance test while being more computationally flexible and efficient. The geometric significance test can be readily applied to pointwise significance patches at various pointwise significance levels in wavelet power and coherence spectra. The geometric test determined that features in wavelet power of the North Atlantic Oscillation (NAO) are indistinguishable from a red-noise background, suggesting that the NAO is a stochastic, unpredictable process, which could render difficult the future projections of the NAO under a changing global system. The geometric test did, however, identify features in the wavelet power spectrum of an El Niño index (Niño 3.4) as distinguishable from a red-noise background. A topological analysis of pointwise significance patches determined that holes, deficits in pointwise significance embedded in significance patches, are capable of identifying important structures, some of which are undetected by the geometric and areawise tests. The application of the topological methods to ideal time series and to the time series of the Niño 3.4 and NAO indices showed that the areawise and geometric tests perform similarly in ideal and geophysical settings, while the topological methods showed that the Niño 3.4 time series contains numerous phase-coherent oscillations that could be interacting nonlinearly.
Geometric Phase and Nonadiabatic Effects in an Electronic Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Pechal, M.; Berger, S.; Abdumalikov, A. A., Jr.; Fink, J. M.; Mlynek, J. A.; Steffen, L.; Wallraff, A.; Filipp, S.
2012-04-01
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.
Encoding geometric and non-geometric information: a study with evolved agents
Michela Ponticorvo; Orazio Miglino
2010-01-01
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
nonlinearity G-perfect nonlinearity
Poinsot, Laurent
nonlinearity Bent functions Difference sets Application of bent functions 3 Group action based perfect on cryptanalysis 2 Traditional Approach Perfect nonlinearity Bent functions Difference sets Application of bent Basics on cryptography Basics on cryptanalysis 2 Traditional Approach Perfect nonlinearity Bent functions
Digital Planar Surface Segmentation Using Local Geometric Patterns
Yukiko Kenmochi; Lilian Buzer; Akihiro Sugimoto; Ikuko Shimizu
2008-01-01
This paper presents a hybrid two-step method for segmenting a 3D grid-point cloud into planar surfaces by using discrete-geometry\\u000a results. Digital planes contain a finite number of local geometric patterns (LGPs). Such a LGP possesses a set of normal vectors.\\u000a By using LGP properties, we first reject non-linear points from a point cloud (edge-based step), and then classify non-rejected\\u000a points
Nonlinear normal modes in multi-mode models of an inertially coupled elastic structure
Fengxia Wang; Anil K. Bajaj
2007-01-01
Nonlinear normal modes for elastic structures have been studied extensively in the literature. Most studies have been limited\\u000a to small nonlinear motions and to structures with geometric nonlinearities. This work investigates the nonlinear normal modes\\u000a in elastic structures that contain essential inertial nonlinearities. For such structures, based on the works of Crespo da\\u000a Silva and Meirovitch, a general methodology is
Soliton mode locking by nonlinear Faraday rotation
NASA Astrophysics Data System (ADS)
Wabnitz, S.; Westin, E.; Frey, R.; Flytzanis, C.
1996-11-01
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. .
Global Tracking Control Structures for Nonlinear Singularly Perturbed Aircraft
Valasek, John
Global Tracking Control Structures for Nonlinear Singularly Perturbed Aircraft Systems Anshu for a general class of nonlinear singularly perturbed systems is addressed. A motivating example is an aircraft tracking of both fast and slow states is developed using geometric singular perturbation methods. Global
Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight
Soon-Jo Chung; Jean-Jacques E. Slotine; David W. Miller
2007-01-01
This paper describes a fully decentralized nonlinear control law for spin- ning tethered formation flight, based on exploiting geometric symmetries to reduce the original nonlinear dynamics into simpler stable dynamics. Motivated by oscillation synchronization in biological systems, we use con- traction theory to prove that a control law stabilizing a single-tethered spacecraft can also stabilize arbitrary large circular arrays of
Goldberg, P.W.
1993-04-01
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.
