Effects of geometric nonlinearities on the response of optimized box beam structures
NASA Technical Reports Server (NTRS)
Ragon, S.; Gurdal, Z.
1993-01-01
The present minimum-mass designs for a two-spar rectangular box beam were derived on the basis of linear-buckling FEM analysis constraints. In order to ascertain the effects of any geometric nonlinearities on these designs, each was subjected to a geometrically nonlinear FEM analysis. In all cases, the structure collapses below the design load, and does so in a mode which differs from that of linear theory. This discrepancy is attributable to such nonlinear panel-interaction mechanisms as rib-crusing loads. The optimized design is highly sensitive to crushing loads, relative to the nonoptimal design.
Geometric nonlinear dynamic analysis of curved beams using curved beam element
NASA Astrophysics Data System (ADS)
Pan, Ke-Qi; Liu, Jin-Yang
2011-12-01
Instead of using the previous straight beam element to approximate the curved beam, in this paper, a curvilinear coordinate is employed to describe the deformations, and a new curved beam element is proposed to model the curved beam. Based on exact nonlinear strain-displacement relation, virtual work principle is used to derive dynamic equations for a rotating curved beam, with the effects of axial extensibility, shear deformation and rotary inertia taken into account. The constant matrices are solved numerically utilizing the Gauss quadrature integration method. Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system. The present results are compared with those obtained by commercial programs to validate the present finite method. In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation, comparison of the results of the present formulation with those of the ADAMS software are made. Furthermore, the present results obtained from linear formulation are compared with those from nonlinear formulation, and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.
NASA Astrophysics Data System (ADS)
Torabizadeh, Mohammad Amin
2013-07-01
A new method is developed to derive equilibrium equations of Metal-Ceramic beams based on first order shear deformation plate theory which is named first order shear deformation beam theory2(FSDBT2). Equilibrium equations obtained from conventional method (FSDBT1) is compared with FSDBT2 and the case of cylindrical bending of Metal-Ceramic composite plates for non-linear thermomechanical deformations and various loadings and boundary conditions. These equations are solved by using three different methods (analytical, perturbation technique and finite element solution). The through-thickness variation of the volume fraction of the ceramic phase in a Metal-Ceramic beam is assumed to be given by a power-law type function. The non-linear strain-displacement relations in the von-Kármán sense are used to study the effect of geometric non-linearity. Also, four other representative averaging estimation methods, the linear rule, Mori-Tanaka, Self-Consistent and Wakashima-Tsukamoto schemes, by comparing with the power-law type function are also investigated. Temperature distribution through the thickness of the beams in thermal loadings is obtained by solving the one-dimensional heat transfer equation. Finally it is concluded that for Metal-Ceramic composites, these two theories result in identical static responses. Also the displacement field and equilibrium equations in the case of cylindrical bending of Metal-Ceramic plates are the same as those supposed in FSDBT2.
A geometrical nonlinear eccentric 3D-beam element with arbitrary cross-sections
F. Gruttmann; R. Sauer; W. Wagner
1998-01-01
In this paper a finite element formulation of eccentric space curved beams with arbitrary cross-sections is derived. Based on a Timoshenko beam kinematic, the strain measures are derived by exploitation of the Green-Lagrangean strain tensor. Thus, the formulation is conformed with existing nonlinear shell theories. Finite rotations are described by orthogonal transformations of the basis systems from the initial to
Information geometric nonlinear filtering
NASA Astrophysics Data System (ADS)
Newton, Nigel J.
2015-06-01
This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with the quadratic variation of the process of posterior distributions in this metric. Apart from providing a suitable setting in which to study such information-theoretic properties, the Hilbert manifold has an appropriate topology from the point of view of multi-objective filter approximations. A general class of finite-dimensional exponential filters is shown to fit within this framework, and an intrinsic evolution equation, involving Amari's -1-covariant derivative, is developed for such filters. Three example systems, one of infinite dimension, are developed in detail.
Geometric and Material Nonlinear Structural Analysis
NASA Technical Reports Server (NTRS)
Whitcomb, J. D.; Dattaguru, B.
1986-01-01
GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is twodimensional finite-element stress-analysis program supporting fracturemechanics studies of debonding and delamination. GAMNAS options include linear, geometricnonlinear, material-nonlinear, and combined geometric- and material-nonlinear analysis.
NASA Astrophysics Data System (ADS)
Silwal, Baikuntha
The objective of this study is to investigate the accuracy and computational efficiency of two commonly used formulations for performing the geometrically nonlinear thermal analysis of plane framed structures. The formulations considered are the followings: the Beam-Column formulation and the updated Lagrangian version of the finite element formulation that has been adopted in the commercially well-known software SAP2000. These two formulations are used to generate extensive numerical data for three plane frame configurations, which are then compared to evaluate the performance of the two formulations. The Beam-Column method is based on an Eulerian formulation that incorporates the effects of large joint displacements. In addition, local member force-deformation relationships are based on the Beam-Column approach that includes the axial strain, flexural bowing, and thermal strain. The other formulation, the SAP2000, is based on the updated Lagrangian finite element formulation. The results for nonlinear thermal responses were generated for three plane structures by these formulations. Then, the data were compared for accuracy of deflection responses and for computational efficiency of the Newton-Raphson iteration cycles required for the thermal analysis. The results of this study indicate that the Beam-Column method is quite efficient and powerful for the thermal analysis of plane frames since the method is based on the exact solution of the differential equations. In comparison to the SAP2000 software, the Beam-Column method requires fewer iteration cycles and fewer elements per natural member, even when the structures are subjected to significant curvature effects and to restrained support conditions. The accuracy of the SAP2000 generally depends on the number of steps and/or the number of elements per natural member (especially four or more elements per member may be needed when structure member encounters a significant curvature effect). Succinctly, the Beam-Column formulation requires considerably fewer elements per member, fewer iteration cycles, and less time for thermal analysis than the SAP2000 when the structures are subjected to significant bending effects.
Topology optimization of structures with geometrical nonlinearities
Gea, Hae Chang
Topology optimization of structures with geometrical nonlinearities Hae Chang Gea *, Jianhui Luo structures. Ó 2001 Published by Elsevier Science Ltd. Keywords: Topology optimization; Geometrical by Neves et al. [18], and the design of compliant mechanisms using topology optimization has also been
Geometrically nonlinear behavior of piezoelectric laminated plates
Oded Rabinovitch
2005-01-01
The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of
Nonlinear combining of laser beams
Lushnikov, Pavel M
2014-01-01
We propose to combine multiple laser beams into a single diffraction-limited beam by the beam self-focusing (collapse) in the Kerr medium. The beams with the total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with the Kerr nonlinearity. Random fluctuations during propagation eventually trigger strong self-focusing event and produce diffraction-limited beam carrying the critical power.
Diffractive nonlinear geometric optics for short pulses
NASA Astrophysics Data System (ADS)
Alterman, Deborah Ann
The propagation of laser light has been studied through shortwave asymptotics. For lasers which produce pulses as short as several picoseconds, the light is assumed to have the form of a modulated wavetrain with slowly varying envelope and rapidly oscillating phase. This slowly varying envelope approximation leads to the nonlinear Schrödinger equation when applied to nonlinear Maxwell's equations. The slowly varying envelope assumption does not hold for ultrafast lasers. In this thesis, an alternative description, valid for ultrafast laser pulses, is derived and analyzed. For medium time scales, in the regime of geometric optics, the approximate short pulse solutions and wavetrain solutions satisfy the same nonlinear profile equation. On longer, or diffractive time scales, the short pulse approximation satisfies a different profile equation than the wavetrain solution. The short pulse approximation is proved valid for each time scale, with the relative error between exact and approximate solution going to zero in both L2 and L? in the short wavelength limit.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
NASA Astrophysics Data System (ADS)
Fan, Wei; Liu, Jin-Yang
2013-10-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
NASA Astrophysics Data System (ADS)
Fan, Wei; Liu, Jin-Yang
2013-09-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Airy beams: a geometric optics perspective.
Vo, Sophie; Fuerschbach, Kyle; Thompson, Kevin P; Alonso, Miguel A; Rolland, Jannick P
2010-12-01
Theoretically formulated in the 1970s within the context of nonrelativistic quantum mechanics, Airy beams have been experimentally realized for the first time only recently, paving the way to innovative optical techniques. While their remarkable features, a non-diffracting property and a transverse shift of the intensity maximum during propagation, are currently theoretically described from the wave optics viewpoint, here their exact relation to rays and geometric wavefront aberrations is revealed using a wavefront family that includes two-dimensional Airy beams. Several members of this family are computationally and experimentally implemented here. The lateral shift of Airy beams during propagation is presented in the context of the three-dimensional caustic representation. This new description allows re-emphasizing the use of "Airy-like" beams in computational imaging for depth of focus extension. PMID:21119741
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.
Nonlinear Geometric Effects in Bioinspired Multistable Structures
NASA Astrophysics Data System (ADS)
Chen, Zi; Guo, Qiaohang; Chu, Kevin; Shillig, Steven; Li, Chi; Chen, Wenzhe; Taber, Larry; Holmes, Douglas
2013-03-01
Nature features many thin shell structures with spontaneous curvatures, where mechanical instabilities play important roles in the morphogenesis and functioning of the organisms. However, the large deformation and instability phenomena of shells due to geometric nonlinearity, which often arise in morphogenesis and nanofabrication, remain incompletely understood. Here, we create spontaneously curved shapes with pre-strains in tabletop experiments, and study their instabilities with a minimal theory based on linear elasticity. The development of such theoretical and experimental approaches will promote quantitative understanding of the morphogenesis of growing soft tissues, and meet the emergent needs of designing stretchable electronics, artificial muscles and bio-inspired robots. Nature features many thin shell structures with spontaneous curvatures, where mechanical instabilities play important roles in the morphogenesis and functioning of the organisms. However, the large deformation and instability phenomena of shells due to geometric nonlinearity, which often arise in morphogenesis and nanofabrication, remain incompletely understood. Here, we create spontaneously curved shapes with pre-strains in tabletop experiments, and study their instabilities with a minimal theory based on linear elasticity. The development of such theoretical and experimental approaches will promote quantitative understanding of the morphogenesis of growing soft tissues, and meet the emergent needs of designing stretchable electronics, artificial muscles and bio-inspired robots. Zi Chen and Qiaohang Guo contributed equally. This work was supported by National Science Foundation of China (No. 11102040), American Academy of Mechanics Founder's Award, and Society in Science - Branco Weiss fellowship, administered by ETH.
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.
On Nonlinear Polynomial Selection and Geometric Progression (mod N) for
International Association for Cryptologic Research (IACR)
On Nonlinear Polynomial Selection and Geometric Progression (mod N) for Number Field Sieve Namhun. In this paper, we generalize Montgomery's method [7] using small geometric progression (GP) (mod N) to construct sieve, geometric progression, LLL algo- rithm 1 Introduction The number field sieve (NFS) [6, 11
Robustness of continuous-variable entanglement via geometrical nonlinearity
NASA Astrophysics Data System (ADS)
Djorwé, Philippe; Engo, S. G. Nana; Woafo, Paul
2014-08-01
We propose a scheme to generate robust stationary continuous-variable entanglement in optomechanical systems, based on geometrical nonlinearity that occurs for large mechanical displacements. Such nonlinearity is often used to correct the dynamics of the systems in the strong-coupling regime. It appears that geometrical nonlinearity enhances the entanglement and shifts its maximum towards high detuning values. Using the experimental parameters, we find that such a scheme generates a very robust entanglement against thermal decoherence even at room temperature. Our results show that geometrical nonlinearity affects entanglement as the optomechanical quantum interface.
Dynamics of shallow shells with geometrical nonlinearity interacting with fluid
I. D. Breslavsky; E. A. Strel’nikova; K. V. Avramov
2011-01-01
The vibrations of the shallow shell with geometrical nonlinearity submerged in a fluid are considered. Interaction of the shell with a fluid is described by linear hypersingular integral equation, which is solved by the boundary element method. The vibrations of the shell are described by the nonlinear finite-degree-of-freedom system. The vibrations are studied by the Shaw–Pierre nonlinear modes.
Seismic Analysis of Transmission Towers Considering Both Geometric and Material Nonlinearities
Ying-Hui Lei; Yu-Lin Chien
2005-01-01
In this paper, the dynamic behavior of a group of transmission towers linked together through electrical wires and subjected to a strong ground motion will be investigated in detail. In performing the seismic analysis, the wires and the towers concerned are modeled, respectively, by using the efficient cable elements and the 3-D beam elements considering both geometric and material nonlinearities.
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...
Supercritical geometric optics for nonlinear Schrodinger equations
Thomas Alazard; Rémi Carles
2007-04-27
We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To overcome this issue, we introduce new unknown functions, which are defined nonlinearly in terms of the wave function itself. This approach provides a local version of the modulated energy functional introduced by Y.Brenier. The system we obtain is hyperbolic symmetric, and the justification of WKB analysis follows.
Asynchronous variational Lie group integration for geometrically exact beam dynamics
Leyendecker, Sigrid
Asynchronous variational Lie group integration for geometrically exact beam dynamics F. Demoures1] is derived in the Lie group setting (SO (3) for the representation of rotational degrees of freedom, variational integrators, Lie group integrator, multi-time-step, dis- crete mechanics, geometric integration 1
T. Kobayashi; K. Yoshikawa; E. Takaoka; M. Nakazawa; Y. Shikama
2002-01-01
A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1\\/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat
Soares, W C; Caetano, D P; Hickmann, J M
2006-05-29
We investigate theoretically and experimentally the decomposition of high-order Bessel beams in terms of a new family of nondiffracting beams, referred as Hermite-Bessel beams, which are solutions of the Helmholtz equation in Cartesian coordinates. Based on this decomposition we develop a geometrical representation of first-order Bessel beams, equivalent to the Poincaré sphere for the polarization states of light and implement an unitary transformation within our geometrical representation using linear optical elements. PMID:19516610
8 Variational Lie Group Formulation of Geometrically Exact Beam
Leyendecker, Sigrid
8 Variational Lie Group Formulation of Geometrically Exact Beam Dynamics: Synchronous and since the pre- sented integrator is derived in the Lie group setting (SO (3) for the representation, Lie group methods and beam dynamics. Their most recent developments are discussed in the following
The comparative body model in material and geometric nonlinear analysis of space R\\/C frames
Boris Trogrlic; Ante Mihanovic
2008-01-01
Purpose – This paper aims to present a new numerical model for the stability and load-bearing capacity computation of space reinforced-concrete (R\\/C) frame structures. Both material and geometric nonlinearities are taken into account. The R\\/C cross-sections are assumed to undergo limited distortion under torsional action. Design\\/methodology\\/approach – A simple, global discretization using beam-column finite elements is preferred to a full,
Geometric nonlinear analysis of microbeam under electrostatic loading
Murgude, Nikhil C.
2001-01-01
to substantiate this research. The deflection of beams is studied for various cases of loading, i.e., constant loading, linear loading and nonlinear loading. Both linear and non-linear behavior of the microbeams are studied for the above mentioned cases...
Bounding solutions of geometrically nonlinear viscoelastic problems
NASA Technical Reports Server (NTRS)
Stubstad, J. M.; Simitses, G. J.
1985-01-01
Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.
Bounding solutions of geometrically nonlinear viscoelastic problems
NASA Technical Reports Server (NTRS)
Stubstad, J. M.; Simitses, G. J.
1986-01-01
Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.
A. Senechal; O. Thomas; J.-F. Deü
The large amplitude non-linear vibratory behavior of a rotating cantilever beam is addressed in this study. The motivation of this work is to built a simplified model for analyzes of turbomachinery and turbopropeller blades vibrations in the geometrically non-linear regime. Since blades are designed more and more flexible, in particular when composite materials are used, quantifying the amount of non-
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.
Geometric methods for nonlinear many-body quantum systems
Mathieu Lewin
2010-12-10
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to provide a simple proof of the famous HVZ theorem in the repulsive case. In a second step we recall the method of geometric localization in Fock space as proposed by Derezi\\'nski and G\\'erard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and prove nonlinear versions of the HVZ theorem, in the spirit of works of Friesecke. In the last section we study translation-invariant many-body systems comprising a nonlinear term, which effectively describes the interactions with a second system. As an example, we prove the existence of the multi-polaron in the Pekar-Tomasevich approximation, for certain values of the coupling constant.
Nonlinear distortion of intense THz beams
NASA Astrophysics Data System (ADS)
Lombosi, Cs; Polónyi, Gy; Mechler, M.; Ollmann, Z.; Hebling, J.; Fülöp, J. A.
2015-08-01
Near- and far-field beam profiles were measured for THz pulses generated in LiNbO3 by optical rectification of 200 fs pulses with a tilted pulse front. The variation of the THz beam size and a dramatically increasing divergence angle with increasing pump fluence were observed in the (horizontal) plane of the pulse front tilt. No significant variation was observed in the vertical direction. The reason for the observed nonlinear beam distortion is the shortening of the effective interaction length for THz generation caused by the combined effect of pump spectral broadening and angular dispersion in the tilted pulse front geometry. Our results indicate that nonlinear THz beam distortion effects have to be taken into account when designing intense THz sources and related experiments.
Benchmark case studies in optimization of geometrically nonlinear structures
A. Suleman; R. Sedaghati
2005-01-01
A structural optimization algorithm is developed for truss and beam structures undergoing large deflections against instability. The method combines the nonlinear buckling analysis using the displacement control technique, with the optimality criteria approaches. Several benchmark case studies illustrate the procedure and the results are compared with examples reported in the literature. It is shown that a design based on the
Injection of beam shaped locally with nonlinear optics.
Wang, C.-X.; Accelerator Systems Division
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.
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.
Nonlinear feedback control of slewing beams
M. Tadi
2006-01-01
This paper is concerned with feedback control of slewing beams. It allows for the hub to have finite rotation which leads to a fully nonlinear system. It uses the method of state-dependent Riccati equation (SDRE) to obtain feedback control laws. The model assumes finite rigid body rotations and infinitesimal (small) elastic displacements. It considers both the classical Euler–Bermoulli model and
Spiraling elliptic beam in nonlocal nonlinear media.
Liang, Guo; Guo, Qi; Cheng, Wenjing; Yin, Naiqiang; Wu, Ping; Cao, Hongmin
2015-09-21
Analytically discussed is the dynamical properties of the spiraling elliptic beams in nonlocal nonlinear media. This class of spiraling elliptic beams carry the orbital angular momentum (OAM), and can rotate on the cross section perpendicular to the propagation direction during the propagations. The optical intensity, the beam width, and specially the angular velocity are both analytically and numerically discussed in details. We shown that both the deviations from the critical power and the deviations from the critical OAM can make the spiraling elliptic beams breathe. The decrease (increase) of the OAM or the increase (decrease) of the power can both make the spiraling elliptic breathers contract (diffract), however, there still exist differences between them. The rotating speed can be changed by the input optical power or the input OAM, which may have potential applications in the controlling of the optical beams. PMID:26406663
Quantum nature of a nonlinear beam splitter
NASA Astrophysics Data System (ADS)
Belinsky, A. V.; Shulman, M. Kh
2014-10-01
This is a review of a very interesting (in the authors' view) phenomenon — the operation of a nonlinear light beam splitter. The beam splitter is a flat interface between two transparent dielectrics, at least one of which exhibits Kerr nonlinearity, i.e., its refractive index depends on the transmitted radiation intensity. Interestingly, quantum and classical theories make directly opposite predictions about the phase fluctuations of the output radiation of this device. In classical theory, the phases remain unchanged; in quantum theory, the phases fluctuate in accordance with the amplitude–phase uncertainty relation. The origin of this difference is established at the fundamental level. A further remarkable point about this quantum paradox is that not only is the source beam split in two but one can also create conditions where the two split parts are respectively dominated by amplitude noise and phase noise, thus allowing the selection of photon fluctuations. Results of original studies are summarized and further developed.
Nonlinear evolution of the auroral electron beam
Maggs, J.E. (Univ. of California, Los Angeles (USA))
1989-04-01
The nonlinear spatial evolution of the auroral electron beam and beam-generated electrostatic whistler noise is followed from source to atmosphere. Changes in beam parameters are determined by using the equations of conservation of total particle and wave energy and momentum flux density. Wave power fluxes are calculated by numerically integrating the wave kinetic equation. Levels of beam generated noise are quantified by using thermal levels of Cerenkov radiation as a source. Wave refraction and source geometry as well as beam recoil and thermalization influence beam generated power flux spectra. Beam parameters evolve on ionospheric scale lengths, and their positive slope feature in velocity space is maintained over thousands of kilometers of altitude even though they can generate wave energy density fluxes sufficient to modify the ionospheric density profile. For a beam source at 7,000 km altitude, peak fluxes of electrostatic whistler noise as high as 10{sup {minus}10} W/m{sup 2} Hz can be generated in the altitude region between 3,000 and 5,000 km. Beams with densities large enough to be unstable at the source altitude generate sufficient wave noise at the plasma frequency to disrupt the source structure.
Generation of linear and nonlinear nonparaxial accelerating beams
Chen, Zhigang
Generation of linear and nonlinear nonparaxial accelerating beams Peng Zhang,1,2 Yi Hu,3 Drake. ID 166290); published July 9, 2012 We study linear and nonlinear self-accelerating beams propagating experimental demonstration of linear and nonlinear nonparaxial accelerating beams (NABs) propagating along
Vector algorithms for geometrically nonlinear 3D finite element analysis
NASA Technical Reports Server (NTRS)
Whitcomb, John D.
1989-01-01
Algorithms for geometrically nonlinear finite element analysis are presented which exploit the vector processing capability of the VPS-32, which is closely related to the CYBER 205. By manipulating vectors (which are long lists of numbers) rather than individual numbers, very high processing speeds are obtained. Long vector lengths are obtained without extensive replication or reordering by storage of intermediate results in strategic patterns at all stages of the computations. Comparisons of execution times with those from programs using either scalar or other vector programming techniques indicate that the algorithms presented are quite efficient.
NASA Astrophysics Data System (ADS)
Wang, Dongwei
Recent research and development of adaptive materials, smart structures and structronic systems have opened a new era to aerospace and structural engineering. Effective control of these intelligent structures and systems using piezoelectric materials can enhance operation precision, accuracy and reliability. This research is to investigate the dynamics, vibration sensing and control of the geometrically nonlinear distributed piezothermoelastic structures subjected to the combined mechanical, electrical, and thermal excitations by the finite element method. Based on the layerwise constant shear angle theory, the curved hexahedral and triangular piezothermoelastic shell elements are proposed. The generic finite element formulations for vibration sensing and control analysis of nonlinear piezothermoelastic shell structures are derived based on the total Lagrangian virtual work principle. Dynamic system equations, equations of electric potential outputs, and feedback control forces are derived and discussed. The modified Newton-Raphson method is used for efficient dynamic analysis of the nonlinear piezothermoelastic structural systems. Different control algorithms are implemented. The feedback control forces generated from the distributed actuator can effectively enhance system damping and suppress system vibration via proper feedback control techniques. Comprehensive case studies are performed to evaluate the accuracy of the newly developed piezothermoelastic shell elements and to validate the finite element code. Dynamics and vibration sensing/control of nonlinear piezothermoelastic beam and plate systems are analyzed. Distributed piezoelectric films placed on the beam and plate structures respectively serving as sensor and actuators are discussed. The effect of geometric nonlinearity is to stiffen the beam and plate structures and the control effect becomes worse when geometric nonlinearity becomes significant. It shows that negative velocity control scheme is effective to dynamically and electrically induced oscillations. However, it is not effective to the vibrations induced by the steady-state thermal field. Accordingly, one additional control voltage is required to control thermally induced offset. The non-constant curvature structures such as conical shells and toroidal shells are also investigated in linear analysis. Various actuator layouts for these shell structures are proposed and the control effectiveness of the actuators is evaluated. It is suggested that an in-depth understanding of shell dynamics and dominating modes is a must in the effective design and layout of distributed actuators to maximize the distributed control effects.
Geometrical nonlinear stability analyses of cable-truss domes.