Noncommutative geometric regularization
Kempf, A. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW (United Kingdom)] [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW (United Kingdom)
1996-10-01
Studies in string theory and in quantum gravity suggest the existence of a finite lower bound to the possible resolution of lengths which, quantum theoretically, takes the form of a minimal uncertainty in positions {Delta}{ital x}{sub 0}. A finite minimal uncertainty in momenta {Delta}{ital p}{sub 0} has been motivated from the absence of plane waves on generic curved spaces. Both effects can be described as small noncommutative geometric features of space-time. In a path integral approach to the formulation of field theories on noncommutative geometries, we can now generally prove IR regularization for the case of noncommutative geometries which imply minimal uncertainties {Delta}{ital p}{sub 0} in momenta. {copyright} {ital 1996 The American Physical Society.}
Geometric Algebra for Subspace Operations
T. A. Bouma; L. Dorst; H. G. J. Pijls
2001-01-01
The set theory relations \\\\in, \\\\backslash, \\\\Delta, \\\\cap, and \\\\cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \\\\in, \\\\backslash, and \\\\Delta are easily subsumed by Geometric Algebra for Euclidean metrics. A short computation shows that the meet (\\\\cap) and join (\\\\cup) are resolved in a projection operator
Compass routing on geometric networks
Evangelos Kranakis; Harvinder Singh; Jorge Urrutia
1999-01-01
this paper we study local routing algorithms on geometric networks. Formally speaking, suppose that we want to travel from a vertex s to a vertex t of a geometric network. A routing algorithm is called a local routing algorithm if it satisfies the following conditions:
Circle actions in geometric quantisation
NASA Astrophysics Data System (ADS)
Solha, Romero
2015-01-01
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.
A Primer on Geometric Mechanics
Christian Lessig
2012-06-14
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance of the subject for an understanding of "mechanics".
Beam profiling monitors beam shaping
Carlos B. Roundy; Larry Green
2005-01-01
Evaluating the success of beam shaping techniques requires the measurement of the resulting beam profile. Laser beam profilers have been used extensively throughout the laser industry to enable users to evaluate the \\
Progress with Tevatron Electron Lens Head-On Beam-Beam Compensation
Valishev, A.; Kuznetsov, G.; Shiltsev, V.; Stancari, G.; Zhang, X.
2010-05-19
Tevatron electron lenses have been successfully used to mitigate bunch-to-bunch differences caused by longrange beam-beam interactions. For this purpose, the electron beam with uniform transverse density distribution was used. Another planned application of the electron lens is the suppression of tune spread due to head-on beam-beam collisions. For this purpose, the transverse distribution of the E{sup -} beam must be matched to that of the antiproton beam. In 2009, the Gaussian profile electron gun was installed in one of the Tevatron electron lenses. We report on the first experiments with non-linear beam-beam compensation. Discussed topics include measurement and control of the betatron tune spread, importance of the beam alignment and stability, and effect of electron lens on the antiproton beam lifetime.
Stochastic pump effect and geometric phases in dissipative and stochastic systems
N. A. Sinitsyn
2009-04-15
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).
M. Ghadimi; Morteza Dardel; M. H. Pashaei; M. M. Barzegari
In this study, the thermal flutter characteristics of an imperfect cantilever plate under aerodynamic loads are investigated. The plate is assumed to be rectangular and functionally graded (FG). The plate is modeled based on first-order shear deformation theory (FSDT), and the Von-Karman strain-displacement relations are used to model the geometric nonlinearity. Geometric imperfections are modeled as strain energy, which causes
Nonlinear Transformational Optics and Electromagnetic and Acoustic Fields Concentrators
NASA Astrophysics Data System (ADS)
Boardman, A. D.; Grimalsky, V. V.; Rapoport, Yu. G.
2011-10-01
A nonlinear electromagnetic field (energy) concentrator is considered and the new method of nonlinear transformational optics is developed. This method includes two connected techniques: the complex geometrical optics (CGO) and the full-wave nonlinear solution. A possibility of the strong "nonlinear superfocusing" of a field in a small volume is predicted theoretically and a tendency to formation of "hot spot(s)" is shown. The proposed method of nonlinear energy concentration may be perspective for solar cells, subwavelength imaging, high harmonic generation etc.