Gao, Bo-qing; Lu, Qun-Xin; Dong, Shi-Lin
2003-01-01
The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable-truss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise-span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise-span ratio. The buckling of the structure is characterized by a global collapse at small rise-span ratio; that the torsional buckling of the radial truss occurs at big rise-span ratio; and that at proper rise-span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously. PMID:12765286
Nonlinear and collective phenomena in beam physics
Chattopadhyay, S. [ed.] [Lawrence Berkeley National Lab., CA (United States); Cornacchia, M. [ed.] [Stanford Linear Accelerator Center, CA (United States); Pellegrini, C. [ed.] [Univ. of California, Los Angeles, CA (United States)
1997-12-31
The participants were presented with a choice of four groups, each addressing a particular problem. For each group there was a Speaker, who gave the opening lecture, and a Coordinator, who led the discussions and presented a summary of the work on the last day. The Workshop was organized in such a way as to leave as much time as possible to discussions and to minimize the number of formal plenary talks. The Group on Single Particle Dynamics was charged with review of the status and the discussion of new ideas on the nonlinear dynamics of a single particle in accelerators. The Group on Production and Dynamics of High Brightness Beams covered the advances on production, acceleration, transport, and monitoring of high brightness beams, including coherent and radiation effects. The Group on Beam Dynamics in Plasmas covered the subjects of Plasma Lenses, Electron Beam Driven Wakefields, Laser Wakefields, Self-Modulated Laser Wakefields, Crossed Beam Wakefields, and the generation, acceleration, and focusing of low emittance, high energy, high current short pulses. The charge to the Group on Plasma Phenomena in Beams was to survey the status and recent ideas on transverse and longitudinal oscillations in high density relativist beams, including parametric instabilities and filamentation.
Nonlinear geometric influence on the mechanical behavior of shape memory alloy helical springs
NASA Astrophysics Data System (ADS)
Savi, Marcelo A.; Pacheco, Pedro Manuel C. L.; Garcia, Mauricio S.; Aguiar, Ricardo A. A.; de Souza, Luís Felipe G.; da Hora, Rodolpho B.
2015-03-01
This paper investigates the nonlinear geometric effect on the mechanical behavior of shape memory alloy (SMA) helical springs. First, the SMA wires are characterized, and then the design and fabrication of SMA helical springs are discussed. Experimental tensile tests are carried out to show the nonlinear geometric influence. Results show a coupling between constitutive and geometric nonlinearities that defines the spring stiffness. Two springs with different geometries are built from SMA wires to define springs with both weak and strong nonlinear geometric influence. Numerical analyses are developed, using the finite element method to confirm the general conclusions shown in our experimental observations.
NASA Technical Reports Server (NTRS)
Muravyov, Alexander A.; Turner, Travis L.; Robinson, Jay H.; Rizzi, Stephen A.
1999-01-01
In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.
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
A finite element method for nonlinear forced vibrations of beams
NASA Technical Reports Server (NTRS)
Mei, C.; Decha-Umphai, K.
1984-01-01
Techniques for defining a finite element model (FEM) for analysis of nonlinear vibrations in beam structures subjected to harmonic excitation are presented. The resulting model covers longitudinal deformation and inertial effects. The nonlinear oscillations of a beam element under forced excitation are modeled by a harmonic force matrix based on first order approximations of the Jacobian elliptic forcing function. Harmonic force and nonlinear stiffness matrices are derived and the nonlinear forced responses of beams are calculated under various boundary conditions. The results of FEM computations for simply-supported and clamped beams show that midplane stretching caused by large deflections increases the nonlinearity. Axially-restrained beams experience only hardening nonlinearity, while axially-free beams have reduced nonlinearity in deformation and inertia and an increase in linearity due to large deflection.
Geometric studies on variable radius spiral cone-beam scanning.
Yea, Yangbo; Zhu, Jiehua; Wang, Ge
2004-06-01
The goal is to perform geometric studies on cone-beam CT scanning along a three-dimensional (3D) spiral of variable radius. First, the background for variable radius spiral cone-beam scanning is given in the context of electron-beam CT/micro-CT. Then, necessary and sufficient conditions are proved for existence and uniqueness of PI lines inside the variable radius 3D spiral. These results are necessary steps toward exact cone-beam reconstruction from a 3D spiral scan of variable radius, adapting Katsevich's formula for the standard helical cone-beam scanning. It is shown in the paper that when the longitudinally projected planar spiral is not always convex toward the origin, the PI line may not be unique in the envelope defined by the tangents of the spiral. This situation can be avoided by using planar spirals whose curvatures are always positive. Using such a spiral, a longitudinally homogeneous region inside the corresponding 3D spiral is constructed in which any point is passed by one and only one PI line, provided the angle omega between planar spiral's tangent and radius is bounded by [omega - 90 degrees] < or = < epsilon for some positive epsilon < or = 32.48 degrees. If the radius varies monotonically, this region is larger and one may allow epsilon < or = 51.85 degrees. Examples for 3D spirals based on logarithmic and Archimedean spirals are given. The corresponding generalized Tam-Danielsson detection windows are also formulated. PMID:15259650
NONLINEAR DYNAMICS OF A CANTILEVER BEAM ACTUATED BY PIEZOELECTRIC LAYERS
Rimon, Elon
NONLINEAR DYNAMICS OF A CANTILEVER BEAM ACTUATED BY PIEZOELECTRIC LAYERS IN SYMMETRIC Dynamics of a Cantilever Beam Actuated by Piezoelectric Layers in Symmetric and Asymmetric Configuration K Abstract The nonlinear equations of motion for a cantilever beam, covered by piezoelectric PZT layers
Beam stability and nonlinear dynamics. Summary report
Parsa, Z.
1996-12-31
A {open_quotes}Beam Stability and Nonlinear Dynamics{close_quotes} Symposium was held October 3-5, 1996 at the Institute for Theoretical Physics (ITP) in Santa Barbara. This was one of the 3 symposia hosted by the ITP and supported by its sponsor, the National Science Foundation, as part of our {open_quotes}New Ideas for Particle Accelerators{close_quotes} program. The symposia was organized and chaired by Dr. Zohreh Parsa of ITP/ Brookhaven National Laboratory. The purpose of this symposium was to deal with some of the fundamental theoretical problems of accelerator physics by bringing together leaders from accelerator physics communities, mathematics, and other fields of physics. The focus was on nonlinear dynamics and beam stability. The symposium began with some defining talks on relevant mathematical topics such as single-particle Hamiltonian dynamics, chaos, and new ideas in symplectic integrators. The physics topics included single-particle and many-particle dynamics. These topics concern circular accelerators in which particles circulate for a very large number of turns as well as linear accelerators where space charge and wakefields induced in accelerating cavities play a strong role. A major question is to determine the best model for numerical simulations in order to accurately reproduce behavior of beams in real accelerators and to predict long-term or long distance stability. Comparison with experiment is recognized as an important tool in improving models.
Geometric studies on variable radius spiral cone-beam scanning Yangbo Yea)
Ye, Yangbo
EBCT techniques. First, it is not in cone- beam geometry and does not support spiral/helical scanningGeometric studies on variable radius spiral cone-beam scanning Yangbo Yea) and Jiehua Zhu for publication 31 March 2004; published 24 May 2004 The goal is to perform geometric studies on cone-beam CT
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1985-01-01
The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.
Overview of magnetic nonlinear beam dynamics in the RHIC
Luo,Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, f.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, g.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.
2009-05-04
In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed.
NASA Astrophysics Data System (ADS)
Jacques, N.; Daya, E. M.; Potier-Ferry, M.
2010-09-01
This paper deals with geometrically nonlinear vibrations of sandwich beams with viscoelastic materials. For this purpose, a new finite element formulation has been developed, in which a zig-zag model is used to describe the displacement field. The viscoelastic behaviour is handled by using hereditary integrals and their relationships with complex moduli. An efficient solution procedure based on the harmonic balance method is also developed. To demonstrate its abilities, various problems of nonlinear vibrations of sandwich beams are considered. First, the results derived from the proposed approach are compared with those of nonlinear dynamic analyses using direct time integration and to experimental data. Then, the influence of the vibration amplitude on the damping properties of sandwich beams is investigated. The effect of an initial axial strain is also examined.
Nonlinear vibrations of axially moving Timoshenko beams under weak and strong external excitations
NASA Astrophysics Data System (ADS)
Tang, You-Qi; Chen, Li-Qun; Yang, Xiao-Dong
2009-03-01
In this paper, nonlinear vibrations under weak and strong external excitations of axially moving beams are analyzed based on the Timoshenko model. The governing nonlinear partial-differential equation of motion is derived from Newton's second law, accounting for the geometric nonlinearity caused by finite stretching of the beams. The complex mode approach is applied to obtain the transverse vibration modes and the natural frequencies of the linear equation. The method of multiple scales is employed to investigate primary resonances, nonsyntonic excitations, superharmonic resonances, and subharmonic resonances. Some numerical examples are presented to demonstrate the effects of a varying parameter, such as axial speed, external excitation amplitudes, and nonlinearity, on the response amplitudes for the first and second modes, when other parameters are fixed. The stability of the response amplitudes is investigated and the boundary of instability is located.
NASA Astrophysics Data System (ADS)
Mareishi, Soraya; Kalhori, Hamed; Rafiee, Mohammad; Hosseini, Seyedeh Marzieh
2015-01-01
This paper presents an analytical solution for nonlinear free and forced vibration response of smart laminated nano-composite beams resting on nonlinear elastic foundation and under external harmonic excitation. The structure is under a temperature change and an electric excitation through the piezoelectric layers. Different distribution patterns of the single walled aligned and straight carbon nanotubes (SWCNTs) through the thickness of the beam are considered. The beam complies with Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. The nonlinearity is due to the mid-plane stretching of the beam and the nonlinear stiffness of the elastic foundation. The Multiple Time Scales perturbation scheme is used to perform the nonlinear dynamical analysis of functionally graded carbon nanotube-reinforced beams. Analytical expressions of the nonlinear natural frequencies, nonlinear dynamic response and frequency response of the system in the case of primary resonance have been presented. The effects of different parameters including applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the carbon nanotubes on the nonlinear natural frequencies and frequency-response curves are presented. It is found that the volume fractions of SWCNTs as well as their distribution pattern significantly change the behavior of the system.
Nonlinearities and effects of transverse beam size in beam position monitors
Sergey S. Kurennoy
2001-01-01
The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The nonlinearities and corrections to BPM signals due to a finite transverse beam size
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.
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.
A. O. Rasskazov; V. M. Trach; V. N. Gupalyuk
1999-01-01
The finite-difference method and the Trefftz-Reissner variational principle are used to obtain a system of equations in mixed\\u000a from to describe the stability and geometric nonlinearity of composite shells of revolution. Methods are developed and an\\u000a algorithm is proposed to calculate the components of the geometrically nonlinear subcritical stress-strain state and to use\\u000a those components to determine the “upper” critical
A Differential Geometric Approach to Nonlinear Filtering : the Projection Filter \\Lambda
LeGland, François
A Differential Geometric Approach to Nonlinear Filtering : the Projection Filter \\Lambda Damiano filters with finite di mensional filters, using the differential geometric ap proach to statistics. We define rigorously the projection filter in the case of exponential families. We propose a convenient
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.
Nonlinearities and Effects of Transverse Beam Size in Beam Position Monitors (revised)
Sergey S. Kurennoy
The fields produced by a long beam with a given trans- verse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calcu- lated and compared to those produced by a pencil beam. The non-linearities and corrections to BPM signals due to a finite transverse
Nonlinear system identification of frictional effects in a beam with a bolted joint connection
NASA Astrophysics Data System (ADS)
Eriten, Melih; Kurt, Mehmet; Luo, Guanyang; Michael McFarland, D.; Bergman, Lawrence A.; Vakakis, Alexander F.
2013-08-01
We perform nonlinear system identification (NSI) of the effects of frictional connections in the dynamics of a bolted beam assembly. The methodology utilized in this work combines experimental measurements with slow-flow dynamic analysis and empirical mode decomposition, and reconstructs the dynamics through reduced-order models. These are in the form of single-degree-of-freedom linear oscillators (termed intrinsic modal oscillators—IMOs) with forcing terms derived directly from the experimental measurements through slow-flow analysis. The derived reduced order models are capable of reproducing the measured dynamics, whereas the forcing terms provide important information about nonlinear damping effects. The NSI methodology is applied to model nonlinear friction effects in a bolted beam assembly. A 'monolithic' beam with identical geometric and material properties is also tested for comparison. Three different forcing (energy) levels were considered in the tests in order to study the energy-dependencies of the damping nonlinearities induced in the beam from the bolted joint. In all cases, the NSI methodology employed was successful in identifying the damping nonlinearities, their spatial distributions and their effects of the vibration modes of the structural component.
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.; Hodges, Dewey H.
1987-01-01
The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.
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.
NASA Astrophysics Data System (ADS)
Hammerand, Daniel C.
Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically 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. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to the continual generation of the assembled internal load vector, tangent stiffness matrix, and deformation-dependent external load vectors. Rather, for small deformations, the appropriate deformation-independent stiffness matrices and load vectors to be used for all times can be determined once at the start of the analysis. Of course, the time-dependent viscoelastic effects need to be correctly taken into account in both types of analyses. The present work details both geometrically-linear and nonlinear triangular flat shell formulations for linear viscoelastic composites. The accuracy and capability of the formulations are shown through a range of numerical examples involving beams, rings, plates, and shells.
Nonlinear dynamics of inhomogeneous mismatched charged particle beams
Nunes, R. P. [Departamento de Engenharia Eletrica, Escola de Engenharia, Universidade Federal do Rio Grande do Sul, Ave. Osvaldo Aranha 103, 90035-190, Porto Alegre, RS (Brazil); Rizzato, F. B. [Departamento de Fisica, Instituto de Fisica, Universidade Federal do Rio Grande do Sul, P.O. Box: 15051, 91501-970, Porto Alegre, RS (Brazil)
2012-08-13
This work analyzes the transversal dynamics of an inhomogeneous and mismatched charged particle beam. The beam is azimuthally symmetric, initially cold, and evolves in a linear channel permeated by an external constant magnetic field. Based on a Lagrangian approach, a low-dimensional model for the description of the beam dynamics has been obtained. The small set of nonlinear dynamical equations provided results that are in reasonable agreement with that ones observed in full self-consistent N-particle beam numerical simulations.
Kazuhisa Ogawa; Shuhei Tamate; Hirokazu Kobayashi; Toshihiro Nakanishi; Masao Kitano
2015-04-08
We experimentally observed nonlinear variations in the three-vertex geometric phase in a two- photon polarization qutrit. The three-vertex geometric phase is defined by three quantum states, which generally forms a three-state (qutrit) system. By changing one of the three constituent states, we observed two rapid increases in the three-vertex geometric phase. The observed variations are inherent in a three-state system and cannot be observed in a two-state system. We used a time-reversed two-photon interferometer to measure the geometric phase with much more intense signals than those of a typical two-photon interferometer.
Beam steering via peak power decay in nonlinear waveguide arrays
Droulias, Sotiris
We report the experimental observation and theoretical analysis of a novel beam-steering effect in periodic waveguide arrays that arises from the interplay between discrete diffraction, Kerr nonlinearity and any mechanism ...
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.
Geometric Nonlinearities in Field Theory, Condensed Matter and Analytical Mechanics
Jan Jerzy S?awianowski
2010-10-15
There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at all, without nonlinearity. Particularly interesting are essential, non-perturbative nonlinearities which are not described by correction terms imposed on some well-defined linear background. Our idea in this paper is that there exists some mysterious, not yet understood link between essential, physically relevant nonlinearity and dynamical symmetry, first of all, large symmetry groups. In some sense the problem is known even in soliton theory, where the essential nonlinearity is often accompanied by the infinite system of integrals of motion, thus, by infinite-dimensional symmetry groups. Here we discuss some more familiar problems from the realm of field theory, condensed matter physics, and analytical mechanics, where the link between essential nonlinearity and high symmetry is obvious, even if not yet fully understood.
NASA Astrophysics Data System (ADS)
Gao, Jie
2009-02-01
In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.
A Geometric Calibration Methodology for Single-Head Cone-Beam X-Ray Systems
Kostas J. Kyriakopoulos; P. Yiannakos; V. Kallipolites; K. Domales
1999-01-01
During X-ray based quality inspection, accurate reconstruction of a 3D object model from a set of its 2D X-ray projections requires efficient geometric calibration, i.e., accurate estimation of the geometric parameters of the setup. We present a calibration methodology for the estimation of the geometric parameters of single-head cone-beam X-ray radiography systems. Our method is related to known approaches regarding
NONLINEAR FINITE ELEMENT ANALYSIS OF BEAM-COLUMN SUBASSEMBLIES
Vecchio, Frank J.
NONLINEAR FINITE ELEMENT ANALYSIS OF BEAM-COLUMN SUBASSEMBLIES by Gulsah Sagbas A Thesis submitted seismic assessment of beam-column subassemblies has been an important objective for many research groups over the years. Experimental and analytical research on different aspects of these members by various
Optical beam tracking based on nonlinear lens mechanism
NASA Astrophysics Data System (ADS)
Koujelev, Alexander S.; Dudelzak, Alexander E.
2007-09-01
Optical free-space communications involving moving parties require precise beam pointing and mutual tracking of communicating transceivers. The existing variety of tracking techniques is still the major limiting factor in free-space laser communications. Here we propose a technique for optical beam tracking and shaping that utilize nonlinear optical properties of materials. In our proof-of-concept experiment a thin layer of a nematic liquid crystal (NLC) with high thermal nonlinearity was used to produce a thermal lens induced by the incoming optical beam. That beam modulated the NLC refractive index. As the transmitted optical beam passed through the same layer the beam intensity was modulated in the far field. A sharp intensity maximum was formed at the distant communicating party position proving the device's tracking capability. Numerical modeling showed very good agreement with the experiment. The technique offers - many advantages and is simple to implement.
Nonlinear self-collimated sound beams in sonic crystals
NASA Astrophysics Data System (ADS)
Hamham, El Mokhtar; Jiménez, Noé; Picó, Rubén; Sánchez-Morcillo, Víctor J.; García-Raffi, Lluís M.; Staliunas, Kestutis
2015-08-01
We report the propagation of high-intensity sound beams in a sonic crystal, under self-collimation or reduced-divergence conditions. The medium is a fluid with elastic quadratic nonlinearity, where the dominating nonlinear effect is harmonic generation. The conditions for the efficient generation of narrow, nondiverging beam of second harmonic are discussed. Numerical simulations are in agreement with the analytical predictions made, based on the linear dispersion characteristics in modulated media and the nonlinear interaction in a quadratic medium under phase matching conditions.
Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.
2006-01-01
Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.
Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction
Van Stryland, Eric
Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction Manuel, 2013 We modify the well-known photothermal beam deflection technique to study ultrafast nonlinearities. We apply the previously developed technique of photo- thermal beam deflection, used extensively
Generation of optical vortex beams by nonlinear wave mixing.
Bahabad, Alon; Arie, Ady
2007-12-24
It is shown that optical vortex beams can be generated from a non-vortex fundamental beam by an optical frequency conversion process taking place within a twisted nonlinear photonic crystal. This is done without any first-order (linear) refractive optics. Through such a proposed structure, all-optical switching of vortices with different helicities is made possible, as well as the simultaneous application of counter-rotating vortex beams of different frequencies. PMID:19551056
NASA Astrophysics Data System (ADS)
Du, Dianlou; Yang, Xiao
2015-02-01
The algebraic-geometrical solutions of three (2 + 1)-dimensional equations (including mKP equation and coupled mKP equation) are discussed by Hamiltonian approach. First, the Poisson structure on CN × RN is introduced to give a Hamiltonian system associated with the derivative nonlinear Schrödinger (DNLS) hierarchy. The Hamiltonian system is proved to be Liouville integrable, accordingly the solutions of three (2 + 1)-dimensional nonlinear equations can be solved by three compatible Hamiltonian flows. Second, the canonical separated variables and Hamilton-Jacobi theory is used to definite action-angle variables for Hamiltonian flows. At last, by Riemann-Jacobi inversion, the algebraic-geometrical solutions of three (2 + 1)-dimensional nonlinear equations are obtained. Besides, the algebraic-geometrical solutions of the first two DNLS equations are also given.
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 ...
Shape Reconstruction Incorporating Multiple Non-linear Geometric Constraints
Fisher, Bob
Academic Publishers. Printed in the Netherlands. revisedpaper.tex; 6/04/2000; 15:35; p.1 #12;2 3D scanning deals with the reconstruction of 3D geometric shapes based on observed noisy 3D measurements optimization Abbreviations: CAD Computer Aided-design; 3D Three-Dimensional; LS Least squares Table
Donko, Z. [Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest (Hungary); Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D. [Institute for Plasma and Atomic Physics, Ruhr-University Bochum, Bochum 44780 (Germany)
2009-03-30
At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies.
A geometrically exact finite beam element formulation for thin film adhesion and debonding
A geometrically exact finite beam element formulation for thin film adhesion and debonding Roger A formulation is developed that is suitable to describe adhesion and debonding of thin films. The formulation moment within the beam that can play an important role in adhesion and debonding of thin films. The new
Iterative nonlinear beam propagation method and its application in nonlinear devices
Gao, Hanhong
2011-01-01
In this thesis, an iterative nonlinear beam propagation method is introduced and applied to optical devices. This method is based on Hamiltonian ray tracing and the Wigner distribution function. First, wave propagation ...
Development of geometrically-nonlinear finite element analysis for marine risers
Haas, Mark Edward
1987-01-01
cantilever beams that ranged in lengths and were vibrated in and out of water. The thesis compared the linear results to the nonlinear results. Within the dynamic analyses, the element performed poorly since multiple-element models could not be analyzed... without having numerical instabilities. Additional numerical instabilities occured when the nonlinear cantilever beams are analvzed. The poor results from this element in both static and dynamic analyses dictates that future research improves or derives...
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Muravyov, Alexander A.
2002-01-01
Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.
NASA Technical Reports Server (NTRS)
Raju, K. K.; Rao, G. V.; Raju, I. S.
1978-01-01
The effect of geometric nonlinearity on the free flexural vibrations of moderately thick rectangular plates is studied in this paper. Finite element formulation is employed to obtain the non-linear to linear period ratios for some rectangular plates. A conforming finite element of rectangular shape wherein the effects of shear deformation and rotatory inertia are included, is developed and used for the analysis. Results are presented for both simply supported and clamped boundary conditions.
Control and controllability of nonlinear dynamical networks: a geometrical approach
Le-Zhi Wang; Ri-Qi Su; Zi-Gang Huang; Xiao Wang; Wenxu Wang; Celso Grebogi; Ying-Cheng Lai
2015-09-23
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability (multiple coexisting final states or attractors), which are representative of, e.g., gene regulatory networks (GRNs). The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically useful, we consider RESTRICTED parameter perturbation by imposing the following two constraints: (a) it must be experimentally realizable and (b) it is applied only temporarily. We introduce the concept of ATTRACTOR NETWORK, in which the nodes are the distinct attractors of the system, and there is a directional link from one attractor to another if the system can be driven from the former to the latter using restricted control perturbation. Introduction of the attractor network allows us to formulate a controllability framework for nonlinear dynamical networks: a network is more controllable if the underlying attractor network is more strongly connected, which can be quantified. We demonstrate our control framework using examples from various models of experimental GRNs. A finding is that, due to nonlinearity, noise can counter-intuitively facilitate control of the network dynamics.
A Geometrically Nonlinear Shear Deformation Theory for Composite Shells
Yu, Wenbin
generalized strain-displacement relations are nonlinear while the 2-D generalized stress-strain relations turn-dimensional, generalized strains. The large rotation is represented by the general finite rotation of a frame embedded the normal line of the undeformed reference surface is not in general normal to the deformed reference sur
NASA Astrophysics Data System (ADS)
Neto, Alfredo Gay; Martins, Clóvis A.; Pimenta, Paulo M.
2014-01-01
In offshore applications there are elements that can be modeled as long beams, such as umbilical cables, flexible and rigid pipes and hoses, immersed in the sea water, suspended from the floating unit to the seabed. The suspended part of these elements is named "riser" and is subjected to the ocean environment loads, such as waves and sea current. This work presents a structural geometrically-exact 3D beam model, discretized using the finite element method for riser modeling. An updated Lagrangian framework for the rotation parameterization has been used for the description of the exact kinematics. The goal is to perform a complete static analysis, considering the oceanic loads and the unilateral contact with the seabed, extending the current standard analysis for situations in which very large rotations occurs, in particular, large torsion. Details of the nonlinear 3D model and loads from oceanic environment are discussed, including the contact unilateral constraint.
Geometric Nonlinearity: Is it Important for Real-time FEM Surgical Simulation? Michael Wehner
Alterovitz, Ron
of California, Berkeley goldberg@ieor.berkeley.edu 1. Background/Problem In real-time surgery simulation of linear to nonlinear geometry for the soft tissues often modeled in surgery simulation. For a case study of the prostate, we relax one assumption of linear FEM, geometric linearity, and quantify the difference
Geometrically non-linear analysis of plates and shallow shells by dynamic relaxation
G. Ramesh; C. S. Krishnamoorthy
1995-01-01
This paper investigates the application of dynamic relaxation (DR) method to the geometrically non-linear analysis of plates and shells involving large deflections, small rotations and strains. The merits and demerits of two types of approaches suggested for the evaluation of parameters of the DR method are reviewed. An accurate shallow shell element is developed in the present work using Marguerre's
Erasmo Carrera; Horst Parisch
1997-01-01
This paper, which deals with geometrically nonlinear analysis of multilayered shell structures, presents an evaluation of the approximations made when simplified models are introduced. To this purpose, a transverse shear deformable shell finite element formulation including finite rotations and large displacements is employed and von Karman, as well as moderate and small rotation theories, are obtained as particular cases. Classical
Geometrically nonlinear behavior of initially curved plane slender bars and frames
A. Pisanty
1977-01-01
Field equations for the geometrically nonlinear behavior of initially curved plane slender bars and frames comprising such bars are presented. Formulation originates from Continuum Solid Mechanics, allowing for exact expressions of axial deformation and curvature to be accounted for and unrestricted finite displacements to be considered within accepted assumptions regarding slenderness. Equilibrium equations are derived in terms of the curvature
S. Tangaramvong; F. Tin-Loi
2009-01-01
The present paper extends the classical limit analysis of plane frames to account for 2nd-order geometric nonlinearity. Any specified displacement limits can also be included in the proposed analysis. The effect of combined bending moment and axial force is accommodated in the adopted piecewise linearized yield condition, albeit still assumed as perfectly plastic. The main feature of the novel approach
A nonlinear theory for spinning anisotropic beams using restrained warping functions
NASA Technical Reports Server (NTRS)
Ie, C. A.; Kosmatka, J. B.
1993-01-01
A geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.
Suppressing Transverse Beam Halo with Nonlinear Magnetic Fields
Webb, Stephen D; Abell, Dan T; Danilov, Viatcheslav; Nagaitsev, Sergei; Valishev, Alexander; Danilov, Kirill; Cary, John R
2012-01-01
High intensity proton storage rings are central for the development of advanced neutron sources, drivers for the production of pions in neutrino factories or muon colliders, and transmutation of radioactive waste. Fractional proton loss from the beam must be very small to prevent radioac- tivation of nearby structures, but many sources of beam loss are driven by collective effects that increase with intensity. Recent theoretical work on the use of nonlinear magnetic fields to design storage rings with integrable transverse dynamics is extended here to include collective effects, with numerical results showing validity in the presence of very high beam current. Among these effects is the formation of beam halo, where particles are driven to large amplitude oscillations by coherent space charge forces. The strong variation of particle oscillation frequency with amplitude results in nonlinear decoherence that is observed to suppress transverse halo development in the case studied. We also present a necessary gen...
Nonlinear evolution of a relativistic electron beam in a plasma
NASA Astrophysics Data System (ADS)
Kong, Xianglong; Ren, Chuang; Tonge, John
2008-11-01
The most unstable modes in a relativistic electron beam-plasma return current system are oblique [Bret et al. PRE '04]. Nonlinear evolution of these modes is important to fast ignition and can only be simulated with the beam propagating in the simulation plane. Two-dimensional PIC simulations with this `in-plane' configuration show that the system evolves to a quasi-steady state stable to the two-stream instability with no bump on tail in the system distribution function. The most energetic field component is the transverse electric field. The beam retains more than 50% of its initial energy. The beam does not become localized in the transverse direction through filamenting and merging, as observed in previous simulations with the beam propagating out of the simulation plane [Lee and Lampe PRL '73]. The simulations also show that as the beam and plasma temperatures increase, the dominant mode becomes increasingly longitudinal.
Propagation of anomalous vortex beams in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Dai, Zhiping; Yang, Zhenjun; Zhang, Shumin; Pang, Zhaoguang
2015-09-01
The propagation properties of anomalous vortex beams in strongly nonlocal nonlinear media are investigated. Two equivalent analytical expressions for the evolution of anomalous vortex beams are obtained. It is found that the input power plays a key role in the beam evolutions. Selecting a proper input power, the beam width can be broadened or be compressed periodically, even it can keep invariant during propagation. The beam order and the topological charge mainly influence the intensity evolution and the phase evolution, respectively. The evolution period, the beam width, the phase distribution and the intensity distribution are discussed in detail. The results can also be generalized to other equivalent physical systems, such as an optical fractional Fourier transform system or a medium with a quadratic graded refractive index distribution.
Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
Li, Nianbei
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.
Geometric spin Hall effect of light in tightly focused polarization-tailored light beams
NASA Astrophysics Data System (ADS)
Neugebauer, Martin; Banzer, Peter; Bauer, Thomas; Orlov, Sergej; Lindlein, Norbert; Aiello, Andrea; Leuchs, Gerd
2014-01-01
Recently, it was shown that a nonzero transverse angular momentum manifests itself in a polarization-dependent intensity shift of the barycenter of a paraxial light beam [Aiello et al., Phys. Rev. Lett. 103, 100401 (2009), 10.1103/PhysRevLett.103.100401]. The underlying effect is phenomenologically similar to the spin Hall effect of light but does not depend on the specific light-matter interaction and can be interpreted as a purely geometric effect. Thus, it was named the geometric spin Hall effect of light. Here, we experimentally investigate the appearance of this effect in tightly focused vector beams. We use an experimental nanoprobing technique in combination with a reconstruction algorithm to verify the relative shifts of the components of the electric energy density and the shift of the intensity in the focal plane. By that, we experimentally demonstrate the geometric spin Hall effect of light in a highly nonparaxial beam.
Nonlinear geometrically adaptive finite element model of the coilbox
Troyani, N. [Univ. de Oriente, Puerto La Cruz (Venezuela). Dept. de Mecanica
1996-12-01
Hot bar heat loss in the transfer table, the rolling stage between rougher stands and finishing stands in a hot mill, is of major concern for reasons for energy consumption, metallurgical uniformity, and rollability. A mathematical model, as well as the corresponding numerical solution, is presented for the evolution of temperature in a coiling and uncoiling bar in hot mills in the form of a parabolic partial differential equation for a shape-changing domain. The space discretization is achieved via a computationally efficient geometrically adaptive finite element scheme that accommodates the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Finally, some numerical results are presented.
A shear-shear torsional beam model for nonlinear aeroelastic analysis of tower buildings
NASA Astrophysics Data System (ADS)
Piccardo, G.; Tubino, F.; Luongo, A.
2015-08-01
In this paper, an equivalent one-dimensional beam model immersed in a three-dimensional space is proposed to study the aeroelastic behavior of tower buildings: linear and nonlinear dynamics are analyzed through a simple but realistic physical modeling of the structure and of the load. The beam is internally constrained, so that it is capable to experience shear strains and torsion only. The elasto-geometric and inertial characteristics of the beam are identified from a discrete model of three-dimensional frame, via a homogenization process. The model accounts for the torsional effect induced by the rotation of the floors around the tower axis; the macroscopic shear strain is produced by bending of the columns, accompanied by negligible rotation of the floors. Nonlinear aerodynamic forces are evaluated through the quasi-steady theory. The first aim is to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions. Furthermore, the role of aerodynamic nonlinearities on the galloping post-critical behavior is analyzed through a perturbation solution which permits to obtain a reduced one-dimensional dynamical system, capable of capturing the essential dynamics of the problem.
A shear-shear torsional beam model for nonlinear aeroelastic analysis of tower buildings
NASA Astrophysics Data System (ADS)
Piccardo, G.; Tubino, F.; Luongo, A.
2014-09-01
In this paper, an equivalent one-dimensional beam model immersed in a three-dimensional space is proposed to study the aeroelastic behavior of tower buildings: linear and nonlinear dynamics are analyzed through a simple but realistic physical modeling of the structure and of the load. The beam is internally constrained, so that it is capable to experience shear strains and torsion only. The elasto-geometric and inertial characteristics of the beam are identified from a discrete model of three-dimensional frame, via a homogenization process. The model accounts for the torsional effect induced by the rotation of the floors around the tower axis; the macroscopic shear strain is produced by bending of the columns, accompanied by negligible rotation of the floors. Nonlinear aerodynamic forces are evaluated through the quasi-steady theory. The first aim is to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions. Furthermore, the role of aerodynamic nonlinearities on the galloping post-critical behavior is analyzed through a perturbation solution which permits to obtain a reduced one-dimensional dynamical system, capable of capturing the essential dynamics of the problem.
Nonlinear optical catastrophe from a smooth initial beam.
Deykoon, A M; Soskin, M S; Swartzlander, G A
1999-09-01
We observed an optical cusp diffraction catastrophe with an initially smooth but elongated Gaussian beam with an aspect ratio of 2:1. Nonlinear and linear diffraction regimes account for the near-field elliptical annulus and the far-field spatially complex astroid. PMID:18073991
Self-accelerating parabolic beams in quadratic nonlinear media Ido Dolev, Ana Libster, and Ady Arie
Arie, Ady
Self-accelerating parabolic beams in quadratic nonlinear media Ido Dolev, Ana Libster, and Ady Arie://apl.aip.org/authors #12;Self-accelerating parabolic beams in quadratic nonlinear media Ido Dolev,a) Ana Libster, and Ady
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.
Geometric Nonlinear Computation of Thin Rods and Shells
NASA Astrophysics Data System (ADS)
Grinspun, Eitan
2011-03-01
We develop simple, fast numerical codes for the dynamics of thin elastic rods and shells, by exploiting the connection between physics, geometry, and computation. By building a discrete mechanical picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting, we produce numerical codes that not only are consistent in a classical sense, but also reproduce qualitative, characteristic behavior of a physical system----such as exact preservation of conservation laws----even for very coarse discretizations. As two recent examples, we present discrete computational models of elastic rods and shells, with straightforward extensions to the viscous setting. Even at coarse discretizations, the resulting simulations capture characteristic geometric instabilities. The numerical codes we describe are used in experimental mechanics, cinema, and consumer software products. This is joint work with Miklós Bergou, Basile Audoly, Max Wardetzky, and Etienne Vouga. This research is supported in part by the Sloan Foundation, the NSF, Adobe, Autodesk, Intel, the Walt Disney Company, and Weta Digital.
NASA Astrophysics Data System (ADS)
Asadi, Hamed; Eynbeygi, Mehdi; Wang, Quan
2014-07-01
The instability of geometrically imperfect shape memory alloy (SMA) fibers reinforced with hybrid laminated composite (SMAHC) plates and subjected to a uniform thermal loading is analytically investigated. The material properties of the SMAHC plates are assumed to be functions of temperature. Nonlinear equations of the plates’ thermal stability are derived based on a higher order shear deformation theory incorporating von Karman geometrical nonlinearity via stationary potential energy. The structural recovery stress, which is generated by martensitic phase transformation of the prestrained SMA fibers, is calculated based on the one-dimensional thermodynamic constitutive model by Brinson. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, in which systems of equations are solved by introducing an analytical approach. Closed-form formulations are presented to determine the load-deflection path and critical buckling temperature of the plate. Based on the developed closed-form solutions, ample numerical results are presented to provide an insight into the effects of the volume fraction, prestrain, location and orientation of the SMA fibers, composite plate geometry, geometrical imperfection and temperature dependence on the stability of the SMAHC plates. It is shown that a proper application of SMA fibers results in a considerable delay of the thermal bifurcation and controllable thermal post-buckling deflection of the SMAHC plate.
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.
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
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
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
Nonlinear transmission line based electron beam driver
French, David M.; Hoff, Brad W.; Tang Wilkin; Heidger, Susan; Shiffler, Don [Directed Energy Directorate, Air Force Research Laboratory, Kirtland AFB, New Mexico 87117 (United States); Allen-Flowers, Jordan [Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721 (United States)
2012-12-15
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.
Multisymplectic Lie group variational integrator for a geometrically exact beam in R3
NASA Astrophysics Data System (ADS)
Demoures, François; Gay-Balmaz, François; Kobilarov, Marin; Ratiu, Tudor S.
2014-10-01
In this paper we develop, study, and test a Lie group multisymplectic integrator for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum map conservations associated to the temporal and spatial discrete evolutions.
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.
S. V. Levyakov; V. V. Kuznetsov
2011-01-01
This paper is an attempt to construct a computationally effective curved triangular finite element for geometrically nonlinear\\u000a analysis of elastic shear deformable shells fabricated from functionally graded materials. The focus is on the concise finite-element\\u000a formulation under the demand of accuracy-simplicity trade-off. To this end, a nonconventional approach based on the invariants\\u000a of the natural strains of fibers parallel to
Constructing a new geometric numerical integration method to the nonlinear heat transfer equations
NASA Astrophysics Data System (ADS)
Hashemi, M. S.
2015-05-01
In this paper, we construct a new geometric integration method which is based on the Lie group SL (2, R) to solve the nonlinear longitudinal convective-radiative-conduction fin equation. SL (2, R) -shooting method and related algorithm to find a high accuracy solutions are discussed. Finally, effects of thermal conductivity parameter, surface emissivity parameter, convection-conduction and radiation-conduction parameters are illustrated on the performance of fins.
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
Accurate technique for complete geometric calibration of cone-beam computed tomography systems.
Cho, Youngbin; Moseley, Douglas J; Siewerdsen, Jeffrey H; Jaffray, David A
2005-04-01
Cone-beam computed tomography systems have been developed to provide in situ imaging for the purpose of guiding radiation therapy. Clinical systems have been constructed using this approach, a clinical linear accelerator (Elekta Synergy RP) and an iso-centric C-arm. Geometric calibration involves the estimation of a set of parameters that describes the geometry of such systems, and is essential for accurate image reconstruction. We have developed a general analytic algorithm and corresponding calibration phantom for estimating these geometric parameters in cone-beam computed tomography (CT) systems. The performance of the calibration algorithm is evaluated and its application is discussed. The algorithm makes use of a calibration phantom to estimate the geometric parameters of the system. The phantom consists of 24 steel ball bearings (BBs) in a known geometry. Twelve BBs are spaced evenly at 30 deg in two plane-parallel circles separated by a given distance along the tube axis. The detector (e.g., a flat panel detector) is assumed to have no spatial distortion. The method estimates geometric parameters including the position of the x-ray source, position, and rotation of the detector, and gantry angle, and can describe complex source-detector trajectories. The accuracy and sensitivity of the calibration algorithm was analyzed. The calibration algorithm estimates geometric parameters in a high level of accuracy such that the quality of CT reconstruction is not degraded by the error of estimation. Sensitivity analysis shows uncertainty of 0.01 degrees (around beam direction) to 0.3 degrees (normal to the beam direction) in rotation, and 0.2 mm (orthogonal to the beam direction) to 4.9 mm (beam direction) in position for the medical linear accelerator geometry. Experimental measurements using a laboratory bench Cone-beam CT system of known geometry demonstrate the sensitivity of the method in detecting small changes in the imaging geometry with an uncertainty of 0.1 mm in transverse and vertical (perpendicular to the beam direction) and 1.0 mm in the longitudinal (beam axis) directions. The calibration algorithm was compared to a previously reported method, which uses one ball bearing at the isocenter of the system, to investigate the impact of more precise calibration on the image quality of cone-beam CT reconstruction. A thin steel wire located inside the calibration phantom was imaged on the conebeam CT lab bench with and without perturbations in source and detector position during the scan. The described calibration method improved the quality of the image and the geometric accuracy of the object reconstructed, improving the full width at half maximum of the wire by 27.5% and increasing contrast of the wire by 52.8%. The proposed method is not limited to the geometric calibration of cone-beam CT systems but can be used for many other systems, which consist of one or more point sources and area detectors such as calibration of megavoltage (MV) treatment system (focal spot movement during the beam delivery, MV source trajectory versus gantry angle, the axis of collimator rotation, and couch motion), cross calibration between Kilovolt imaging and MV treatment system, and cross calibration between multiple imaging systems. Using the complete information of the system geometry, it was demonstrated that high image quality in CT reconstructions is possible even in systems with large geometric nonidealities. PMID:15895580
Nonlinear beam splitter in Bose-Einstein-condensate interferometers
Pezze, L.; Smerzi, A.; Berman, G. P.; Bishop, A. R.; Collins, L. A.
2006-09-15
A beam splitter is an important component of an atomic/optical Mach-Zehnder interferometer. Here we study a Bose-Einstein condensate beam splitter, realized with a double well potential of tunable height. We analyze how the sensitivity of a Mach-Zehnder interferometer is degraded by the nonlinear particle-particle interaction during the splitting dynamics. We distinguish three regimes, Rabi, Josephson and Fock, and associate to them a different scaling of the phase sensitivity with the total number of particles.
NASA Technical Reports Server (NTRS)
Robinson, J. C.
1979-01-01
Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.
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.
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.
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
Topology optimization of geometrically nonlinear structures including thermo-mechanical coupling
NASA Astrophysics Data System (ADS)
Pajot, Joseph M.
The goal of this research is to develop an efficient and robust methodology for the topology optimization of geometrically nonlinear structures actuated by thermal expansion. The corotational finite element method is used to model the geometric nonlinearity because its element independent nature and linear elastic element core provide a flexibility to introduce thermal loads and formulate analytical sensitivities for any element type. To create thermal expansion, this work uses both prescribed temperature changes and localized heat generation via Joule heating, where electrical and thermal conduction are additionally considered. In this coupled multi-physics problem, emphasis is put on material models and coupling to maintain accuracy and efficiency. One-way coupling is shown to be equivalent to a small strain assumption, and the proper modeling of convection properties in topology optimization is addressed. To model the thermal and electrical conduction in planar layered materials, an averaged (smeared) model based on the smoothed properties of the individual layers is introduced. Large displacement structures are prone to exhibit buckling and limit point behavior. To include instabilities in topology optimization, specialized techniques are introduced to overcome inherent numerical difficulties. A nodal density transformation is introduced to isolate structurally relevant eigenmodes, and a homotopy between linear and nonlinear finite elements is provided to limit the effects of mesh distortion. The proposed methodology is successfully applied to micro-mechanism applications capable of a three-dimensional range of motion, including novel designs reflective of the manufacturing technology used in the micro-electro-mechanical (MEMS) community.
NASA Astrophysics Data System (ADS)
Ogawa, Kazuhisa; Tamate, Shuhei; Kobayashi, Hirokazu; Nakanishi, Toshihiro; Kitano, Masao
2015-06-01
We observed experimentally nonlinear variations in the three-vertex geometric phase in a two-photon polarization qutrit. The three-vertex geometric phase is defined by three quantum states, which generally form a three-state (qutrit) system. By changing one of the three constituent states, we observed two rapid increases in the three-vertex geometric phase. The observed variations are inherent in a three-state system and cannot be observed in a two-state system. We used a time-reversed two-photon interferometer to measure the geometric phase with much more intense signals than those of a typical two-photon interferometer.
Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.
Shemer, Keren; Voloch-Bloch, Noa; Shapira, Asia; Libster, Ana; Juwiler, Irit; Arie, Ady
2013-12-15
We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump's radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new "virtual beam" having multiple values of OAM that are determined by the nonlinear process. PMID:24343019
Nonlinear analysis of frames with flexible connections
Miodrag Sekulovic; Ratko Salatic
2001-01-01
The effects of flexibility and eccentricity in the nodal connections of plane frames due to static loading are considered in this paper. A numerical model that includes both nonlinear connection behavior and geometric nonlinearity of the structure is developed. Two types of geometric nonlinear analysis are considered: with and without the bowing effect influence. The stiffness matrix for the beam
Geometrical and Dynamical Aspects of Nonlinear Higher-Order Riccati Systems
José F. Cariñena; Partha Guha; Manuel F. Rañada
2015-07-02
We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on $S^1$, whichn in turn is related to the stability algebra of Virasoro orbit. Using Darboux integrability method we obtain the first-integral of SORE and the results are applied to the study of its Lagrangian and Hamiltonian description. We unveil the relation between the Darboux polynomials and master symmetries associated to second-order Riccati. Using these results we show the existence of a Lagrangian description for the related system, and the Painlev\\'e II equation is analysed.
Geometrically nonlinear analysis of stiffened composite panels with various end-support conditions
NASA Technical Reports Server (NTRS)
Stoll, Frederick
1993-01-01
Recent enhancements to the NLPAN computer code are presented. NLPAN is a finite strip method for the geometrically nonlinear static analysis of prismatic composite structures subjected to in-plane and pressure loading. Refinements to the original approach of NLPAN are noted, and the modifications necessary to model clamped ends, eccentrically loaded ends, and ends with rotationally elastic support are discussed. Analytical predictions for axially loaded stiffened panels with various types of end support are compared with experimental measurements. Overall there is good agreement between analytical results and test results. The method is successful in modelling key mechanisms which can cause elastic collapse.
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.
Geredeli, Pelin G.; Webster, Justin T.
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.
Geometrical method for thermal instability of nonlinearly charged BTZ Black Holes
Hendi, Seyed Hossein; Panah, Behzad Eslam
2015-01-01
In this paper we consider three dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity. Whereas for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes.
Online optimization of storage ring nonlinear beam dynamics
NASA Astrophysics Data System (ADS)
Huang, Xiaobiao; Safranek, James
2015-08-01
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.
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.
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
Electromagnetic and geometric characterization of accelerated ion beams by laser ablation
NASA Astrophysics Data System (ADS)
Nassisi, V.; Velardi, L.; Side, D. Delle
2013-05-01
Laser ion sources offer the possibility to get ion beam useful to improve particle accelerators. Pulsed lasers at intensities of the order of 108 W/cm2 and of ns pulse duration, interacting with solid matter in vacuum, produce plasma of high temperature and density. The charge state distribution of the plasma generates high electric fields which accelerate ions along the normal to the target surface. The energy of emitted ions has a Maxwell-Boltzmann distribution which depends on the ion charge state. To increase the ion energy, a post-acceleration system can be employed by means of high voltage power supplies of about 100 kV. The post acceleration system results to be a good method to obtain high ion currents by a not expensive system and the final ion beams find interesting applications in the field of the ion implantation, scientific applications and industrial use. In this work we compare the electromagnetic and geometric properties, like emittance, of the beams delivered by pure Cu, Y and Ag targets. The characterization of the plasma was performed by a Faraday cup for the electromagnetic characteristics, whereas a pepper pot system was used for the geometric ones. At 60 kV accelerating voltage the three examined ion bunches get a current peak of 5.5, 7.3 and 15 mA, with a normalized beam emittance of 0.22, 0.12 and 0.09 ? mm mrad for the targets of Cu, Y, and Ag, respectively.
Nonlinear Finite Element Analysis of FRP Strengthened Reinforced Concrete Beams
NASA Astrophysics Data System (ADS)
Sasmal, S.; Kalidoss, S.; Srinivas, V.
2012-12-01
This paper focuses on nonlinear analysis of parent and fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beam using general purpose finite element software, ANSYS. Further, it is aimed to investigate the suitability of different elements available in ANSYS library to represent FRP, epoxy and interface. 3-D structural RC solid element has been used to model concrete and truss element is employed for modeling the reinforcements. FRP has been modelled using 3-D membrane element and layered element with number of layers, epoxy is modelled using eight node brick element, and eight node layered solid shell is used to mathematically represent the concrete-FRP interface behavior. Initially, the validation of the numerical model for the efficacy of different elements (SOLID65 for concrete and LINK8 for reinforcement) and material models is carried out on the experimental beam reported in literature. The validated model, elements and material properties is used to evaluate the load-displacement and load-strain response behavior and crack patterns of the FRP strengthened RC beams. The numerical results indicated that significant improvement in the displacement in the strengthened RC beams with the advancement of cracks. The study shows that FRP with shell elements is recommended when single layer of FRP is used. When multi layered FRP is used, solid layered element can be a reasonably good choice whereas the epoxy matrix with linear solid element does not need further complicated model. Interfacial element makes the analysis minimally improved at the cost of complicated modeling issues and considerable computation time. Hence, for nonlinear analysis of usual strengthened structures, unless it is specifically required for, interface element may not be required and a full contact can be assumed at interface.
On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics
NASA Astrophysics Data System (ADS)
Gay-Balmaz, François; Putkaradze, Vakhtang
2015-08-01
We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.
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 ...