Ring for test of nonlinear integrable optics
Valishev, A.; Nagaitsev, S.; Kashikhin, V.; /Fermilab; Danilov, V.; /SNS Project, Oak Ridge
2011-03-01
Nonlinear optics is a promising idea potentially opening the path towards achieving super high beam intensities in circular accelerators. Creation of a tune spread reaching 50% of the betatron tune would provide strong Landau damping and make the beam immune to instabilities. Recent theoretical work has identified a possible way to implement stable nonlinear optics by incorporating nonlinear focusing elements into a specially designed machine lattice. In this report we propose the design of a test accelerator for a proof-of-principle experiment. We discuss possible studies at the machine, requirements on the optics stability and sensitivity to imperfections.
Elimination of delay-free loops in discrete-time models of nonlinear acoustic systems
Gianpaolo Borin; G. De Poli; D. Rocchesso
2000-01-01
Nonlinear acoustic systems are often described by means of nonlinear maps acting as instantaneous constraints on the solutions of a system of linear differential equations. This description leads to discrete-time models exhibiting noncomputable loops. We present a solution to this computability problem by means of geometrical transformation of the nonlinearities and algebraic transformation of the time-dependent equations. The proposed solution
Treatment of material creep and nonlinearities in flexible mulitbody dynamics
M. Xie; F. M. L. Amirouche
1994-01-01
This paper addresses the modeling of the generalized active forces resulting from deformable bodies when subjected to high temperature conditions, elastic-plastic deformations, creep effects, and material nonlinearities. The effects of elastic-plastic deformations are studied making use of the nonlinear stress-strain relationship and the geometrical stiffness concepts. Creep conditions resulting from high temperature are studied through several proposed models. Materials nonlinearities
A refined nonlinear analysis of pre-twisted composite blades
Omri Rand; Shirley M. Barkai
1997-01-01
A nonlinear formulation for the structural behavior of initially twisted solid and thin walled composite blades is presented. The model is designed to handle arbitrary thick solid cross-sections or general thin-walled geometries, and includes three-dimensional out-of-plane warping. The nonlinear scheme enables the inclusion of geometrical nonlinearities in the presence of large initial twist, and is based on a formulation that
Stability analysis of a nonlinear rotating blade with torsional vibrations
NASA Astrophysics Data System (ADS)
Wang, Fengxia; Zhang, Wei
2012-12-01
This paper discusses the stability of a spinning blade having periodically time varying coefficients for both linear model and geometric nonlinear model. To obtain a reduced nonlinear model from nodal space, a standard modal reduction procedure based on matrix operation is developed with essential geometric stiffening nonlinearities retained in the equation of motion. For the linear model, the stability chart with various spinning parameters of the blade is studied via the Bolotin method, and an efficient boundary tracing algorithm is developed to trace the stability boundary of the linear model. For the geometric nonlinear model, the method of multiple time scale is employed to study the steady state solutions, and their stability and bifurcations for the periodically time-varying rotating blade. The backbone curves of steady-state motions are achieved, and the parameter map for stability and bifurcation is developed.
Jacobi equations and particle accelerator beam dynamics
Ricardo Gallego Torrome
2012-03-27
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.
Laser synchrotron radiation from beams and plasmas
Eric Esarey; Sally K. Ride; Phillip Sprangle
1994-01-01
The nonlinear Thomson scattering of intense laser fields from beams and plasmas is analyzed. This theory is valid for laser fields of arbitrary intensities and for electrons of arbitrary energies. The space-charge electrostatic potential is included self-consistently. A laser synchrotron source (LSS), based on nonlinear Thomson scattering, may provide a practical method for generating tunable, near monochromatic, well collimated, short
Beam hysteresis via reorientational self-focusing.
Alberucci, Alessandro; Piccardi, Armando; Kravets, Nina; Assanto, Gaetano
2014-10-15
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