Quality Assurance for the Geometric Accuracy of Cone-Beam CT Guidance in Radiation Therapy
Bissonnette, Jean-Pierre [Radiation Medicine Program, Princess Margaret Hospital, Toronto, Ontario (Canada)], E-mail: jean-pierre.bissonnette@rmp.uhn.on.ca; Moseley, Doug; White, Elizabeth; Sharpe, Michael; Purdie, Tom; Jaffray, David A. [Radiation Medicine Program, Princess Margaret Hospital, Toronto, Ontario (Canada)
2008-05-01
The introduction of volumetric X-ray image-guided radiotherapy systems allows improved management of geometric variations in patient setup and internal organ motion. As these systems become a routine clinical modality, we propose a daily quality assurance (QA) program for cone-beam computed tomography (CBCT) integrated with a linear accelerator. The image-guided system used in this work combines a linear accelerator with conventional X-ray tube and an amorphous silicon flat-panel detector mounted orthogonally from the accelerator central beam axis. This article focuses on daily QA protocols germane to geometric accuracy of the CBCT systems and proposes tolerance levels on the basis of more than 3 years of experience with seven CBCT systems used in our clinic. Monthly geometric calibration tests demonstrate the long-term stability of the flex movements, which are reproducible within {+-}0.5 mm (95% confidence interval). The daily QA procedure demonstrates that, for rigid phantoms, the accuracy of the image-guided process can be within 1 mm on average, with a 99% confidence interval of {+-}2 mm.
Direct determination of cone-beam geometric parameters using the helical phantom
NASA Astrophysics Data System (ADS)
Xu, M.; Zhang, C.; Liu, X.; Li, D.
2014-10-01
Estimation of a set of parameters that describe the geometry of the cone-beam computed tomography system plays an important role in the geometrical calibration. In the calibration process, the helical phantom consisting of spherical markers arranged on a helical trajectory has been widely applied. To directly determine the complete nine geometric calibration parameters using the helical phantom, we propose a novel calibration method using explicit mathematical formulae. In the method, the geometric characteristics of the helix are utilized by converting the helix to delicately designed parallelograms. Then, the projections of the intersection points of the diagonals of parallelograms are obtained and used to identify the projections of the phantom coordinate axes, which are integrated into the calibration algorithm to calculate the geometric parameters. Our method makes full use of the markers, and has the property that flexible selection of the phantom coordinate system, which can deal with degenerate cases. To validate this method, simulation studies with various system geometries, different number of markers and different noise types are performed. A comparison of our proposed method with projection matrix method is also presented. The results show that our method can provide comparable accuracy of parameter estimation with the projection matrix method. The estimation of piercing points is even better using our method, which shows a factor of 8 × error reduction. The small animal studies also verify the accuracy and robustness of the proposed method.
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.
Lin, Tai-Chia; Beli?, Milivoj R.; Petrovi?, Milan S.; Chen, Goong; Department of Mathematics and Institute for Quantum Science and Engineering, Texas A and M University, College Station, Texas 77843
2014-01-15
Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.
Hoffstaetter, Georg
Results from Orbit and Optics Improvement by Evaluating the Nonlinear Beam Position Monitor. Because the previous system of evaluating signals from beam position monitors (BPMs) was accurate only measurements. BACKGROUND CESR measures beam position and betatron phase with approximately one hundred beam
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.
Focused ion beam techniques for fabricating geometrically-complex components and devices.
Mayer, Thomas Michael; Adams, David Price; Hodges, V. Carter; Vasile, Michael J.
2004-03-01
We have researched several new focused ion beam (FIB) micro-fabrication techniques that offer control of feature shape and the ability to accurately define features onto nonplanar substrates. These FIB-based processes are considered useful for prototyping, reverse engineering, and small-lot manufacturing. Ion beam-based techniques have been developed for defining features in miniature, nonplanar substrates. We demonstrate helices in cylindrical substrates having diameters from 100 {micro}m to 3 mm. Ion beam lathe processes sputter-define 10-{micro}m wide features in cylindrical substrates and tubes. For larger substrates, we combine focused ion beam milling with ultra-precision lathe turning techniques to accurately define 25-100 {micro}m features over many meters of path length. In several cases, we combine the feature defining capability of focused ion beam bombardment with additive techniques such as evaporation, sputter deposition and electroplating in order to build geometrically-complex, functionally-simple devices. Damascene methods that fabricate bound, metal microcoils have been developed for cylindrical substrates. Effects of focused ion milling on surface morphology are also highlighted in a study of ion-milled diamond.
Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity
NASA Astrophysics Data System (ADS)
Sun, Xiuting; Jing, Xingjian
2015-10-01
The study proposes a novel vibration isolator with 3D quasi-zero-stiffness (QZS) property. The remarkable feature of the proposed system is to apply symmetrically scissor-like structures (SLS) in the horizontal directions, together with a traditional spring-mass-damper system assembled vertically with positive stiffness. With the mathematical modeling of the proposed system, it is shown that the stiffness and damping properties are nonlinear due to nonlinear geometric relations within the SLSs and both can be adjusted via structural parameters of the system. Theoretical analysis with the harmonic balance method reveals that the system can demonstrate QZS property in 3 directions, and can achieve much better 3D vibration isolation performance, including high-static and quasi-zero-dynamic stiffness, and much larger displacement range around equilibrium, compared with an existing QZS system in the literature. The results provide a novel and significant multi-direction vibration isolation method using structural nonlinearity with noticeable performance but using only passive elements.
NASA Astrophysics Data System (ADS)
Hamilton, Mark F.
1990-12-01
This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.
R. Sugaya
2008-01-01
Acceleration and heating of a relativistic electron beam due to nonlinear electron Landau and cyclotron damping of electromagnetic waves in a magnetized plasma are investigated theoretically and numerically on the basis of the relativistic kinetic wave and transport equations derived from the relativistic Vlasov-Maxwell equations. Two electromagnetic waves interact nonlinearly with the relativistic electron beam, satisfying the resonance condition of
Mode transition and nonlinear self-oscillations in the beam-driven collisional discharge plasma
Lee, Hae June
Mode transition and nonlinear self-oscillations in the beam-driven collisional discharge plasma Hae Received 13 February 1998; accepted 19 May 1998 Nonlinear dynamics and self-oscillations in a dc beam is in good agreement with the simulation results. The mechanism of low frequency self-oscillation
ON NONLINEAR VIBRATION OF NONUNIFORM BEAM WITH RECTANGULAR CROSS-SECTION AND PARABOLIC THICKNESS
Caruntu, Dumitru I. - Mechanical Engineering Department, University of Texas
ON NONLINEAR VIBRATION OF NONUNIFORM BEAM WITH RECTANGULAR CROSS-SECTION AND PARABOLIC THICKNESS the factorization method. This beam with constant width and parabolic thickness is a good approximation of the gear with rectangular cross-section, constant width, parabolic thickness variation and a sharp end. The nonlinear model
Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes
Min Sup Hur; Hae June Lee; Jae Koo Lee
1998-01-01
Nonlinear phenomena in a driven plasma diode are studied using a fluid code and the particle-in-cell simulation code xpdp1. When a uniform electron beam is injected to a bounded diode filled with uniform ion background, the beam is destabilized by the Pierce instability and a perturbation grows to exhibit nonlinear oscillations including chaos. Two standard routes to chaos, period doubling
Light beams with general direction and polarization: Global description and geometric phase
NASA Astrophysics Data System (ADS)
Nityananda, R.; Sridhar, S.
2014-02-01
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 S2 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 S2×C2?{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 S2×S2 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, CP2, 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 S2×S2. 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.
Paradox of a nonlinear beam splitter and its resolution
NASA Astrophysics Data System (ADS)
Belinsky, A. V.; Volkov, D. V.; Dmitriev, A. V.; Shulman, M. Kh.
2013-11-01
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.
Integrability and chaos in nonlinearly coupled optical beams
David, D.
1989-01-01
This paper presents a study, using dynamical systems methods, of the equations describing the polarization behavior of two nonlinearly coupled optical beams counterpropagating in a nonlinear medium. In the travelling-wave regime assumption, this system possesses a Lie-Poisson structure on the manifold C{sup 2} {times} C{sup 2}. In the case where the medium is assumed to be isotropic, this system exhibits invariance under the Hamiltonian action of two copies of the rotation group, S{sup 1}, and actually reduces to a lower-dimensional system on the two-sphere, S{sup 2}. We study the dynamics on the reduced space and examine the structure of the phase portrait by determining the fixed points and infinite-period homoclinic and heteroclinic orbits; we concentrate on presenting some exotic behaviour that occurs when some parameters are varied, and we also show special solutions associated with some of the above-mentioned orbits. Last, we demonstrate the existence of complex dynamics when the system is subject to certain classes of Hamiltonian perturbations. To this end, we make use of the Melnikov method to analytically show the occurrence of either horseshoe chaos, or Arnold diffusion. 19 refs.
Hamiltonian chaos in a nonlinear polarized optical beam
David, D.; Holm, D.D.; Tratnik, M.V. )
1989-01-01
This lecture concerns the applications of ideas about temporal complexity in Hamiltonian systems to the dynamics of an optical laser beam with arbitrary polarization propagating as a traveling wave in a medium with cubically nonlinear polarizability. We use methods from the theory of Hamiltonian systems with symmetry to study the geometry of phase space for this optical problem, transforming from C{sup 2} to S{sup 3} {times} S{sup 1}, first, and then to S{sup 2} {times} (J, {theta}), where (J, {theta}) is a symplectic action-angle pair. The bifurcations of the phase portraits of the Hamiltonian motion on S{sub 2} are classified and displayed graphically. These bifurcations take place when either J (the beam intensity), or the optical parameters of the medium are varied. After this bifurcation analysis has shown the existence of various saddle connections on S{sup 2}, the Melnikov method is used to demonstrate analytically that the traveling-wave dynamics of a polarized optical laser pulse develops chaotic behavior in the form of Smale horseshoes when propagating through spatially periodic perturbations in the optical parameters of the medium. 20 refs., 7 figs.
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.
Light beams with general direction and polarization: Global description and geometric phase
Nityananda, R.; Sridhar, S.
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.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H., Jr.
2002-01-01
The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.
Three wave mixing of airy beams in a quadratic nonlinear photonic crystals and Ady Arie
Arie, Ady
. Airy beams were shown to be useful for optical micro- manipulation of small particles,5 three wave mixing processes of accelerating Airy beams in quadratic nonlinear crystals. In order process between two accelerating beam enable to set the acceleration rate and direction of the generated
Hoffstaetter, Georg
Evaluation of Beam Position Monitors in the Nonlinear Regime Richard W. Helms and Georg H Beam Position Monitors (BPMs) consists of four button-type electrodes mounted Â¤ush with. The four signals from each BPM are used to determine the beam position and betatron phase advance. Our
C. Dewdney; J. P. Vigier; A. Kyprianidis; M. A. Dubois
1984-01-01
The introduction of a causal quantum potential (which vanishes for coherent light beams) in the Einstein-de Broglie theory of light implies an enhancement of some photon individual energy E = hv in the intersection region of coherent laser beams. This property not only interprets nonlinear effects already observed in highly focused laser beams, but also yields new predictions which can
Nonlinear tubular Bragg diffraction and all-optical switching over Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Shalaby, M.
1999-05-01
In this paper we show the nonlinear diffraction of a weak beam on a Laguerre-Gaussian (LG) beam of high intensity, where a part of the weak beam is transformed to the shape of a LG beam. We also show the rotation of a second LG beam influenced by this LG beam until their petals overlap. It is, to our knowledge, the first time that a soliton interaction extends to beams of LG profile. This work can be useful in all optical switching and signal processing.
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.
Simplified nonlinear response simulation of composite steel–concrete beams and CFST columns
Huiling Zhao; Sashi K. Kunnath; Yong Yuan
2010-01-01
A computationally efficient macromodeling scheme to simulate the nonlinear behavior of composite structural connections consisting of steel–concrete composite beams and concrete-filled steel tubular (CFST) columns is investigated. The model proposed for composite beams, validated using four full scale composite beam tests, incorporates partial interaction between the concrete slab and the steel beam. The model proposed for CFST columns adopts fiber-based
NASA Astrophysics Data System (ADS)
Moroni, Giovanni; Syam, Wahyudin P.; Petrò, Stefano
2014-08-01
Product quality is a main concern today in manufacturing; it drives competition between companies. To ensure high quality, a dimensional inspection to verify the geometric properties of a product must be carried out. High-speed non-contact scanners help with this task, by both speeding up acquisition speed and increasing accuracy through a more complete description of the surface. The algorithms for the management of the measurement data play a critical role in ensuring both the measurement accuracy and speed of the device. One of the most fundamental parts of the algorithm is the procedure for fitting the substitute geometry to a cloud of points. This article addresses this challenge. Three relevant geometries are selected as case studies: a non-linear least-squares fitting of a circle, sphere and cylinder. These geometries are chosen in consideration of their common use in practice; for example the sphere is often adopted as a reference artifact for performance verification of a coordinate measuring machine (CMM) and a cylinder is the most relevant geometry for a pin-hole relation as an assembly feature to construct a complete functioning product. In this article, an improvement of the initial point guess for the Levenberg-Marquardt (LM) algorithm by employing a chaos optimization (CO) method is proposed. This causes a performance improvement in the optimization of a non-linear function fitting the three geometries. The results show that, with this combination, a higher quality of fitting results a smaller norm of the residuals can be obtained while preserving the computational cost. Fitting an ‘incomplete-point-cloud’, which is a situation where the point cloud does not cover a complete feature e.g. from half of the total part surface, is also investigated. Finally, a case study of fitting a hemisphere is presented.
Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity
NASA Astrophysics Data System (ADS)
Sharma, Prerana
2015-07-01
This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel-Kramers-Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.; Nguyen, Duc T.
2008-01-01
A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.
NASA Astrophysics Data System (ADS)
Wang, Ya-Guang; Yu, Fang
2014-09-01
In this paper, the stability of supersonic contact discontinuities in the three-dimensional compressible isentropic steady Euler flows is investigated by using the nonlinear geometric optics. We construct the asymptotic expansions of highly oscillatory contact discontinuities when a planar contact discontinuity is perturbed by a small amplitude high frequency oscillatory incident wave, and deduce there exists a large amplification of amplitudes in the reflected and refracted oscillatory waves when the high frequency oscillatory wave strikes the contact discontinuity front at three critical angles. Moreover, we obtain that the leading profiles of highly oscillatory waves are described by an initial boundary value problem of Burgers-transport equations, and the leading profile of contact discontinuity front satisfies an initial value problem of a Hamilton-Jacobi equation, respectively. The amplification phenomenon shows that this supersonic contact discontinuity is only weakly stable in the sense of Wang and Yu ["Stability of contact discontinuities in three-dimensional compressible steady flows," J. Differ. Equ. 255, 1278-1356 (2013)].
Geometric calibration of a mobile C-arm for intraoperative cone-beam CT
Daly, M. J.; Siewerdsen, J. H.; Cho, Y. B.; Jaffray, D. A.; Irish, J. C.
2008-01-01
A geometric calibration method that determines a complete description of source-detector geometry was adapted to a mobile C-arm for cone-beam computed tomography (CBCT). The non-iterative calibration algorithm calculates a unique solution for the positions of the source (Xs,Ys,Zs), detector (Xd,Yd,Zd), piercing point (Uo,Vo), and detector rotation angles (?,?,?) based on projections of a phantom consisting of two plane-parallel circles of ball bearings encased in a cylindrical acrylic tube. The prototype C-arm system was based on a Siemens PowerMobil modified to provide flat-panel CBCT for image-guided interventions. The magnitude of geometric nonidealities in the source-detector orbit was measured, and the short-term (?4 h) and long-term (?6 months) reproducibility of the calibration was evaluated. The C-arm exhibits large geometric nonidealities due to mechanical flex, with maximum departures from the average semicircular orbit of ?Uo=15.8 mm and ?Vo=9.8 mm (for the piercing point), ?X and ?Y=6–8 mm and ?Z=1 mm (for the source and detector), and ???2.9°, ???1.9°, and ???0.8° (for the detector tilt?rotation). Despite such significant departures from a semicircular orbit, these system parameters were found to be reproducible, and therefore correctable by geometric calibration. Short-term reproducibility was <0.16 mm (subpixel) for the piercing point coordinates, <0.25 mm for the source-detector X and Y, <0.035 mm for the source-detector Z, and <0.02° for the detector angles. Long-term reproducibility was similarly high, demonstrated by image quality and spatial resolution measurements over a period of 6 months. For example, the full-width at half-maximum (FWHM) in axial images of a thin steel wire increased slightly as a function of the time (?) between calibration and image acquisition: FWHM=0.62, 0.63, 0.66, 0.71, and 0.72 mm at ?=0 s, 1 h, 1 day, 1 month, and 6 months, respectively. For ongoing clinical trials in CBCT-guided surgery at our institution, geometric calibration is conducted monthly to provide sufficient three-dimensional (3D) image quality while managing time and workflow considerations of the calibration and quality assurance process. The sensitivity of 3D image quality to each of the system parameters was investigated, as was the tolerance to systematic and random errors in the geometric parameters, showing the most sensitive parameters to be the piercing point coordinates (Uo,Vo) and in-plane positions of the source (Xs,Ys) and detector (Xd,Yd). Errors in the out-of-plane position of the source (Zs) and detector (Zd) and the detector angles (?,?,?) were shown to have subtler effects on 3D image quality. PMID:18561688
Nonlinear in-plane warping deformation in elastically coupled open thin-walled beams
Omri Rand
2001-01-01
A study of the nonlinear in-plane warping in open thin-walled composite beams is presented. The analysis is based on a generic nonlinear formulation of the governing equations for the in-plane deformation which are solved by a numerical minimization procedure. The minimization process employs energy considerations to determine the in-plane-warping deformation of generic elastically coupled orthotropic beams. The study shows that
Davidson, Ronald C.; Qin, Hong
2015-09-21
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius r w . The average axial electric field is expressed as z >=–(?/?z)=–ebg???b/?z – ebg2r2w?3?b/?z3, where g0 and g2 are constant geometric factors, ?b(z,t)=?dpz Fb (z,pz,t) is the line density of beam particles, and F b (z,pz,t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations ofmore »the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where Fb = const in a bounded region of pz-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field.« less
Yasuhiro Watanabe; Masayuki Ishihara; Naotake Noda
2009-01-01
Nonlinear transient behavior of a piezothermoelastic laminate including the dynamic deformation deviated arbitrarily from the equilibrium state is analyzed. As an analytical model, we consider a laminated beam composed of the elastic structural layers and the piezoelectric layers subjected to mechanical, thermal and electrical loads as disturbances or intended control procedures. The deformation of the beam is analyzed by the
Nonlinear charge and current neutralization of an ion beam pulse in a pre-formed plasma
Kaganovich, Igor
Nonlinear charge and current neutralization of an ion beam pulse in a pre-formed plasma Igor D of the calculation is the quantitative prediction of the degree of charge and current neutralization of the ion beam. Particle-in-cell simulations and fluid calculations of current and charge neutralization have been
Effects of Geometric Azimuthal Asymmetries of the PPM Stack on Electron Beam Characteristics
NASA Technical Reports Server (NTRS)
Kory, Carol L.
2000-01-01
The effects of geometric azimuthally asymmetric properties of a periodic permanent magnet (PPM) focusing stack on electron beam characteristics obtained using a fully three dimensional (3D) particle-in-cell (PIC) code will be presented. The simulation model, using MAFIA (Solution of MAxwell's equations by the Finite-Integration-Algorithm), incorporates 3D behavior of the beam immersed in static fields calculated directly from the exact geometry and material properties of the 3D magnetic focusing structure. The Hughes 8916H, 18-40 GHz helical TWT for the millimeter-wave power module (MMPM) was used as a prototype. Firstly, the effects of C-magnets used at the input and output of the TWT to allow for coupling of the RF signal into and out of the tube are considered. The 8916H input and output C-magnets differ because coaxial couplers are used at the input and waveguide couplers are used at the output The repositioning of the beam from its central axis due to the inclusion of the output C-magnet was found to be most significant. The modeled output C-magnet and its orientation in the Cartesian coordinate system is shown, and a two-dimensional beam profile including the output C-magnet is also shown. A table presents the shift of the beam center off the central axis relative to the average radius of the beam at the longitudinal points A, B and C designated on an enclosed figure. Secondly, the addition of shunts, or rectangular iron pieces applied manually by a skilled technician in order to improve beam transmission, is considered. The shunts are applied to the top of the tube; thus, azimuthal symmetry of the focusing stack is interrupted. Although shunts are typically added during RF focusing, they are also typically added at the input section of the tube where RF forces are minimal, making an electron optics analysis meaningful. Because several shunts are usually applied to one pole piece, the simulations have been simplified by modeling a half washer with the same radius and longitudinal length as a shunt over the entire x, positive-y half of the transverse plane. A modeled pole piece and shunt as described are shown. Lastly, in order to study the effects of magnet misalignments, a magnet in the PPM stack was arbitrarily chosen and adjusted so that its central axis was shifted both 0.7 percent and 1.0 percent of the magnet outer diameter in the positive-y direction. In practice, positioning the magnets so that their central axis is accurately aligned with the central axis of the tube is challenging. Thus, it is a strong possibility that one or more magnets will be misaligned relative to the tube central axis.
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
Concatenated beam splitters, optical feed-forward, and the nonlinear sign gate
NASA Astrophysics Data System (ADS)
Jacobs, Kurt; Dowling, Jonathan P.
2006-12-01
We consider a nonlinear sign gate implemented using a sequence of two beam splitters, and consider the use of further sequences of beam splitters to implement feed-forward so as to correct an error resulting from the first beam splitter. We obtain similar results to Scheel [Phys. Rev. A 73, 034301 (2006)], in that we also find that our feed-forward procedure is only able to produce a very minor improvement in the success probability of the original gate.
Bolted large seismic steel beam-to-column connections Part 2: numerical nonlinear analysis
S. M Takhirov; E. P Popov
2002-01-01
A large bolted steel moment-resisting connection was studied by nonlinear numerical analysis. This connection was a single-sided beam-to-column assembly that is representative of exterior beam-to-column connections. It was composed of a W36 × 150 Grade 50 beam and a W14 × 283 Grade 50 column. The T-stubs were cut from W40 × 264 sections of Grade 50 steel. The T-stub
C. Dewdney; A. Kyprianidis; J. P. Vigier; M. A. Dubois
1984-01-01
Summary The introduction of a causal quantum potential (which vanishes for coherent light beams) in the Einstein-de Broglie theory\\u000a of light implies an enhancement of some photon individual energyE =hv in the intersection region of coherent laser beams. This property not only interprets nonlinear effects already observed\\u000a in highly focused laser beams, but also yields new predictions which can be tested
Saito, Kyosuke; Tanabe, Tadao; Oyama, Yutaka
2015-04-01
In this paper, we describe our theoretical investigation and calculations for a terahertz (THz)-wave profile generated by difference frequency mixing (DFM) of focused, cylindrically symmetric, and polarized optical vector beams. Using vector diffraction theory, the second-order nonlinear polarization was estimated from the electric field components of the optical pump beams penetrating uniaxial, birefringent nonlinear optics (NLO) crystals, GaSe and CdSe. The approximate beam patterns of the THz waves were simulated using DFM formulation. The intensity patterns of the THz waves for GaSe and CdSe showed sixfold symmetry and cylindrical symmetry, respectively, based on the nonlinear susceptibility tensor of the crystals. As the phase-matching angle ?(PM) was constant with respect to the c axis of the NLO crystals, an annular vector beam with a narrow width was expected. PMID:25967188
Nonlinear generation of whistler waves by an ion beam
K. Akimoto; D. Winske
1989-01-01
An electromagnetic hybrid code is used to simulate a new mechanism for whistler wave generation by an ion beam. First, a field-aligned ion beam becomes unstable to the electromagnetic ion\\/ion right-hand resonant instability which generates large amplitude MHD-like waves. These waves then trap the ion beam and increase its effective temperature anisotropy. As a result, the growth rates of the
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
Porras, Miguel A; Losada, Juan Carlos
2015-01-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward H\\"ankel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines de NL-UBB attractor is given. Steady or unsteady propagation depends on whether the attracting NL-UBB has a small, exponentially growing, unstable mode. In case of unsteady propagation, periodic, quasi-periodic or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
Davidson, Ronald C
2015-01-01
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius $r_{w}$. The average axial electric field is expressed as $\\langle E_{z}\\rangle=-(\\partial/\\partial z)\\langle\\phi\\rangle=-e_{b}g_{0}\\partial\\lambda_{b}/\\partial z-e_{b}g_{2}r_{w}^{2}\\partial^{3}\\lambda_{b}/\\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $\\lambda_{b}(z,t)=\\int dp_{z}F_{b}(z,p_{z},t)$ is the line density of beam particles, and $F_{b}(z,p_{z},t)$ satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (solitons) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (a) the nonlinear waterbag distribution, w...
Refraction of nonlinear light beams in nematic liquid crystals
Xia, Wenjun
2013-07-01
Optical spatial solitons in nematic liquid crystals, termed nematicons, have become an excellent test bed for nonlinear optics, ranging from fundamental effects to potential uses, such as designing and demonstrating ...
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 ...
Farr, J. B.; Schoenenberg, D.; Dessy, F.; De Wilde, O.; Bietzer, O.
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.
Horizontal geometrical reaction time model for two-beam nacelle LiDARs
NASA Astrophysics Data System (ADS)
Beuth, Thorsten; Fox, Maik; Stork, Wilhelm
2015-06-01
Wind energy is one of the leading sustainable energies. To attract further private and state investment in this technology, a broad scaled drop of the cost of energy has to be enforced. There is a trend towards using Laser Doppler Velocimetry LiDAR systems for enhancing power output and minimizing downtimes, fatigue and extreme forces. Since most used LiDARs are horizontally setup on a nacelle and work with two beams, it is important to understand the geometrical configuration which is crucial to estimate reaction times for the actuators to compensate wind gusts. In the beginning of this article, the basic operating modes of wind turbines are explained and the literature on wind behavior is analyzed to derive specific wind speed and wind angle conditions in relation to the yaw angle of the hub. A short introduction to the requirements for the reconstruction of the wind vector length and wind angle leads to the problem of wind shear detection of angled but horizontal homogeneous wind fronts due to the spatial separation of the measuring points. A distance is defined in which the wind shear of such homogeneous wind fronts is not present which is used as a base to estimate further distance calculations. The reaction time of the controller and the actuators are having a negative effect on the effective overall reaction time for wind regulation as well. In the end, exemplary calculations estimate benefits and disadvantages of system parameters for wind gust regulating LiDARs for a wind turbine of typical size. An outlook shows possible future improvements concerning the vertical wind behavior.
Beam propagation method for wide-field nonlinear wave mixing microscope
NASA Astrophysics Data System (ADS)
Lv, Yong-Gang; Ji, Zi-Heng; Yu, Wen-Tao; Shi, Ke-Bin
2015-09-01
We develop a nonlinear beam propagation method for signal generation in inhomogeneous medium for wide-field nonlinear wave mixing microscope. Experimental results performed in wide-field coherent anti-Stokes Raman imaging have shown good agreement with the developed theory. Project supported by the National Natural Science Foundation of China (Grant Nos. 11174019, 61322509 and 11121091) and the National Basic Research Program of China (Grant No. 2013CB921904).
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.
Measurement of nonlinear observables in the Large Hadron Collider using kicked beams
NASA Astrophysics Data System (ADS)
Maclean, E. H.; Tomás, R.; Schmidt, F.; Persson, T. H. B.
2014-08-01
The nonlinear dynamics of a circular accelerator such as the Large Hadron Collider (LHC) may significantly impact its performance. As the LHC progresses to more challenging regimes of operation it is to be expected that the nonlinear single particle dynamics in the transverse planes will play an increasing role in limiting the reach of the accelerator. As such it is vital that the nonlinear sources are well understood. The nonlinear fields of a circular accelerator may be probed through measurement of the amplitude detuning: the variation of tune with single particle emittance. This quantity may be assessed experimentally by exciting the beam to large amplitudes with kicks, and obtaining the tunes and actions from turn-by-turn data at Beam Position Monitors. The large amplitude excitations inherent to such a measurement also facilitate measurement of the dynamic aperture from an analysis of beam losses following the kicks. In 2012 these measurements were performed on the LHC Beam 2 at injection energy (450 GeV) with the nominal magnetic configuration. Nonlinear coupling was also observed. A second set of measurements were performed following the application of corrections for b4 and b5 errors. Analysis of the experimental results, and a comparison to simulation are presented herein.
Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor
NASA Technical Reports Server (NTRS)
Danielson, D. A.; Hodges, D. H.
1987-01-01
A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion extension, shear deformation, and warping of an initially curved and twisted beam.
Nonlinear beam kinematics by decomposition of the rotation tensor
NASA Technical Reports Server (NTRS)
Danielson, D. A.; Hodges, D. H.
1987-01-01
A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion, extension, shear deformation, and warping of an initially curved and twisted beam.
Sugaya, R. [Department of Physics, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577 (Japan)
2008-01-15
Acceleration and heating of a relativistic electron beam due to nonlinear electron Landau and cyclotron damping of electromagnetic waves in a magnetized plasma are investigated theoretically and numerically on the basis of the relativistic kinetic wave and transport equations derived from the relativistic Vlasov-Maxwell equations. Two electromagnetic waves interact nonlinearly with the relativistic electron beam, satisfying the resonance condition of {omega}{sub k}-{omega}{sub k{sup '}}-(k{sub perpendicular}-k{sub perpendicula=} r{sup '})v{sub d}-(k{sub parallel}-k{sub parallel}{sup '})v{sub b}{approx_equal}m{omega}{sub ce}, where v{sub b} and v{sub d} are the parallel and perpendicular velocities of the relativistic electron beam, respectively, and {omega}{sub ce} is the relativistic electron cyclotron frequency for the electron beam. The beat waves whose frequency is near the frequency of the extraordinary wave are excited by two electromagnetic waves. The beat waves resonate with the relativistic electron beam and accelerate efficiently. Nonlinear electron Landau and cyclotron damping of the electromagnetic waves has been studied by the numerical analysis of the relativistic nonlinear wave-particle coupling coefficients, assuming the relativistic electron beam with the relativistic drifted Maxwellian momentum distribution without the cross-field drift (v{sub d}=0), and it was verified that the highly relativistic electron beam with the energy of {beta}m{sub e}c{sup 2} < or approx. 5 TeV can be accelerated efficiently by the Compton scattering and the beat-wave excited extraordinary waves, where {beta}=(1-v{sub b}{sup 2}/c{sup 2}){sup -1/2}. For comparison, the equations of motion for the beam electrons trapped in the beat wave in the frame of reference moving with v{sub b} are analyzed. The detailed acceleration mechanism was clarified and the qualitative agreement with the numerical results was obtained.
Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes
Min Sup Hur; Hae June Lee; Jae Koo Lee
1998-01-01
Department of Physics, Pohang University of Science and Technology, Pohang 790-784, South Korea ~Received 20 January 1998! Nonlinear phenomena in a driven plasma diode are studied using a ?uid code and the particle-in-cell simulation code XPDP1.When a uniform electron beam is injected to a bounded diode filled with uniform ion background, the beam is destabilized by the Pierce instability and
Nonlinear formation of holographic images of obscurations in laser beams
Kurapov, Alexander
conducted in the nonlinear regime corresponding to a typical solid-state laser operation. In this regime-intensity images to be formed downstream from obscurations in the laser chain.2,3 The peak fluences with nonlin- ear properties similar to those of our high-power solid-state lasers. The computer models
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
NASA Astrophysics Data System (ADS)
Tokluoglu, Erinc K.
Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged fields generated by beam-plasma instabilities can be responsible for defocusing and distorting beams propagating in background plasma. This can be problematic in inertial fusion applications where the beam is intended to propagate ballistically as the background plasma neutralizes the beam space charge and current. We used particle-in-cell (PIC) code LSP to numerically investigate the defocusing effects in an ion beam propagating in background plasma experiences as it is exposed to the non-linear fields generated by Two-Stream instability between beam ions and plasma electrons. Supported by theory and benchmarked by the numerical solutions of governing E&M equations, the simulations were used to find and check scaling laws for the defocusing forces in the parameter space of beam and plasma density as well as the beam ion mass. A transition region where the defocusing fields peak has been identified, which should be avoided in the design of experimental devices. We further proposed a diagnostic tool to identify the presence of the two-stream instability in a system with parameters similar to the National Drift Compression Experiment II (NDCX-II) and conducted proof-of concept simulations. In the case of electron beam propagating in background plasma instability driven collisionless scattering and plasma heating is observed. 1-D simulations conducted in EDIPIC were benchmarked in LSP to study the excitation and time-evolution of electron-electron Two-Stream instability. Coupling of electron dynamics via non-linear ponderomotive force created by instability generated fields with ion cavities and Ion-Acoustic mode excitation was observed. Furthermore 2-D simulations of an electron-beam in a background plasma was performed. Many of the effects in observed in 1-D simulations were replicated. Morever generation of oblique modes with transverse wave numbers were observed in the simulations, which resulted in significant transverse scattering of beam electrons and the time evolution of the turbulent spectrum was studied via Fourier techniques. It is plausible that the
Nonlinear Charge and Current Neutralization of an Ion Beam Pulse in a Pre-formed Plasma
Igor D. Kaganovich; Gennady Shvets; Edward Startsev; Ronald C. Davidson
2001-01-30
The propagation of a high-current finite-length ion beam in a cold pre-formed plasma is investigated. The outcome of the calculation is the quantitative prediction of the degree of charge and current neutralization of the ion beam pulse by the background plasma. The electric magnetic fields generated by the ion beam are studied analytically for the nonlinear case where the plasma density is comparable in size with the beam density. Particle-in-cell simulations and fluid calculations of current and charge neutralization have been performed for parameters relevant to heavy ion fusion assuming long, dense beams with el >> V(subscript b)/omega(subscript b), where V(subscript b) is the beam velocity and omega subscript b is the electron plasma frequency evaluated with the ion beam density. An important conclusion is that for long, nonrelativistic ion beams, charge neutralization is, for all practical purposes, complete even for very tenuous background plasmas. As a result, the self-magnetic force dominates the electric force and the beam ions are always pinched during beam propagation in a background plasma.
Concatenated beam splitters, optical feed-forward and the nonlinear sign gate
Kurt Jacobs; Jonathan P. Dowling
2006-06-26
We consider a nonlinear sign gate implemented using a sequence of two beam splitters, and consider the use of further sequences of beam splitters to implement feed-forward so as to correct an error resulting from the first beam splitter. We obtain similar results to Scheel et al. [Scheel et al., Phys. Rev. A 73, 034301 (2006)], in that we also find that our feed-forward procedure is only able to produce a very minor improvement in the success probability of the original gate.
On the nonlinear deformation geometry of Euler-Bernoulli beams. [rotary wings
NASA Technical Reports Server (NTRS)
Hodges, D. H.; Ormiston, R. A.; Peters, D. A.
1980-01-01
Nonlinear expressions are developed to relate the orientation of the deformed beam cross section, torsion, local components of bending curvature, angular velocity, and virtual rotation to deformation variables. The deformed beam kinematic quantities are proven to be equivalent to those derived from various rotation sequences by identifying appropriate changes of variable based on fundamental uniqueness properties of the deformed beam geometry. The torsion variable used is shown to be mathematically analogous to an axial deflection variable commonly used in the literature. Rigorous applicability of Hamilton's principle to systems described by a class of quasi-coordinates that includes these variables is formally established.
Propagation of spatial solitons generated by Gaussian beams in a non-linear Kerr medium
NASA Astrophysics Data System (ADS)
Burak, Dariusz
1995-09-01
##e author analyzes the propagation of light space solitons (first and second order) generated by Gauss-Hermit beams of the fundamental and second orders in a non-linear Kerr medium. The author numerically determines the relationship of the parameters of the excited solitons to the parameters of the initial Gauss-Hermit beams. The author analytically determines the threshold amplitudes required for the generation of a soliton of any order using excitation by a fundamental Gauss beam. The author discovered self-focusing of the initial beams in the near field, followed by the generation of soliton beams in the far field. The author determined the parameters of a fundamental Gauss beam necessary for its self confinement in a Kerr medium (propagation without a change in shape) and for maximum conversion of its power to a soliton beam. The excitation of a Kerr medium by a second order Gauss-Hermit beam may only result in the generation of an even number of solitons. In this case, below the threshold amplitude, the initial beam is subject to non-linear diffraction, while above the threshold amplitude it generates two solitons which are propagated symmetrically in directions from the axis of propagation of the coordinate system. The relative angle of propagation of the solitons decreases with an increase in the amplitude of the initial beam, up to the generation of a pulsating soliton. The author has developed a variational approximation of the non-linear propagation of zero- and second-order Gauss Hermit beams. The author determines the form of the soliton in a variational approximation of a fundamental-order Gauss beam. The author analytically determines the approximate parameters of a first-order soliton generated by a Gauss beam. The author discusses the agreement between the variational approximation of propagation and an exact (numerical) solution of a propagation equation. The author demonstrates that the propagation of second order solitons may be quite adequately approximated by the propagation of a second-order Gauss-Hermit beam with variationally defined parameters.
Aberration correction by nonlinear beam-mixing: generation of a pseudo point sound source
J. Seo; J. J. Choi; T. L. Hall; J. B. Fowlkes; M. O'Donnell; C. A. Cain
2004-01-01
Nonlinear beam-mixing with microbubbles was explored to create a pseudo point source for aberration correction of therapeutic ultrasound. A damping coefficient for a bubble driven by a dual frequency sound field was derived by revisiting Prosperetti's linearized damping model. As a result, the overall damping term for dual frequency was obtained by linear summation of two damping terms for each
Aberration correction by nonlinear beam mixing: generation of a pseudo point sound source
Jongbum Seo; J. J. Choi; J. B. Fowlkes; M. O'Donnell; C. A. Cain
2005-01-01
Nonlinear beam mixing with microbubbles was explored to create a pseudo point source for aberration correction of therapeutic ultrasound. A damping coefficient for a bubble driven by a dual frequency sound field was derived by revisiting Prosperetti's linearized damping model. As a result, the overall damping term for dual frequency was obtained by linear summation of two damping terms for
Michael Spata
2012-08-01
An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.
Wang Xiaosheng; She Weilong; Lee Wingkee
2006-10-15
We present detailed theoretical studies of optical spatial solitons (SSs) supported by photoisomerization nonlinearity in a polymer sample. One-dimensional dark and bright SSs and their existence curves are presented. Several combinations of polarizations of the signal and background beams can be used to form the SSs.
Effect of material nonlinearity in unidirectional composites on the behavior of beam structures
G. A. Abu-Farsakh; S. A. Barakat; N. R. Al-Zoubi
2000-01-01
The present study is made to investigate the effect of material nonlinearity in unidirectional composites on the behavior of beams, where the fiber orientation is considered. The effect of these two factors on deflection, bending moment and external reactions is investigated. In order to achieve these objectives, a computer subroutine based on secant mechanical property is incorporated in a main
Unconventional finite element method for nonlinear analysis of beams and plates
Kim, Wooram
2009-05-15
of it on the nonlinear analysis. Models were developed based on the weighted residual method. The effect of inclusion of additional variables is compared with other mixed models to show the advantage of the one type of model over other models. For beam problems the Euler-Bernoulli...
Influence of nonadiabaticity and nonlinearity on the operation of cold-atom beam splitters
Stickney, James A.; Zozulya, Alex A.
2003-07-01
The operation of cold-atom beam splitters is analyzed in the context of Bose-Einstein condensate interferometry. We introduce two representative geometries of the splitting region and study influence of nonlinearity and nonadiabaticity on the splitting and the recombination of the condensate for both geometries.
Nonlinear Optical Effects on ISI-Smoothed Beams in KrF Fusion Drivers
NASA Astrophysics Data System (ADS)
Lehmberg, R. H.; Pawley, C. J.; Deniz, A. V.
2000-10-01
Induced Spatial Incoherence (ISI) allows rapid and effective smoothing of speckle structure in the focal beam, but its application to fusion drivers may be complicated by nonlinear refraction in the optical components that can significantly distort the beam's envelope profile. Nonlinear refraction can introduce curvature over the entire profile and scatter ~ 15% of the light into a low intensity halo. These effects arise because the transient hot spots in the ISI speckle begin to self-focus as they propagate through the laser optics, and thus pass through focus before they reach the target. We report the first experimental confirmation of this distortion using a 4 ns 248 nm ISI beam at intensities ~ 0.5 GW/cm^2 propagating through KrF-grade fused silica, giving an average nonlinear phase perturbation B ~ 0.5 radian. We also present measurements of the nonlinear refractive index and two-photon absorption coefficient in fused silica at 4 ns, and discuss the impact of nonlinear optical effects on the design of future KrF fusion drivers.
NASA Astrophysics Data System (ADS)
Coakley, K. J.; Dewey, M. S.; Yue, A. T.; Laptev, A. B.
2009-12-01
Many experiments at neutron scattering facilities require nearly monochromatic neutron beams. In such experiments, one must accurately measure the mean wavelength of the beam. We seek to reduce the systematic uncertainty of this measurement to approximately 0.1%. This work is motivated mainly by an effort to improve the measurement of the neutron lifetime determined from data collected in a 2003 in-beam experiment performed at NIST. More specifically, we seek to reduce systematic uncertainty by calibrating the neutron detector used in this lifetime experiment. This calibration requires simultaneous measurement of the responses of both the neutron detector used in the lifetime experiment and an absolute black neutron detector to a highly collimated nearly monochromatic beam of cold neutrons, as well as a separate measurement of the mean wavelength of the neutron beam. The calibration uncertainty will depend on the uncertainty of the measured efficiency of the black neutron detector and the uncertainty of the measured mean wavelength. The mean wavelength of the beam is measured by Bragg diffracting the beam from a nearly perfect silicon analyzer crystal. Given the rocking curve data and knowledge of the directions of the rocking axis and the normal to the scattering planes in the silicon crystal, one determines the mean wavelength of the beam. In practice, the direction of the rocking axis and the normal to the silicon scattering planes are not known exactly. Based on Monte Carlo simulation studies, we quantify systematic uncertainties in the mean wavelength measurement due to these geometric errors. Both theoretical and empirical results are presented and compared.
THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES
Chang, Philip; Lamberts, Astrid; Broderick, Avery E.; Shalaby, Mohamad; Pfrommer, Christoph; Puchwein, Ewald
2014-12-20
Very high energy gamma-rays from extragalactic sources produce pairs from the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the ''oblique'' instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here we show with numerical calculations that the effective damping rate is 8 × 10{sup –4} the growth rate of the linear instability, which is sufficient for the ''oblique'' instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wave numbers and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long-wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long-wavelength modes, this scenario represents the ''worst case'' scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the ''oblique'' instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.
Mimicking the cochlear amplifier in a cantilever beam using nonlinear velocity feedback control
NASA Astrophysics Data System (ADS)
Joyce, Bryan S.; Tarazaga, Pablo A.
2014-07-01
The mammalian cochlea exhibits a nonlinear amplification which allows mammals to detect a large range of sound pressure levels while maintaining high frequency sensitivity. This work seeks to mimic the cochlea’s nonlinear amplification in a mechanical system. A nonlinear, velocity-based feedback control law is applied to a cantilever beam with piezoelectric actuators. The control law reduces the linear viscous damping of the system while introducing a cubic damping term. The result is a system which is positioned close to a Hopf bifurcation. Modelling and experimental results show that the beam with this control law undergoes a one-third amplitude scaling near the resonance frequency and an amplitude-dependent bandwidth. Both behaviors are characteristic of data obtained from the mammalian cochlea. This work could provide insight on the biological cochlea while producing bio-inspired sensors with a large dynamic range and sharp frequency sensitivity.
Existence of optical solitons on wavelength division multiplexed beams in a nonlinear fiber.
Yeh, C; Bergman, L A
1999-08-01
A simple analytic expression for the initial fundamental optical solitons on wavelength division multiplexed (WDM) beams in a nonlinear fiber has been found. For an ideal fiber with no loss and uniform group-velocity dispersion (GVD) in the anomalous GVD region, the initial form is [1+2(M-1)](-1/2) sech(tau), where M is the number of WDM beams and tau is the normalized time. Computer simulation shows that these initial pulses on WDM beams in this fiber will propagate undistorted without change in their shapes for arbitrarily long distances. The discovery of the existence of solitons on WDM beams presents the ultimate goal for optical fiber communication on multiple wavelength beams in a single fiber. PMID:11970026
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.
Modeling transient response of PN junction diode under radiation beams considering nonlinear effects
NASA Astrophysics Data System (ADS)
Shi, Jie
Diodes are used as dosimeter to measure the delivered dose from the radiation beams of linear accelerators used in the radiation therapy field. Diode sensitivity S, defined as charge collected per unit absorbed dose, has been found to increase with an increase in instantaneous dose rate r of the radiation beam. In order to calculate the dependence of S on r, one has to solve for the excess minority-carrier concentration Deltap (= Deltan) from the carrier transportation equation. This equation is a nonlinear partial different equation (PDE), with two variables of space coordinate x and time t. The nonlinear term in the PDE is the net recombination-generation (R-G) rate U. The historical solutions were either the transient solution from the linear PDE or the steady state solution from the nonlinear differential equation. This dissertation solves the nonlinear PDE with simplified nonlinear term U. The analytical solution is the first to include both transient and nonlinearity at the same time. The analytical solution for Deltap (x, t) from the PDE is used to derive the current density J p of the minority carriers and the diode sensitivity S. A computer software program has also been developed to numerically solve the non-simplified PDE. The agreement of the calculations for Deltap (x) and Jp (t) is excellent between the numerical and the analytical solutions, proving the analytical solution is legitimate. A theoretical model is established with the analytical solution to explain the r dependence of diode sensitivity S under pulsed radiation beam. The sensitivity of several different types of diodes was measured with the 18 MV photon beam of a medical linear accelerator. The diode sensitivity from the experiment is compared with the calculations from both the analytical and the numerical solutions. The theoretical calculations yield the instantaneous dose rate dependence of the diode sensitivity. The agreement is generally good between the theory and the experiments. The results are discussed and possible error sources are analyzed.
Propagation dynamics of modified hollow Gaussian beams in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Dai, Zhiping; Yang, Zhenjun; Zhang, Shumin; Pang, Zhaoguang; You, Kaiming
2015-02-01
We investigate here a new class of optical beams: modified hollow Gaussian beams (MHGBs) in strongly nonlocal nonlinear media (SNNM). A set of analytical expressions for the propagation properties is deduced and some numerical simulations are also carried out to illustrate the propagation properties. It is found that the evolution of the MHGBs in SNNM is periodical, which is the result of the competition between nonlinearity and diffraction. The second-order moment beam width of the MHGBs can keep invariant during propagation like a soliton when the input power equals the critical power, otherwise it varies periodically like a breather. However, the patterns of transverse intensity are always changing with the propagation distance increasing, which is different from solitons or breathers. It is also found that the evolution curve of on-axis intensity may manifest itself in a concave, a platform, or a Gaussian-like shape depending on the input power.
Hoffstaetter, Georg
Orbit and optics improvement by evaluating the nonlinear beam position monitor response of beam position monitor (BPM) pickup response. We first describe the calculation of the BPM pickup with approximately 100 beam position monitors (BPMs) dis- tributed around the storage ring. Each BPM consists of four
Nonlinear modes of an intense laser beam interacting with a periodic lattice of nanoparticle
NASA Astrophysics Data System (ADS)
Sepehri Javan, N.; Homami, S. H. H.
2015-08-01
Self-guided nonlinear propagation of an intense laser beam through a periodic lattice of nanoparticle is studied. Using a perturbative method, a cubic nonlinear wave equation describing the laser-nanoparticle interaction in the weakly relativistic regime is derived. Transverse Eigen modes of the laser, nonlinear dispersion relation and its related group velocity are obtained. It is shown that the best fitted function to the transverse profile is Gaussian. Effect of the laser amplitude and also the ratio of nanoparticles radius to their separation on the nonlinear dispersion and amplitude profiles are investigated. It is found that the increase in the just mentioned parameters leads to the localization of transverse profile around the propagation axis.
Awtar, Shorya
doctoral degree I feel our brain-storming sessions were the most educational. I am truly grateful to him encouragement. My mother is probably the reason I started my Ph.D. degree. She is also the one who has inspired.2.2.4 Nonlinearity due to trapeze effect 13 1.2.2.5 Nonlinearity due to cross-sectional warping 13 1.2.3 Energy
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.
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
NASA Astrophysics Data System (ADS)
Minkovski, N.; Petrov, G. I.; Saltiel, S. M.; Albert, O.; Etchepare, J.
2004-09-01
Nonlinear polarization rotation and generation of a polarization component orthogonal to the input beam were observed along fourfold axes of YVO4 and BaF2 crystals. We demonstrate experimentally that in both crystals the angle of rotation is proportional, at low intensities, to the square of the product of the input intensity and the crystal length and is the result of simultaneous action of two third-order processes. This type of nonlinear polarization rotation is driven by the real part of the cubic susceptibility. The recorded energy exchange between the two orthogonal components can exceed 10%. It is to our knowledge the highest energy-conversion efficiency achieved in a single beam nonresonant ?(3) interaction. A simple theoretical model is elaborated to describe the dependence of nonlinear polarization rotation and orthogonal polarization generation on the intensity of the input beam at both low- and high-intensity levels. It reveals the potential contributions from the real and the imaginary parts of the susceptibility tensor. Moreover, this kind of measurement is designed to permit the determination of the magnitude and the sign of the anisotropy of the real part of third-order nonlinearity in crystals with cubic or tetragonal symmetry on the basis of polarization-rotation measurements. The ?xxxx(3) component of the third-order susceptibility tensor and its anisotropy sign and amplitude value for BaF2 and YVO4 crystals are estimated and discussed.
Optimal Vibration Estimation of a Non-Linear Flexible Beam Mounted on a Rotating Compliant Hub
NASA Astrophysics Data System (ADS)
El-Sinawi, A.; Hamdan, M. N.
2003-01-01
To eliminate the need for sensor placement on rotating flexible beams such as turbine blades, helicopter rotors and like applications, a new approach has been developed based on the linear quadratic estimator (LQE) technique for estimating the vibration of any point on the span of a rotating flexible beam mounted on a compliant hub ( plant) in the presence of process and measurements noise. A non-linear model of the plant is utilized in this study to mimic the actual plant behavior. The corresponding plant dynamics of the LQE are in the form of a reduced order linear model constructed from the eigenvalues and eigenfuctions of a finite element dynamic model of the plant formulated in the state space. A virtual hub deflection (that mimics the actual measurement of the vertical hub deflection needed by the estimation process) is generated by the non-linear model of the plant. The LQE reconstructs the states of the plant, including transverse deflection of the beam at any point, from the measurements of the vertical deflection of the hub, assuming that it is the most accessible state for measurement. Estimated beam tip deflection obtained by the proposed technique is then compared to the tip deflection generated by the non-linear model and the results show good agreement.
Patil, Mayuresh
-Aspect-Ratio Wings Mayuresh J. Patil, Dewey H. Hodges Georgia Institute of Technology, Atlanta, Georgia and Carlos E the results of nonlinear aeroelastic analysis of a representative large-aspect-ratio wing. The effects sensing and also for communications relay. Such aircraft have slender wings (aspect ratio of the order
Lee, S. Y.
2014-04-07
We had carried out a design of an ultimate storage ring with beam emittance less than 10 picometer for the feasibility of coherent light source at X-ray wavelength. The accelerator has an inherent small dynamic aperture. We study method to improve the dynamic aperture and collective instability for an ultimate storage ring. Beam measurement and accelerator modeling are an integral part of accelerator physics. We develop the independent component analysis (ICA) and the orbit response matrix method for improving accelerator reliability and performance. In collaboration with scientists in National Laboratories, we also carry out experimental and theoretical studies on beam dynamics. Our proposed research topics are relevant to nuclear and particle physics using high brightness particle and photon beams.
Nonlinear physics and energetic particle transport features of the beam-plasma instability
Carlevaro, Nakia; Montani, Giovanni; Zonca, Fulvio
2015-01-01
In this paper, we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume $n$ cold supra-thermal beams and investigate the self-consistent evolution in the presence of the complete spectrum of nearly degenerate Langmuir modes. A qualitative transport estimation is obtained by computing the Lagrangian Coherent Structures of the system on given temporal scales. This leads to the splitting of the phase space into regions where the local transport processes are relatively faster. The general theoretical framework is applied to the case of the nonlinear dynamics of two cold beams, for which numerical simulation results are illustrated and analyzed.
Non-linear centre of gravity on LHCb Vertex Locator test beam data
NASA Astrophysics Data System (ADS)
Richards, S.
2015-07-01
Cluster position reconstruction for the LHCb Vertex Locator test beam software currently uses a linear centre of gravity algorithm. To investigate possible improvements of this approach, a study was performed that made use of a non-linear centre-of-gravity algorithm. All of the sensors in this study were Timepix chips with a 300 ? m layer of p-on-n silicon. The position resolutions obtained with the linear centre-of-gravity ranged between 5.5 ? m and 6.1 ? m. Applying the tuned non-linear algorithm reduces these by at least 0.6 ? m.
NASA Astrophysics Data System (ADS)
Perez, Ricardo; Wang, X. Q.; Mignolet, Marc P.
2014-12-01
The focus of this investigation is on a first assessment of the predictive capabilities of nonlinear geometric reduced order models for the prediction of the large displacement and stress fields of panels with localized geometric defects, the case of a notch serving to exemplify the analysis. It is first demonstrated that the reduced order model of the notched panel does indeed provide a close match of the displacement and stress fields obtained from full finite element analyses for moderately large static and dynamic responses (peak displacement of 2 and 4 thicknesses). As might be expected, the reduced order model of the virgin panel would also yield a close approximation of the displacement field but not of the stress one. These observations then lead to two "enrichment" techniques seeking to superpose the notch effects on the virgin panel stress field so that a reduced order model of the latter can be used. A very good prediction of the full finite element stresses, for both static and dynamic analyses, is achieved with both enrichments.
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.
Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma
NASA Astrophysics Data System (ADS)
Wang, Yunliang; Shukla, P. K.; Eliasson, B.
2013-01-01
We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schrödinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.
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)
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.
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.
Geometrically nonlinear design sensitivity analysis on parallel-vector high-performance computers
NASA Technical Reports Server (NTRS)
Baddourah, Majdi A.; Nguyen, Duc T.
1993-01-01
Parallel-vector solution strategies for generation and assembly of element matrices, solution of the resulted system of linear equations, calculations of the unbalanced loads, displacements, stresses, and design sensitivity analysis (DSA) are all incorporated into the Newton Raphson (NR) procedure for nonlinear finite element analysis and DSA. Numerical results are included to show the performance of the proposed method for structural analysis and DSA in a parallel-vector computer environment.
C. Lenyk; T. Fleming; K. Cartwright
2004-01-01
Summary form only given. We present the theory of the magnetron instability, which is developed using a fluid plasma description. A 1-D non-linear steady-state model is developed for relativistic and non-relativistic planar and cylindrical smooth-bore magnetron geometries. To this steady-state background, 1-D and 2-D linear perturbation analyses are applied to determine the modes and growth rates for the magnetron instability
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Feng, Bin-Lu; Rui, Wen-Juan; Zhang, Xiang-Zhi
2015-07-01
With the help of a simple Lie algebra, an isospectral Lax pair, whose feature presents decomposition of element (1, 2) into a linear combination in the temporal Lax matrix, is introduced for which a new integrable hierarchy of evolution equations is obtained, whose Hamiltonian structure is also derived from the trace identity in which contains a constant ? to be determined. In the paper, we obtain a general formula for computing the constant ?. The reduced equations of the obtained hierarchy are the generalized nonlinear heat equation containing three-potential functions, the mKdV equation and a generalized linear KdV equation. The algebro-geometric solutions (also called finite band solutions) of the generalized nonlinear heat equation are obtained by the use of theory on algebraic curves. Finally, two kinds of gauge transformations of the spatial isospectral problem are produced. Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014) and the National Natural Science Foundation of China under Grant No. 11371361, the Fundamental Research Funds for the Central Universities (2013XK03) as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016
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.
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.
NASA Astrophysics Data System (ADS)
Grigoriev, K. S.; Makarov, V. A.; Perezhogin, I. A.
2015-08-01
Expressions for the electric field at a sum frequency generated by a collinear elliptically polarized Gaussian beam and circularly polarized Laguerre-Gaussian beam in an isotropic chiral nonlinear medium are obtained in quadratures. The amount and locations of C points in the cross section of a signal beam at a sum frequency are shown to be dependent on frequency and diffraction lengths ratios of fundamental beams and on the ellipticity degree of the Gaussian beam's polarization ellipse. Possible values of total topological charges of the emergent C points are determined by the topological charge of the Laguerre-Gaussian beam and remain constant while the radiation propagates in nonlinear media. In case of nonzero total topological charge C lines form helical structures, the parameters of which depend on the wave-vector mismatch. Otherwise, C lines form a loop. As the wave-vector mismatch grows the loop undergoes deformation and breaks up, creating new C lines.
Nonlinear vibrations of non-uniform beams by the MTS asymptotic expansion method
NASA Astrophysics Data System (ADS)
Clementi, F.; Demeio, L.; Mazzilli, C. E. N.; Lenci, S.
2015-09-01
The frequency response curves of a non-uniform beam undergoing nonlinear oscillations are determined analytically by the multiple time scale method, which provides approximate, but accurate results. The axial inertia in neglected, and so the equations of motion are statically condensed on the transversal displacement only. The nonlinearity due to the stretching of the axis of the beam is considered. The effects of variable cross-section, of variable material properties and of the distributed axial loading are taken into account in the formulation. They have been illustrated by means of two examples and are also compared with existing results. The main result of this work is that the effects of any type of non-uniformity can be detected by simple formulas.
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.
Mechanical modeling of the nonlinear response of beam-to-column joints
Minas E. Lemonis; Charis J. Gantes
2009-01-01
A methodology for the estimation of the complete moment–rotation curve of structural beam-to-column joints is presented in this paper. The methodology is based on the component method and is materialized through appropriate mechanical models that are analyzed nonlinearly. The cases examined in this work include bolted connections with end-plates and with angles. Significant consideration is devoted to the reliable simulation
Quasi-periodic solutions of a quasi-periodically forced nonlinear beam equation
NASA Astrophysics Data System (ADS)
Wang, Yi
2012-06-01
In this paper, one quasi-periodically forced nonlinear beam equation utt+uxxxx+?u+?g(?t,x)u3=0,?>0,x?[0,?] with hinged boundary conditions is considered. Here ? is a small positive parameter, g( ?t, x) is real analytic in all variables and quasi-periodic in t with a frequency vector ? = ( ?1, ?2, … , ?m). It is proved that the above equation admits small-amplitude quasi-periodic solutions.
Nonlinear dust-plasma interactions of a cross-beam system in interplanetary space
NASA Astrophysics Data System (ADS)
Jammalamadaka, S.; Araneda, J.; McKenzie, J. F.; Grünwaldt, H.
1998-10-01
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.
Nonlinear self-focus of pulsed-wave beams in Kerr media
Judkins, J.B.
1992-12-31
A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.
Frequency analysis of finite beams on nonlinear Kelvin-Voight foundation under moving loads
NASA Astrophysics Data System (ADS)
Ansari, M.; Esmailzadeh, E.; Younesian, D.
2011-03-01
The vibration of an Euler-Bernoulli beam, resting on a nonlinear Kelvin-Voight viscoelastic foundation, traversed by a moving load is studied in the frequency domain. The objective is to obtain the frequency responses of the beam and the effects of different parameters on the system response. The parameters include the magnitude and speed of the moving load and the foundation nonlinearity and its damping coefficient. The solution is obtained by using the Galerkin method in conjunction with the multiple scales method (MSM). The governing nonlinear partial differential equations of motion are discretized into sets of nonlinear ordinary differential equations. Subsequently, the solution is calculated for different harmonics by using the MSM as one of the powerful perturbation techniques. The steady-state responses of the main harmonic as well as its two super-harmonics are then obtained. As a case study, a conventional railway track is dynamically simulated and the jump phenomenon in the response is observed for three harmonics. Moreover, a thorough stability analysis of the system is carried out.
Radiation force on a nonlinear microsphere by a tightly focused Gaussian beam.
Pobre, Romeric; Saloma, Caesar
2002-12-20
We determine the characteristics of the radiation force that is exerted on a nonresonant nonlinear (Kerr-effect) rigid microsphere by a strongly focused Gaussian beam when diffraction and interference effects are significant (sphere radius a < or = illumination wavelength lambda). The average force is calculated from the surface integral of the energy-momentum tensor consisting of incident, scattered, and internal electromagnetic field vectors, which are expressed as multipole spherical-wave expansions. The refractive index of a Kerr microsphere is proportional to the internal field intensity, which is computed iteratively by the Rytov approximation (residual error of solution, 10(-30). The expansion coefficients for the field vectors are calculated from the approximated index value. Compared with that obtained in a dielectric (linear) microsphere in the same illumination conditions, we find that the force magnitude on the Kerr microsphere is larger and increases more rapidly with both a and the numerical aperture of the focusing objective. It also increases nonlinearly with the beam power unlike that of a linear sphere. The Kerr nonlinearity also leads to possible reversals of the force direction. The proposed technique is applicable to other types of weak optical nonlinearity. PMID:12510940
Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
Bliokh, Konstantin Yu. [Institute of Radio Astronomy, Kharkov, 61002 (Ukraine); A.Ya. Usikov Institute of Radiophysics and Electronics, Kharkov, 61085 (Ukraine); Department of Physics, Bar-Ilan University, Ramat Gan, 52900 (Israel)
2006-07-28
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.
Ultrahigh Brilliance Multi-MeV ?-Ray Beams from Nonlinear Relativistic Thomson Scattering.
Sarri, G; Corvan, D J; Schumaker, W; Cole, J M; Di Piazza, A; Ahmed, H; Harvey, C; Keitel, C H; Krushelnick, K; Mangles, S P D; Najmudin, Z; Symes, D; Thomas, A G R; Yeung, M; Zhao, Z; Zepf, M
2014-11-28
We report on the generation of a narrow divergence (?_{?}<2.5??mrad), multi-MeV (E_{max}?18??MeV) and ultrahigh peak brilliance (>1.8×10^{20}??photons?s^{-1}?mm^{-2}??mrad^{-2} 0.1% BW) ?-ray beam from the scattering of an ultrarelativistic laser-wakefield accelerated electron beam in the field of a relativistically intense laser (dimensionless amplitude a_{0}?2). The spectrum of the generated ?-ray beam is measured, with MeV resolution, seamlessly from 6 to 18 MeV, giving clear evidence of the onset of nonlinear relativistic Thomson scattering. To the best of our knowledge, this photon source has the highest peak brilliance in the multi-MeV regime ever reported in the literature. PMID:25494074
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.
Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
A. Mahdifar; R. Roknizadeh; M. H. Naderi
2006-04-25
In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using non-linear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs modell. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface is appeared as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
Genuinely resultant shell finite elements accounting for geometric and material non-linearity
NASA Astrophysics Data System (ADS)
Chroscielewski, J.; Makowski, J.; Stumpf, H.
1992-07-01
A general theoretical and numerical framework for the fully nonlinear analysis of shells is presented. It is shown how to derive 2D governing equations for shells and the corresponding finite element discretizations from basic laws of classical continuum mechanics. The finite elements for shells avoid time-consuming through-the-thickness integration to evaluate element matrices typical for the degenerated shell element concept. Drilling degree-of-freedom and the associated drilling couples enter the formulation in a very natural way at the theoretical level. Particular attention is given to the treatment of the finite rotations through an arbitrary parametrization of the rotation group and the interpolation procedure of SO(3)-valued functions. Small strain and finite strain problems are based on the same foundation and are recommended to be studied separately.
Shi, Jicong; Jin, Lihui; Kheawpum, Orithai
2004-03-01
In cases of multibunch operation in storage-ring colliders, serious long-range beam-beam effects could be due to many parasitic collisions that are localized inside interaction regions or/and distributed around the ring. To reduce the long-range beam-beam effects, the compensation of long-range beam-beam interaction with magnetic multipole correctors based on minimizations of nonlinearities in one-turn or sectional maps of a collider has been proposed. With Large Hadron Collider as a test model, the effectiveness of the multipole compensation of long-range beam-beam interactions was studied in terms of improvement of dynamic aperture and reduction of emittance growth. The emittance growth was studied with a self-consistent beam-beam simulation. The study showed that both the local and global compensation of long-range beam-beam interactions with magnetic multipole correctors are very effective in increasing the dynamic aperture and improving the linearity of the phase-space region relevant to the beams. PMID:15089422
NASA Astrophysics Data System (ADS)
Shi, Jicong; Jin, Lihui; Kheawpum, Orithai
2004-03-01
In cases of multibunch operation in storage-ring colliders, serious long-range beam-beam effects could be due to many parasitic collisions that are localized inside interaction regions or/and distributed around the ring. To reduce the long-range beam-beam effects, the compensation of long-range beam-beam interaction with magnetic multipole correctors based on minimizations of nonlinearities in one-turn or sectional maps of a collider has been proposed. With Large Hadron Collider as a test model, the effectiveness of the multipole compensation of long-range beam-beam interactions was studied in terms of improvement of dynamic aperture and reduction of emittance growth. The emittance growth was studied with a self-consistent beam-beam simulation. The study showed that both the local and global compensation of long-range beam-beam interactions with magnetic multipole correctors are very effective in increasing the dynamic aperture and improving the linearity of the phase-space region relevant to the beams.
Zambrini, Roberta
Twin beams, nonlinearity, and walk-off in optical parametric oscillators Roberta Zambrini and Maxi) crystal, decays into two highly correlated twin signal photons at lower frequencies 1 , 2. Nonclassical of single photon pairs. Cavity effects introduce a threshold, yielding two in- tense laserlike twin beams
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
Kioussis, Nicholas
thickness 3.25 meters that has a 0.38 m layer of ice on the surface. Light travels from the top of the pond. Calculate the time for light to travel through the ice (and then through the water) by dividing the distance1 Chapter 26: Geometrical Optics 8. The image shows a light beam that is oriented 15.0° from
Nariyuki, Y.; Hada, T.; Tsubouchi, K.
2014-10-01
The damping process of field-aligned, low-frequency right-handed polarized nonlinear Alfvén waves (NAWs) in solar wind plasmas with and without proton beams is studied by using a two-dimensional ion hybrid code. The numerical results show that the obliquely propagating kinetic Alfvén waves (KAWs) excited by beam protons affect the damping of the low-frequency NAW in low beta plasmas, while the nonlinear wave-wave interaction between parallel propagating waves and nonlinear Landau damping due to the envelope modulation are the dominant damping process in high beta plasmas. The nonlinear interaction between the NAWs and KAWs does not cause effective energy transfer to the perpendicular direction. Numerical results suggest that while the collisionless damping due to the compressibility of the envelope-modulated NAW plays an important role in the damping of the field-aligned NAW, the effect of the beam instabilities may not be negligible in low beta solar wind plasmas.
Geometrically nonlinear analysis of hyperelastic solids by high-order tetrahedral finite elements
NASA Astrophysics Data System (ADS)
Pascon, João P.; Coda, Humberto B.
2010-06-01
The purpose of this study is to develop a computer code for accurate prediction of the mechanical behavior of hyperelastic solids under large deformation and finite strains. It is used, in the present work, the Lagrangian positional version of the Finite Element Method, in which the degrees of freedom are current positions instead of displacements. The main mechanical variables are the Green-Lagrange strain and the second Piola-Kirchhoff stress tensors. Isoparametric tetrahedral solid finite element of any approximation degree is employed with full integration in order to obtain accuracy. In order to be general, it is developed a numerical strategy to determine the shape functions coefficients of any order, following tetrahedral basis. The solid equilibrium is achieved at the current position by means of the Minimal Potential Energy Principle regarding positions and is solved by the Newton-Raphson iterative scheme. It is important to mention that the adopted constitutive laws are nonlinear, isotropic and homogeneous hyperelastic, normally used in mechanical analysis of elastomers, with the near compressibility assumption. It is applied the Flory decomposition, i.e., the multiplicative split of the deformation gradient into a volumetric and an isochoric part. A parallel processing strategy is used to increase the simulation speed and memory capacity, justifying the use of high order elements for solid analysis. Results confirm that the developed computer code is capable of predicting the static behavior of complex problems, such as Cook's membrane and partially loaded block. The shape functions generator code exhibits simplicity and, thus, it may be easily implemented in other finite elements. The increase in the order of approximation and the mesh refinement improve accuracy and, therefore, the proposed methodology together with parallel computing indicate a safe way for further developments in plasticity and damage mechanics for large strain and deformations.
NASA Astrophysics Data System (ADS)
Lajimi, S. A. M.; Friswell, M. I.
2015-04-01
For a nonlinear beam-mass system used to harvest vibratory energy, the two-mode approximation of the response is computed and compared to the single-mode approximation of the response. To this end, the discretized equations of generalized coordinates are developed and studied using a computational method. By obtaining phase-portraits and time-histories of the displacement and voltage, it is shown that the strong nonlinearity of the system affects the system dynamics considerably. By comparing the results of single- and two-mode approximations, it is shown that the number of mode shapes affects the dynamics of the response. Varying the tip-mass results in different structural configurations namely linear, pre-buckled nonlinear, and post-buckled nonlinear configurations. The nonlinear dynamics of the system response are investigated for vibrations about static equilibrium points arising from the buckling of the beam. Furthermore, it is demonstrated that the harvested power is affected by the system configuration.
Reichert, Matthew; Zhao, Peng; Reed, Jennifer M; Ensley, Trenton R; Hagan, David J; Van Stryland, Eric W
2015-08-24
A polarization-resolved beam deflection technique is used to separate the bound-electronic and molecular rotational components of nonlinear refractive transients of molecular gases. Coherent rotational revivals from N_{2}, O_{2}, and two isotopologues of carbon disulfide (CS_{2}), are identified in gaseous mixtures. Dephasing rates, rotational and centrifugal distortion constants of each species are measured. Polarization at the magic angle allows unambiguous measurement of the bound-electronic nonlinear refractive index of air and second hyperpolarizability of CS_{2}. Agreement between gas and liquid phase second hyperpolarizability measurements is found using the Lorentz-Lorenz local field correction. PMID:26368195
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.
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.
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
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
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.
Calibration of a Non-Linear Beam Position Monitor Electronics by Switching Electrode Signals
Gasior, M
2013-01-01
Button electrode signals from beam position monitors embedded into new LHC collimators will be individually processed with front-end electronics based on compensated diode detectors and digitized with 24-bit audio-range ADCs. This scheme allows sub-micrometre beam orbit resolution to be achieved with simple hardware and no external timing. As the diode detectors only operate in a linear regime with large amplitude signals, offset errors of the electronics cannot be calibrated in the classical way with no input. This paper describes the algorithms developed to calibrate the offset and gain asymmetry of these nonlinear electronic channels. Presented algorithm application examples are based on measurements performed with prototype diode orbit systems installed on the CERN SPS and LHC machines.
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
NASA Astrophysics Data System (ADS)
Yin, Lin
2011-10-01
In inertial confinement fusion experiments, Stimulated Raman Scattering (SRS) occurs when electron density fluctuations amplify resonantly by the incident laser beams. These beams comprise several thousands of individual laser speckles. We have found in single-speckle studies that electron trapping lowers the threshold intensity for SRS onset to a value below that from linear theory and enhances scattering. The trapping-induced plasma-wave frequency shift leads to wave-front bowing and self-focusing, processes that saturate SRS and limit scattering within a speckle. With Petaflop-class supercomputers, we have now examined how laser speckles interact with one another through 3D particle-in-cell (PIC) simulations of two interacting speckles and 2D PIC simulations of ensembles of laser speckles (100s of speckles). Our work shows that an intense speckle can destabilize its neighbors, resulting in enhanced emission of particles and waves back to the original speckle, thus affecting its behavior in a manner that is nonlinear and nonlocal. Ensembles of speckles are thus found to collectively lower the SRS onset threshold. Simulations of the hohlraum interior where laser beams overlap show that multi-speckled laser beams at low average intensity (a few times 1014 W/cm2) have correspondingly lower thresholds for enhanced SRS and that SRS saturates through trapping induced nonlinearities (other potential saturation mechanisms are also examined). Results from VPIC simulations and comparison with pF3d results will be discussed that employ inhomogeneous plasma profile taken from rad-hydro modeling of NIF ignition experiments. Implications for experiments at higher laser power will also be discussed. Collaborators: B. Albright, H. Rose, R. Kirkwood, D. Hinkel, B. Langdon, P. Michel, K. Bowers, and B. Bergen
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.
High bitrate free-space communicator using automatic nonlinear all-optical beam tracking
NASA Astrophysics Data System (ADS)
Dudelzak, Alexander E.; Kuzhelev, Alexander S.; Gratton, Daniel; Hotte, Louis; Arimoto, Yoshinori
2005-04-01
The paper presents the results of experimental study of an optical-beam tracking concept involving two systems based on different principles. One is all-optical tracking, which utilizes a nonlinear optical material providing automatic fine-tracking feature. Another is traditional opto-mechanical technology using a quadrant avalanche detector, a voice coil-mirror actuator, control electronics, and computer interface. The possibility of establishing automatic mutual tracking between two communicating parties without involving computer-aided beam addressing has been experimentally proven. Capabilities and limitations of both systems are described. The all-optical system performs better than the traditional one when it tracking laser beam angular disturbances of magnitude of a few mrad and the jitter frequency is high (>=100 Hz). The traditional opto-mechanical system shows higher efficiency at lower jitter frequencies. A combination of an all-optical fine-tracking module and an opto-mechanical coarse tracking module is suggested for applications where using our originally proposed all-optical approach for both coarse and fine beam steering / tracking would be less efficient.
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.
Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.
Dibaji, Seyed Ahmad Reza; Banerjee, Rupak K; Soneson, Joshua E; Myers, Matthew R
2013-11-01
A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements. PMID:24180754
Post-buckling longterm dynamics of a forced nonlinear beam: A perturbation approach
NASA Astrophysics Data System (ADS)
Eugeni, Marco; Dowell, Earl H.; Mastroddi, Franco
2014-04-01
The aim of this paper is to determine by a singular perturbation approach the dynamic response of a harmonically forced system experiencing a pitchfork bifurcation. The model of an extensible beam forced by a harmonic excitation and subject to an axial static buckling is space-discretized by a Galerkin approach and studied by the Normal Form Method for different values of equation parameters influencing the nonlinear dynamic behavior like damping coefficient, load amplitude and frequency. A relevant issue in the perturbation methods is the concept of small and zero divisors which are related to the possibility to build a transformation that simplifies the original studied problem, i.e. to obtain the Normal Form, by eliminating as much as possible nonlinearities in the equations. For nonconservative systems, like structural damped systems, there are no conditions in the prior literature that define what "small" means relatively to a divisor. In the present paper some conditions about the order of magnitude of the divisors with respect to the perturbation entity are given and related to some physical parameters in the governing equations in order to estimate the relevance of some nonlinear effects.
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.
Nonlinear beam generated plasma waves as a source for enhanced plasma and ion acoustic lines
Daldorff, L. K. S.; Pecseli, H. L.; Trulsen, J. K.; Ulriksen, M. I.; Eliasson, B.; Stenflo, L.
2011-05-15
Observations by, for instance, the EISCAT Svalbard Radar (ESR) demonstrate that the symmetry of the naturally occurring ion line in the polar ionosphere can be broken by an enhanced, nonthermal, level of fluctuations (naturally enhanced ion-acoustic lines, NEIALs). It was in many cases found that the entire ion spectrum can be distorted, also with the appearance of a third line, corresponding to a propagation velocity significantly slower than the ion acoustic sound speed. It has been argued that selective decay of beam excited primary Langmuir waves can explain some phenomena similar to those observed. We consider a related model, suggesting that a primary nonlinear process can be an oscillating two-stream instability, generating a forced low frequency mode that does not obey any ion sound dispersion relation. At later times, the decay of Langmuir waves can give rise also to enhanced asymmetric ion lines. The analysis is based on numerical results, where the initial Langmuir waves are excited by a cold dilute electron beam. By this numerical approach, we can detect fine details of the physical processes, in particular, demonstrate a strong space-time intermittency of the electron waves in agreement with observations. Our code solves the full Vlasov equation for electrons and ions, with the dynamics coupled through the electrostatic field derived from Poisson's equation. The analysis distinguishes the dynamics of the background and beam electrons. This distinction simplifies the analysis for the formulation of the weakly nonlinear analytical model for the oscillating two-stream instability. The results have general applications beyond their relevance for the ionospheric observations.
Laxmi, V.N. (Delhi Univ. (India)); Tripathi, V.K. (Indian Inst. of Tech., New Delhi (India))
1990-09-01
An energetic electron beam propagating along the field lines in the ionosphere excites electron Bernstein waves having small group velocity across the beam. Two Bernstein waves may nonlinearly couple with each other to produce electromagnetic waves at sum and difference frequencies. A kinetic theory of this process has been developed using a guiding center formalism. Employing the nonlinear coupling coefficient, an estimate of the electromagnetic emissions at cyclotron harmonics has been made. The emitted field amplitude scales directly as the product of pump wave field strengths and varies inversely with their frequency.
He, Qingbo, E-mail: qbhe@ustc.edu.cn; Xu, Yanyan; Lu, Siliang; Dai, Daoyi [Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2014-04-28
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.
Aberration correction by nonlinear beam mixing: generation of a pseudo point sound source.
Seo, Jongbum; Choi, J J; Fowlkes, J Brian; O'Donnell, Matthew; Cain, Charles A
2005-11-01
Nonlinear beam mixing with microbubbles was explored to create a pseudo point source for aberration correction of therapeutic ultrasound. A damping coefficient for a bubble driven by a dual frequency sound field was derived by revisiting Prosperetti's linearized damping model. As a result, the overall damping term for dual frequency was obtained by linear summation of two damping terms for each frequency. The numerical simulation based on the bubble model suggests that the most efficient size range to generate a 1 MHz frequency from 4 MHz and 5 MHz sound sources is 2.6 to 3.0 microm. Furthermore, this size range constitutes the primary distribution of a specific ultrasound contrast agent. When a chamber of 0.1% of the diluted agent is sonified by 4 MHz and 5 MHz sound beams with 80 degrees incident angle between them, an approximately 100 Pa, 1 MHz difference frequency signal can be measured approximately 10 cm away. In addition, the received 1 MHz difference frequency signal shows omni-directional characteristics, even though the overlap zone of the two sound beams is on the order of the difference frequency wavelength. Therefore, the induced sound source can be considered as a pseudo point source and is expected to be useful for aberration correction for therapeutic ultrasound. PMID:16422409
The coaxial gyrotron with two electron beams. I. Linear theory and nonlinear theory
Liu Shenggang; Yuan Xuesong; Fu Wengjie; Yan Yang; Zhang Yaxin; Li Hongfu; Zhong Renbin [Research Institute of High Energy Electronics, University of Science and Technology of China, Chengdu, Sichuan, 610054 (China)
2007-10-15
The coaxial gyrotron with two electron beams (CGTB) is proposed and investigated in this paper. This paper consists of two parts: the linear theory and nonlinear theory of CGTB are presented in part I and the investigation on the dual frequency operation, a special operation state of CGTB, is given in part II. The magnetron injection gun with two electron beams has been developed, and simulations show that it may work well. It may guarantee that both the electric potential and the ratio of vertical to longitudinal velocities of two electron beams are equal. The results of the calculation show that CGTB has some distinguished advantages: mode competition is improved and output power is enhanced. Thus CGTB may be capable of providing 2-4 MW continuous-wave (CW) at 170 GHz to meet the demand of very high radio frequency CW power 1-2 MW in the ITER [ITER EDA Agreement and Protocol 2 (IAEA, Vienna, 1994)] program and other applications.
Korte, Dorota; Franko, Mladen
2015-01-01
In this work, complex geometrical optics is, for what we believe is the first time, applied instead of geometrical or wave optics to describe the probe beam interaction with the field of the thermal wave in photothermal beam deflection (photothermal deflection spectroscopy) experiments on thin films. On the basis of this approach the thermal (thermal diffusivity and conductivity), optical (energy band gap), and transport (carrier lifetime) parameters of the semiconductor thin films (pure TiO_{2}, N- and C-doped TiO_{2}, or TiO_{2}/SiO_{2} composites deposited on a glass or aluminum support) were determined with better accuracy and simultaneously during one measurement. The results are in good agreement with results obtained by the use of other methods and reported in the literature. PMID:26366490
Y. X. Zhang; M. A. Bradford; R. I. Gilbert
2007-01-01
Based on Mindlin–Reissner thick plate theory and Timoshenko's composite beam functions, a unified displacement-based finite element formulation of a 4-node, 24-DOF rectangular layered plate element is developed in this paper for the nonlinear finite element analysis of thin to moderately thick isotropic plates and reinforced concrete slabs. Timoshenko's composite beam functions that have been successfully used in other applications are
Amorn Pimanmas; Pennung Warnitchai
This paper presents a nonlinear finite element analysis of non-seismically detailed reinforced concrete (RC) beam-column connections under reversed cyclic load. The test of half-scale nonductile reinforced concrete beam-column joints was conducted. The tested specimens represented those of the actual mid-rise reinforced concrete frame buildings designed according to the non-seismic provisions of the American Concrete building code (ACI). The test results
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.
Geometric Effects on Electron Cloud
Wang, L
2007-07-06
The development of an electron cloud in the vacuum chambers of high intensity positron and proton storage rings may limit the machine performances by inducing beam instabilities, beam emittance increase, beam loss, vacuum pressure increases and increased heat load on the vacuum chamber wall. The electron multipacting is a kind of geometric resonance phenomenon and thus is sensitive to the geometric parameters such as the aperture of the beam pipe, beam shape and beam bunch fill pattern, etc. This paper discusses the geometric effects on the electron cloud build-up in a beam chamber and examples are given for different beams and accelerators.
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.
Direct electron beam writing of channel waveguides in nonlinear optical organic crystals.
Mutter, Lukas; Koechlin, Manuel; Jazbinsek, Mojca; Günter, Peter
2007-12-10
We report on optical channel waveguiding in an organic crystalline waveguide produced by direct electron beam patterning. The refractive index profile as a function of the applied electron fluence has been determined by a reflection scan method in the nonlinear optical organic crystal 4-N, N-dimethylamino-4'-N'-methyl-stilbazolium tosylate (DAST). A maximal refractive index reduction of Deltan1 = -0.3 at a probing wave-length of 633 nm has been measured for an electron fluence of 2.6mC/cm(2). Furthermore, a new concept of direct channel waveguide patterning in bulk crystals is presented and waveguiding has been demonstrated in the produced structures by end-fire coupling. Mach-Zehnder modulators have been successfully realized and a first electro-optic modulation at a wavelength of lambda= 1.55mum has been demonstrated therein. PMID:19550973
Lee, Hae June
Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes Min Sup Hur, Hae instability and a perturbation grows to exhibit nonlinear oscillations including chaos. Two standard routes 790-784, South Korea Received 20 January 1998 Nonlinear phenomena in a driven plasma diode are studied
NASA Astrophysics Data System (ADS)
Rosenzweig, J. B.; Barov, N.; Thompson, M. C.; Yoder, R.
2002-12-01
There has been much experimental and theoretical interest in blowout regime of plasma wakefield acceleration (PWFA), which features ultra-high accelerating fields, linear transverse focusing forces, and nonlinear plasma motion. Using an exact analysis, we examine here a fundamental limit of nonlinear PWFA excitation, by an infinitesimally short, relativistic electron beam. The beam energy loss in this case is shown to be linear in charge even for nonlinear plasma response, where a normalized, unitless charge exceeds unity, and relativistic plasma effects become important or dominant. The physical bases for this persistence of linear response are pointed out. As a byproduct of our analysis, we re-examine the issue of field divergence as the point-charge limit is approached, suggesting an important modification of commonly held views of evading unphysical energy loss. Deviations from linear behavior are investigated using simulations with finite length beams. The peak accelerating field in the plasma wave excited behind a finite-length beam is also examined, with the artifact of wave spiking adding to the apparent persistence of linear scaling of the peak field amplitude well into the nonlinear regime. On the other hand, at large enough normalized charge, linear scaling of fields collapses, with serious consequences for plasma wave excitation efficiency. The dramatic implications of these results for observing the collapse of linear scaling in planned experiments are discussed.
NASA Astrophysics Data System (ADS)
Volkova, E. A.; Kandidov, V. P.
1989-03-01
The Monte Carlo method is used in a study of a time-dependent thermal self-interaction of the speckle field of a multimode laser beam. It is shown that representation of such a beam by a superposition of statistically independent transverse modes of an optical resonator provides a satisfactory description of the spatial coherence of the optical field across the beam and also of changes resulting from linear diffraction. The change in the spatial coherence due to the time-dependent thermal self-interaction is governed by the competition between the nonlinear divergence of the beam as a whole and fragmentation of the speckle field. The results obtained are in agreement with the experimental data. It is shown that the replacement of a statistical analysis by a solution of a determinate problem of the self-interaction of a single-mode beam with equivalent parameters underestimates the angular divergence.
Twisting light by nonlinear photonic crystals.
Bloch, Noa Voloch; Shemer, Keren; Shapira, Asia; Shiloh, Roy; Juwiler, Irit; Arie, Ady
2012-06-01
We report the observation of nonlinear interactions in quadratic nonlinear crystals having a geometrically twisted susceptibility pattern. The quasi-angular-momentum of these crystals is imprinted on the interacting photons during the nonlinear process so that the total angular momentum is conserved. These crystals affect three basic physical quantities of the output photons: energy, translational momentum, and angular momentum. Here we study the case of second-order harmonic vortex beams, generated from a gaussian pump beam. These crystals can be used to produce multidimensional entanglement of photons by angular momentum states or for shaping the vortex's structure and polarization. PMID:23003958
NASA Astrophysics Data System (ADS)
Ianetz, D.; Kaganovskii, Yu.; Wilson-Gordon, A. D.
2012-08-01
The spatial dynamics of laser beams in absorbing planar waveguides with a parabolic index profile in a saturable or cubic-quintic medium are calculated using the "collective variable approach" technique. In the absence of losses, we construct diagrams which define regions of self-focusing and self-diffractive beam propagation for both types of media. It is found that propagating pulses exhibit an oscillatory pattern, similar to breathing behavior in homogeneous media. If the incident pulse spatial profile and the center of the index profile are not aligned, the pulse oscillates around the index origin with a "beat" frequency that depends on the graded index. Both the breathing and the beat frequencies are also calculated for other graded-index profiles, such as those with additional higher-power terms, and are found to be extremely sensitive to the index profile. In media with linear and nonlinear absorption, we demonstrate the difference between the breathing behavior in graded-index and homogeneous waveguides.
Bobylev, Yu. B.; Kuzelev, M. V.
2012-06-15
A nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in an isotropic dielectric medium is presented. A quantum model based on the Klein-Gordon equation is used. The growth rates of beam instabilities caused by the effect of stimulated Cherenkov radiation have been determined in the linear approximation. Mechanisms of the nonlinear saturation of relativistic quantum Cherenkov beam instabilities have been analyzed and the corresponding analytical solutions have been obtained.
Mourenas, D.; Beghin, C. )
1991-04-01
This paper investigates the generation mechanism responsible for the packets of electron cyclotron waves induced by an electron beam injected from the Space Shuttle and measured by Spacelab I instruments. The observed electron cyclotron emissions as well as their amplitude modulation are explained using a linear and a nonlinear treatments. Using a linear theory, it is shown that the emissions consist of the electronic Bernstein modes which are generated by an interaction between the neutralization return current and the ambient ionospheric plasma, and not directly by the primary beam. The observation of successive harmonic packets around the fundamental wave is interpreted using a two-dimensional single-wave model of the nonlinear interaction between a finite size ring beam and an infinite homogeneous magnetized plasma. 43 refs.
NASA Technical Reports Server (NTRS)
Graf, Wiley E.
1991-01-01
A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.
NASA Astrophysics Data System (ADS)
Yan, Liping; Chen, Benyong; Zhang, Cen; Zhang, Enzheng; Yang, Ye
2015-08-01
In order to analyze and characterize the periodic nonlinear error resulting from the misalignment of a polarizing beam splitter (PBS) in a laser heterodyne interferometer more accurately, in this paper, starting from the light separating principle of thin-film PBS, we have found that the root cause of the periodic nonlinear error is the frequency mixing induced by the deviation from the Brewster angle of the incident angle or by the rotation of the incident plane when the PBS is misaligned. Moreover, we have established the direct function relationships between the periodic nonlinear error and different PBSs’ misalignment errors for the first time. The theoretical analysis shows that the periodic nonlinear error arising from the PBS’s yaw error is the largest and the maximal nonlinear errors are unequal even if the positive yaw angle is equal to the negative yaw angle. The nonlinear errors are much smaller under the PBS’s roll and pitch errors. The experiments of polarizing leakage and nonlinear error measurement under the PBS’s yaw error demonstrate that the experimental results are in agreement with the theoretical analysis.
NASA Astrophysics Data System (ADS)
Talman, Richard
1999-10-01
Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.
NASA Technical Reports Server (NTRS)
Intrator, T.; Hershkowitz, N.; Chan, C.
1984-01-01
Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.
Carroll, Q
1983-01-01
Below is a review of the main geometrical points made in this paper. 1) Distortion is caused by: a. angling the beam against any spherical anatomy. b. leaving the beam perpendicular to the film when the part is tilted. c. angling the beam perpendicular to the part when it is tilted. 2) Distortion is negligible or absent when: a. angling the beam against a part that is parallel to the film. b. angling the beam one-half of the tilted-part-film angle. c. not angling when the part is parallel to the film. d. tomographing. 3) Magnification is not caused by: a. angling the beam, regardless of tube-to-tabletop distance compensation. b. tomography. 4) To evaluate a radiograph for positioning rotation, tilt, or flexion/extension, the pair of anatomical parts observed should be: a. stable and immovable. b. with their long axes nearly perpendicular to the direction of shift being evaluated. c. as close to the CR or center of the film as possible. d. as far from each other and from the midline as possible. Many of the geometrical factors involved in radiography are more complex than we often appreciate. They are sometimes taught in the form of "blanket" statements or rules that are oversimplified. Nonspecific, vague, or "blanket" questions in this area should be avoided in constructing the registry examinations. Finally, teaching in radiography should be based upon objective, repeatable, and verifiable experimentation rather than on appeal to authority. Such an approach will not only make radiography training more accurate, but also more exciting and fun. PMID:6856809
Ion-beam sputtered (IBS) thin-film interference filters for nonlinear optical imaging
NASA Astrophysics Data System (ADS)
Anderson, Neil; Prabhat, Prashant; Erdogan, Turan
2012-03-01
Nonlinear optical (NLO) microscopy is emerging as a powerful technique for the study of biological samples. By combining several different imaging modalities such as multiphoton (MP) fluorescence, second-harmonic and thirdharmonic generation (SHG and THG), and coherent Raman scattering techniques such as coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS), it is possible to combine the best practices of label and label-free imaging into a single platform capable of imaging structures within single cells and elucidating the health of biological tissue samples, even at the submicron level. Single-substrate, ion-beam-sputtered (IBS) thinfilm interference filters are a key enabling technology in laser-based optical microscopy and play a critical role in multimodal NLO imaging. In microscopy applications, optical filters are used to select and discriminate exactly which wavelengths of light are to be transmitted, reflected and suppressed. In this paper we discuss various important characteristics of hard-coated thin-film interference filters, such as high light throughput, steep edges, and high out-of-band blocking, all of which require careful consideration when designing and manufacturing optical filters for NLO imaging applications. To understand the true performance of hard-coated IBS filters, a simple CARS imaging experiment was performed. We found a 2.6 times increase in signal enhancement and 70% improvement in image contrast when compared to a commercially available filter commonly used in CARS microscopy applications.
NASA Astrophysics Data System (ADS)
Lapsanska, Hana; Chmelickova, Hana; Hrabovsky, Miroslav
2010-10-01
Weld geometric characteristics in laser overlapping spot welding of 0.6-mm AISI 304 stainless steel sheets were investigated. A pulsed Nd:YAG laser with maximal average power of 150 W was used for welding experiments with different laser beam energies in the range of 3.5 J to 6.2 J, keeping all other processing parameters constant. The main objective of these experiments was to study the effect of energy changes and to identify the welding mode in dependency on the beam effective peak power density. Each weld surface and its cross section were analyzed using a laser scanning confocal microscope. The spot diameter on the specimen, weld width, and penetration depth were measured. Three-dimensional surface reconstruction was realized to describe the effect of energy changes on weld surface properties.
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.
G. M. Kulikov; S. V. Plotnikova
2002-01-01
Based on mixed finite-element approximations, a numerical algorithm is developed for solving linear static problems of prestressed multilayer composite shells subjected to large displacements and arbitrarily large rotations. As the sought-for functions, six displacements and eleven strains of the shell faces are chosen, which allows us to use nonlinear deformation relationships exactly representing arbitrarily large displacements of the shell as
NASA Astrophysics Data System (ADS)
Mojahedi, M.; Ahmadian, M. T.; Firoozbakhsh, K.
2013-12-01
The nonlinear dynamic and static deflection of a micro/nano gyroscope under DC voltages and base rotation are investigated. The gyroscope undertakes two coupled bending motions along the drive and sense directions and subjected to electrostatic actuations and intermolecular forces. The nonlinear governing equations of motion for the system with the effect of electrostatic force, intermolecular tractions and base rotation are derived using extended Hamilton principle. Under constant voltage, the gyroscope finds the preformed shape. First, the deflection of the micro/nano gyroscope under electrostatic forces is obtained by static and dynamic analyses. Furthermore, the static and dynamic instability of the system are investigated. Afterward the oscillatory behavior of the pre-deformed micro/nano gyroscope around equilibrium is studied. The effects of intermolecular and nonlinear parameters on the static and dynamic deflection, natural frequencies and instability of the micro/nano gyroscope are studied. The presented model can be used to exactly determine static and the dynamic behavior of vibratory micro/nano gyroscopes.
C. L. Bohn , P. Piot and B. Erdelyi
2008-05-31
According to its original Statement of Work (SOW), the overarching objective of this project is: 'To enhance substantially the understanding of the fundamental dynamics of nonequilibrium high-brightness beams with space charge.' Our work and results over the past three and half years have been both intense and fruitful. Inasmuch as this project is inextricably linked to a larger, growing research program - that of the Beam Physics and Astrophysics Group (BPAG) - the progress that it has made possible cannot easily be separated from the global picture. Thus, this summary report includes major sections on 'global' developments and on those that can be regarded as specific to this project.
Kanagawa, Tetsuya
2015-05-01
This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set. PMID:25994696
NASA Astrophysics Data System (ADS)
Ho, Seng-Tiong; Zhang, Xiaolong; Udo, Maria K.
1995-09-01
We analyze a new scheme for generating squeezed states in a short semiconductor AlxGa 1-xAs waveguide with chi (3) nonlinearity at below half the band-gap energy. We find that for a Gaussian pulse the amount of squeezing achievable is limited by the squeezed-state detection phase mismatch caused by the pump self-phase modulation and is also degraded slightly by the pump-probe phase mismatch that is due to the different nonlinear refractive indices experienced by the pump and the probe beams. We show theoretically that the amount of squeezing observed can be increased by use of either a short pulse or a pulse with matched phase variation as the local oscillator. In a centimeter-long AlxGa1-x As waveguide more than 85% (8.2 dB) of squeezing potentially can be obtained, limited mainly by two-photon absorption.
A result on quasi-periodic solutions of a nonlinear beam equation with a quasi-periodic forcing term
NASA Astrophysics Data System (ADS)
Wang, Yi; Si, Jianguo
2012-02-01
In this paper, a quasi-periodically forced nonlinear beam equation {u_{tt}+u_{xxxx}+? u+\\varepsilon?(t)h(u)=0} with hinged boundary conditions is considered, where ? > 0, {\\varepsilon} is a small positive parameter, {?} is a real analytic quasi-periodic function in t with a frequency vector ? = ( ? 1, ? 2 . . . , ? m ), and the nonlinearity h is a real analytic odd function of the form {h(u)=?_1u+?_{2bar{r}+1}u^{2bar{r}+1}+sum_{k? bar{r}+1}?_{2k+1}u^{2k+1},?_1,?_{2bar{r}+1} neq0, bar{r} in {mathbb {N}}.} The above equation admits a quasi-periodic solution.
Energy harvesting in a nonlinear piezomagnetoelastic beam subjected to random excitation
NASA Astrophysics Data System (ADS)
De Paula, Aline S.; Inman, Daniel J.; Savi, Marcelo A.
2015-03-01
This work addresses the influence of nonlinearities in energy harvesting from a piezomagnetoelastic structure subjected to random vibrations. Nonlinear equations of motion that describe the electromechanical system are given along with theoretical simulations. The numerical analysis presents a comparison between the voltage provided from a linear, nonlinear bistable and nonlinear monostable systems due to random vibration. Experimental performance of the generator exhibits qualitative agreement with the theory, showing an enhancement of piezoelectric power generation in a bistable system when it vibrates around both stable equilibrium points. A relationship between variations in the excitation and a bistable system response is established from numerical simulations, defining a region of enhanced power generation when compared to the linear and nonlinear monostable cases.
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
NASA Astrophysics Data System (ADS)
Zhang, Y. L.; Matsumoto, H.; Omura, Y.
1993-12-01
Both linear and nonlinear interactions between oblique whistler, electrostatic, quasi-upper hybrid mode waves and an electron beam are studied by linear analyses and electromagnetic particle simulations. In addition to a background cold plasma, we assumed a hot electron beam drifting along a static magnetic field. Growth rates of the oblique whistler, oblique electrostatic, and quasi-upper hybrid instabilities were first calculated. We found that there are four kinds of unstable mode waves for parallel and oblique propagations. They are the electromagnetic whistler mode wave (WW1), the electrostatic whistler mode wave (WW2), the electrostatic mode wave (ESW), and the quasi-upper hybrid mode wave (UHW). A possible mechanism is proposed to explain the satellite observations of whistler mode chorus and accompanied electrostatic waves, whose amplitudes are sometimes modulated at the chorus frequency.
Mode transition and nonlinear dynamics in the beam-injected plasma
H. J. Lee; J. K. Lee; Y. Yang; M. S. Huh; Y. B. Kim; M. Yoon; T. H. Chung
1997-01-01
Summary form only given. The motions of electron beams in a discharge plasma are simulated using the 1-D particle-in-cell code (XPDP1). With appropriate pressures, beam current, beam velocity, and voltages, there is mode transition from the anode glow mode (AGM) to the temperature limited mode (TLM). The transition happens when the ionized ions which make the potential positive fill the
Large deflection of flexible tapered functionally graded beam
NASA Astrophysics Data System (ADS)
Davoodinik, A. R.; Rahimi, G. H.
2011-10-01
In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied. In order to derive the fully non-linear equations governing the non-linear deformation, a curvilinear coordinate system is introduced. A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities, infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials. The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam. The effects of taper ratio, inclined end load angle and material property gradient on large deflection of the beam are evaluated. The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.
A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading
L. S. Ma; D. W. Lee
2011-01-01
Due to the variation in material properties through the thickness, bifurcation buckling cannot generally occur for plates or beams made of functionally graded materials (FGM) with simply supported edges. Further investigation in this paper indicates that FGM beams subjected to an in-plane thermal loading do exhibit some unique and interesting characteristics in both static and dynamic behaviors, particularly when effects
Nonlinear forced dynamics of an axially moving viscoelastic beam with an internal resonance
Mergen H. Ghayesh
2011-01-01
The aim of the study described in this paper is to investigate the forced dynamics of an axially moving viscoelastic beam. The governing equation of motion is obtained via Newton's second law of motion and constitutive relations. The viscoelastic beam material is constituted by the Kelvin–Voigt, a two-parameter rheological model, energy dissipation mechanism, in which material, not partial, time derivative
NASA Astrophysics Data System (ADS)
Sederberg, S.; Elezzabi, A. Y.
2015-10-01
Silicon-loaded nanoplasmonic waveguides were integrated onto a micron-scale characterization beam to allow for accurate and efficient nonlinear optical characterization. The waveguides consist of a 95 nm × 340 nm silicon core that is capped by a 60 nm thick gold film. The characterization beam is formed by precision cleaving one waveguide end facet and by deep silicon etching the substrate area adjacent to the other end facet. This configuration allows input radiation to be coupled directly to the waveguides using a microscope objective and output radiation to be out-coupled with a lensed single-mode optical fiber. The fabrication steps are characterized via scanning electron microscopy at various points throughout the process. The fabricated devices are optically characterized using an ultrafast nonlinear pump-probe time-domain spectroscopy setup. Ultrafast all-optical modulation is measured in the waveguides on two timescales: ?1 = 1.98 ± 0.40 ps and ?2 = 17.9 ± 6.8 ps.
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.; Bharuthram, R.; Singh, S. V.; Lakhina, G. S.; Reddy, R. V.
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 Astrophysics Data System (ADS)
Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.
2014-05-01
The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects could be readily achieved.
NASA Astrophysics Data System (ADS)
Bernal, M. A.; deAlmeida, C. E.; David, M.; Pires, E.
2011-12-01
The PENELOPE code is used to determine direct strand break yields corresponding to photons from a 60Co source and 28 and 30 kV x-ray beams impacting on a B-DNA geometrical model, which accounts for five organizational levels of the human genetic material. Direct single, double and total strand break probabilities are determined in a liquid water homogeneous medium with 1.06 g cm-3 density. The spectra produced by the x-ray beams at various depths in the phantom have been used to study the dependence of the damage yield on the depth. The relative biological effectiveness (RBE) is also estimated using the 60Co radiation qualities as the reference. According to this work, the damage probabilities and thus the RBE are, within the uncertainties, similar for both x-ray energies and are independent of the depth into the phantom. Furthermore, the total strand break yield is invariant with respect to the energy of the incident photons. The RBE for low-energy x-ray beams determined here (1.3 ± 0.1) is lower than that reported by Kellerer, taking into account that he used a 200 kV radiation as the reference quality. However, our RBE values are consistent with those determined by Kühne et al (2005 Radiat. Res. 164 669-76), which used the same biological endpoint and reference quality as our study. Also, our RBE values are similar to those determined by Verhaegen and Reniers (2004 Radiat. Res. 162 592-9).
Nonlinear Plasma Waves Excitation by Intense Ion Beams in Background Plasma
Igor D. Kaganovich; Edward A. Startsev; Ronald C. Davidson
2004-04-15
Plasma neutralization of an intense ion pulse is of interest for many applications, including plasma lenses, heavy ion fusion, cosmic ray propagation, etc. An analytical electron fluid model has been developed to describe the plasma response to a propagating ion beam. The model predicts very good charge neutralization during quasi-steady-state propagation, provided the beam pulse duration {tau}{sub b} is much longer than the electron plasma period 2{pi}/{omega}{sub p}, where {omega}{sub p} = (4{pi}e{sup 2}n{sub p}/m){sup 1/2} is the electron plasma frequency and n{sub p} is the background plasma density. In the opposite limit, the beam pulse excites large-amplitude plasma waves. If the beam density is larger than the background plasma density, the plasma waves break. Theoretical predictions are compared with the results of calculations utilizing a particle-in-cell (PIC) code. The cold electron fluid results agree well with the PIC simulations for ion beam propagation through a background plasma. The reduced fluid description derived in this paper can provide an important benchmark for numerical codes and yield scaling relations for different beam and plasma parameters. The visualization of numerical simulation data shows complex collective phenomena during beam entry and exit from the plasma.
Ion-beam-assisted deposition of Au nanocluster/Nb 2O 5 thin films with nonlinear optical properties
NASA Astrophysics Data System (ADS)
Cotell, C. M.; Schiestel, S.; Carosella, C. A.; Flom, S.; Hubler, G. K.; Knies, D. L.
1997-05-01
Gold nanocluster thin films (˜ 200 nm thickness) consisting of metal clusters ˜ 5 nm in size embedded in a matrix of Nb 2O 5 were deposited by ion beam-assisted deposition (IBAD) by coevaporation of Au and Nb with O 2+ ion bombardment. The microstructure and optical characteristics of these films were examined as-deposited and after annealing at 600°C. Annealing crystallized the amorphous oxide matrix and ripened the nanoclusters. A strong linear absorption at the wavelength of the surface plasmon resonance for Au developed as a result of annealing. The linear optical behavior was modeled using Mie scattering theory. Good agreement was found between the nanocluster sizes predicted by the theory and the particle sizes observed experimentally using transmission electron microscopy (TEM). The nonlinear optical (NLO) properties of the nanocluster films were probed experimentally using degenerate four wave mixing and nonlinear transmission. The wavelength was near the peak of the surface plasmon resonance as measured by VIS/UV spectroscopy. Values of | ?xxxx(3)| were 7.3 × 10 -8 and 3.0 × 10 -10 esu for annealed and unannealed samples, respe The dominant mechanism for the nonlinear response was change in dielectric constant due to the generation of a distribution of hot, photoexcited electrons.
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.
NASA Astrophysics Data System (ADS)
Masuda, Arata; Aoki, Junsuke; Iba, Daisuke; Sone, Akira
2010-03-01
In this paper, a nondestructive, in-service structural integrity monitoring methodology that can detect and characterize local structural damages of contact-type, i.e. damages and failures which come along with generation, growth and/or changes of contacting surfaces, such as cracks, debonding, preload-loss in bolted joints, etc., is presented. The presented monitoring system consists of piezoelectric elements bonded on the structural surface, a high-frequency harmonic voltage source, and a current detector. When the structure is subjected to a vibrational load such as operational load at low-frequencies, the scattering conditions for the high-frequency elastic waves in the vicinity of the contact-type damages will change in synchronization with the structural vibration because of the fluctuation of the contact conditions. This nonlinear effects of vibro-acoustic interaction between the low-frequency vibration and the high-frequency wave field causes the change in the driving-point impedance of the structure at the high frequency range, which leads to the significant modulation of the coupled electro-mechanical impedance (or admittance) of the piezoelectric elements. Therefore, if the piezoelectric elements are driven by a fixed amplitude high-frequency harmonic voltage source, the nonlinear fluctuation of the coupled admittance can be observed as the amplitude and phase modulation of the current flowing through the piezoelectric element. A modeling and analytical study of the nonlinear piezoelectric impedance modulation is presented for a beam structure including a crack, utilizing a linear time-varying system theory. A damage evaluation measure is presented based on the dimensionless modal stiffness fluctuation estimated from the instantaneous admittance reconstructed from the demodulated current responses. Furthermore, fundamental strategies and future directions for damage localization based on the nonlinear piezoelectric impedance modulation are briefly discussed.
NASA Astrophysics Data System (ADS)
Kanatani, Kenichi
The “geometric AIC” and the “geometric MDL” have been proposed as model selection criteria for geometric fitting problems. These correspond to Akaike's “AIC” and Rissanen's “BIC” well known in the statistical estimation framework. Another well known criterion is Schwarz' “BIC”, but its counterpart for geometric fitting has not been known. This paper introduces the corresponding criterion, which we call the “geometric BIC”, and shows that it is of the same form as the geometric MDL. Our result gives a justification to the geometric MDL from the Bayesian principle.
Effects of focusing on third-order nonlinear processes in isotropic media. [laser beam interactions
NASA Technical Reports Server (NTRS)
Bjorklund, G. C.
1975-01-01
Third-order nonlinear processes in isotropic media have been successfully used for tripling the efficiency of high-power laser radiation for the production of tunable and fixed-frequency coherent vacuum UV radiation and for up-conversion of IR radiation. The effects of focusing on two processes of this type are studied theoretically and experimentally.
Numerical Modeling of Nonlinear Coupling between Lines/Beams with Multiple Floating Bodies
Yang, Chan K.
2010-07-14
Nonlinear coupling problems between the multiple bodies or between the mooring/riser and the offshore platform are incorporated in the CHARM3D-MultiBody, a fully coupled time domain analysis program for multiple bodies with moorings and risers...
Ali Shan, S.; National Centre For Physics , Shahdra Valley Road, 44000 Islamabad; Pakistan Institute of Engineering and Applied Sciences , Islamabad ; El-Tantawy, S. A.; Moslem, W. M.
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 Technical Reports Server (NTRS)
Hodges, D. H.; Ormiston, R. A.
1973-01-01
The nonlinear partial differential equations for the flapping and lead-lag degrees of freedom of a torisonally rigid, rotating cantilevered beam are derived. These equations are linearized about an equilibrium condition to study the flap-lag stability characteristics of hingeless helicopter rotor blades with zero twist and uniform mass and stiffness in the hovering flight condition. The results indicate that these configurations are stable because the effect of elastic coupling more than compensates for the destabilizing flap-lag Coriolis and aerodynamic coupling. The effect of higher bending modes on the lead-lag damping was found to be small and the common, centrally hinged, spring restrained, rigid blade approximation for elastic rotor blades was shown to be resonably satisfactory for determining flap-lag stability. The effect of pre-cone was generally stabilizing and the effects of rotary inertia were negligible.
NASA Technical Reports Server (NTRS)
Montgomery, D.; Liu, C. S.
1979-01-01
A simplified model of an electromagnetic filamentation instability that arises when two counterstreaming electron beams pass through a uniform ion background is treated by statistical mechanical techniques borrowed from fluid turbulence theory. Accumulation of magnetic energy at long wavelengths is predicted, as observed in the numerical simulations of Lee and Lampe.
Comment on ``Nonlinear Compton scattering and electron acceleration in interfering laser beams''
Yousef I. Salamin
2000-01-01
We point out that, the way it is reported, the solution to the equation of motion of a relativistic electron in the field of two electromagnetic waves advanced recently by Amatuni and Pogorelsky [Phys. Rev. ST Accel. Beams 1, 034001 (1998)] does not handle the case of two copropagating waves differing in frequency. An equivalent form for that solution is
Study of Nonlinear QED Effects in Interacations of Terawatt Laser with High Energy Electron Beam*
McDonald, Kirk
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.6 Emission of a photon by an electron in the eld of a strong electro- magnetic wave . . . . . . . . . . . . . . . . . . . . . . . . . . . laser pulses from an Nd:glass laser at the experiment E144 at the Final Focus Test Beam at SLAC
E. Dumas
We give asymptotic descriptions of smooth oscillating solu- tions of hyperbolic systems with variable coefficients, in the weakly nonlinear diffractive optics regime. The dependence of the coefficientsof the system in the space-time variable (corresponding to propagation in a non-homogeneous medium) implies that the rays are not parallel lines -the same occurs with non-planar initial phases. Approximations are given by WKB
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
Wei, Jingsong; Yan, Hui
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.
Antonio D. Lanzo
2009-01-01
This paper deals with the nonlinear analysis of high-shear deformable elastic plane frame, frequently used to model beam of composite materials, elastomeric beam-like bearings of bridge and seismic isolation, or to model DNA strands and polymer chains. The work uses a FEM approach based on a Cosserat–Timoshenko beam model with an exact geometrical description, evaluating all the axial, shear and
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.
Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system
NASA Technical Reports Server (NTRS)
Whelan, D. A.; Stenzel, R. L.
1985-01-01
It is shown that the unstable electron-plasma waves of a beam-plasma system can generate electromagnetic radiation in a uniform plasma. The generation mechanism is a scattering of the unstable electron plasma waves off ion-acoustic waves, producing electromagnetic waves whose frequency is near the local plasma frequency. The wave vector and frequency matching conditions of the three-wave mode coupling are experimentally verified. The electromagnetic radiation is observed to be polarized with the electric field parallel to the beam direction, and its source region is shown to be localized to the unstable plasma wave region. The frequency spectrum shows negligible intensity near the second harmonic of the plasma frequency. These results suggest that the observed electromagnetic radiation of type III solar bursts may be generated near the local plasma frequency and observed downstream where the wave frequency is near the harmonic of the plasma frequency.
Whealton, J.H.; Raridon, R.J.; Olsen, D.K.; Galambos, J.D.; Holmes, J.A.
1998-06-01
A technique is described which enables high resolution of halo in beam dynamic studies by direct simulation. The method consists in first solving the beam dynamics problem using coarse initial data. The regions of the initial data, which result in beam halo, or extremums in phase space, are identified. The dynamics are resolved by continuing the calculation using initial data points slightly offset from those that result in halo formation, thus filling in the halo structure. The solution is repeated with appropriate scaling of such things as charge per orbit etc. This process may be continued indefinitely. The method can also shed some light on the halo generation in weakly chaotic systems. The scheme is essentially different from the {Delta}f method in that no assumption is made about f{sub 0}. As an example, a bifurcation in a non-trivial space charge dominated homomorphic problem is resolved self-consistently using minor computational resources, rather than having to perform the calculation for 250 trillion effective particles.
NASA Astrophysics Data System (ADS)
El Kadiri, M.; Benamar, R.
2003-06-01
In Parts I and II of this series of papers, a practical simple "multi-mode theory", based on the linearization of the non-linear algebraic equations, written on the modal basis, in the neighbourhood of each resonance, has been developed for beams and fully clamped rectangular plates. Simple explicit formulae have been derived, which allowed, via the so-called first formulation, direct calculation of the basic function contributions to the first three non-linear mode shapes of clamped-clamped and clamped-simply supported beams, and the two first non-linear mode shapes of FCRP. Also, in Part I of this series of papers, this approach has been successively extended, in order to determine the amplitude-dependent deflection shapes associated with the non-linear steady state periodic forced response of clamped-clamped beams, excited by a concentrated or a distributed harmonic force in the neighbourhood of the first resonance. This new approach has been applied in the present work to obtain the NLSSPFR formulation for FCRP, SSRP, and CCCSSRP, leading in each case to a non-linear system of coupled differential equations, which may be considered as a multi-dimensional form of the well-known Duffing equation. The single-mode assumption, and the harmonic balance method, have been used for both harmonic concentrated and distributed excitation forces, leading to one-dimensional non-linear frequency response functions of the plates considered. Comparisons have been made between the curves based on these functions, and the results available in the literature, showing a reasonable agreement, for finite but relatively small vibration amplitudes. A more accurate estimation of the FCRP non-linear frequency response functions has been obtained by the extension of the improved version of the semi-analytical model developed in Part I for the NLSSPFR of beams, to the case of FCRP, leading to explicit analytical expressions for the "multi-dimensional non-linear frequency response function", depending on the forcing level, and the amplitude of the response induced in the range considered for the excitation frequency. Non-linear steady state periodic forced response is denoted in what follows as NLSSPFR.
Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals
Assanto, Gaetano; Minzoni, Antonmaria A.; Smyth, Noel F.; Worthy, Annette L.
2010-11-15
The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions.
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.
NASA Astrophysics Data System (ADS)
Belashov, Vasily
We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega
Optimization of absorption placement using geometrical acoustic models and least squares.
Saksela, Kai; Botts, Jonathan; Savioja, Lauri
2015-04-01
Given a geometrical model of a space, the problem of optimally placing absorption in a space to match a desired impulse response is in general nonlinear. This has led some to use costly optimization procedures. This letter reformulates absorption assignment as a constrained linear least-squares problem. Regularized solutions result in direct distribution of absorption in the room and can accommodate multiple frequency bands, multiple sources and receivers, and constraints on geometrical placement of absorption. The method is demonstrated using a beam tracing model, resulting in the optimal absorption placement on the walls and ceiling of a classroom. PMID:25920877
NONLINEAR OPTICAL PHENOMENA: Phase conjugation upon SBS of a focused laser speckle beam
NASA Astrophysics Data System (ADS)
Bogachev, V. A.; Kochemasov, G. G.; Starikov, F. A.
2008-09-01
The phase conjugation (PC) of a focused Gaussian laser beam with a partial spatial coherence of the wave front is studied numerically and theoretically upon SBS within the framework of a three-dimensional nonstationary SBS model, which takes into account transient processes and SBS saturation. The dependences of the PC coefficient h on the laser radiation power are obtained for different excesses of the angular divergence over the diffraction limit ?. It is found that for the given reflectance of laser radiation from the SBS mirror, the PC coefficient monotonically decreases with increasing the divergence. For example, under the near threshold SBS conditions, h decreases from 70% to 30%, when ? increases from 1 to 10. For the given divergence, the PC coefficient increases with increasing the reflectance and approaches the ideal one (h > 90%) upon deep SBS saturation, when the reflectance exceeds 90%—95%.
NASA Astrophysics Data System (ADS)
Du, Xiangli; Yin, Yaling; Zheng, Gongjue; Guo, Chaoxiu; Sun, Yu; Zhou, Zhongneng; Bai, Shunjie; Wang, Hailing; Xia, Yong; Yin, Jianping
2014-07-01
A new nonlinear optical method to generate a dark hollow beam (DHB) with a dielectric ZnSe crystal is proposed. From Huygens-Fresnel diffraction theory, we calculate the intensity distributions of the DHB and its propagating properties in free space, and study the dependences of the optimal propagation position and the dark-spot size (DSS) of the hollow beam on the waist radius of the incident Gaussian laser beam. Our study shows that the intensity distribution of the DHB presents symmetrical distribution with increasing the propagation distance, the optimal distance zopt becomes farther and the DSS becomes larger with the increase of the waist radius w of the incident Gaussian laser beam. This generated DHB will have applications in the optical guiding and trapping of macroscopic objects, atoms or molecules.
A case study of analysis methods for large deflections of a cantilever beam
NASA Technical Reports Server (NTRS)
Craig, L. D.
1994-01-01
A load case study of geometric nonlinear large deflections of a cantilever beam is presented. The bending strain must remain elastic. Closed form solution and finite element methods of analysis are illustrated and compared for three common load cases. A nondimensional nomogram for each case is presented in the summary.
Competing nonlinearities in quadratic nonlinear waveguide arrays
Competing nonlinearities in quadratic nonlinear waveguide arrays Frank Setzpfandt,1, * Dragomir N demonstrate experimentally the existence of competing focusing and defocusing nonlinearities in a double- tively. If an optical system, however, exhibits so- called competing nonlinearities a laser beam can ex
NSDL National Science Digital Library
2011-01-01
This tool lets learners explore various geometric solids and their properties. Learners can manipulate and color each shape to explore the faces, edges, and vertices, and they can use this tool to investigate the relationship among the number of faces, vertices, and edges. This tool supports the 5-lesson unit "Geometric Solids and Their Properties" (cataloged separately).
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour. PMID:26303922
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
Implementation of beam broadening in low side-lobe phased array antennas
NASA Astrophysics Data System (ADS)
Edison, Thomas
Generally, the broadening of an antenna beam into a sector beam or a shaped beam, by changing only the phase, is accomplished by a nonlinear phase disribution along the direction of the spread. In this paper an alternate implementation of phase distribution in an ordered random manner, for a phased array antenna, is described. The resulting spread pattern is a convolution of the desired geometrical optics pattern with the sharp pencil beam of the full array, and therefore has comparatively low sidelobe characteristics and sharper edges.
NASA Astrophysics Data System (ADS)
Lyubomudrov, O. V.; Shkunov, V. V.
1992-12-01
The problem of propagation of a light beam with speckle in a photorefractive crystal with diffusive photoresponse is solved analytically. While the angular spectrum of the beam remains Gaussian, the beam is deflected, with a rate of rotation proportional to the square of the divergence angle.
NASA Astrophysics Data System (ADS)
Djomo Mbong, T. L. M.; Siewe Siewe, M.; Tchawoua, C.
2015-05-01
This research work is based on the study of the dynamic of one-degree-of freedom nonlinear oscillator representing a built-in clamped-clamped prestressed beam model with a nonlinear damping. First of all, we model this moving structure where we regard the perturbations as a combination of both low-frequency force and high-frequency force. Then, we analyze the occurrence of vibrational resonance, where the response consists of a slow motion and a fast motion respectively with low and high frequencies. Through this, we obtain an approximate analytical expression of the response amplitude and we determine the values of the low frequency and the amplitude of the high-frequency force at which vibrational resonance occurs. The theoretical predictions are found to be in good agreement with numerical results. Moreover, for fixed parameters values of the system, as the nonlinear damping vary, we found appearance and the disappearance of resonance with or without cross-well motion. Secondly, we study the chaotic dynamic of the beam. In this case, critical values of perturbation parameters for the onset of the chaotic motion are specified using Melnikov's method. Hence, the global dynamical changes of the system have been examined by plotting phase portrait, bifurcation diagram and their corresponding Lyapunov exponent.
NASA Astrophysics Data System (ADS)
Krutyansky, Leonid M.; Brysev, Andrew P.; Klopotov, Roman V.; Pernod, Philippe J.; Preobrazhensky, Vladimir L.; Yan, Xiang; Hamilton, Mark F.
2003-10-01
Acoustical imaging in complex media (e.g., biological tissue) can be affected by phase aberrations introduced in a wave during propagation. Wave phase conjugation (WPC) of ultrasound is known for its ability to compensate for phase distortions due to inhomogeneity of the propagation medium, and it can be used for improvement of acoustical imaging under these conditions. In a nonlinear medium harmonics are generated during propagation of an intense beam of ultrasound, and this principle is used in tissue harmonic imaging. The parametric method of WPC permits phase conjugation of a selected frequency component of the probe beam. In this way the peculiarities of WPC can be combined with advantages of harmonic imaging. Automated WPC-focusing of the conjugated second-harmonic component of a focused nonlinear probe beam is studied experimentally and theoretically for the case of a homogeneous medium, and experimentally for a medium with pseudo-random inhomogeneities. The generated conjugate wave can also be sufficiently intense to generate higher-order harmonics, which display enhanced focusing. Improvement of a C-scan harmonic imaging system operating in an inhomogeneous medium is provided as an example.
18.385 Nonlinear Dynamics and Chaos, Fall 2002
Rosales, Rodolfo
Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear ...
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.
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.
NASA Astrophysics Data System (ADS)
Lyubomudrov, O. V.; Shkunov, V. V.
1994-06-01
An analytical solution is given of the propagation of a doubly Gaussian speckle beam in photorefractive crystals. A beam which retains the Gaussian profile of the angular spectrum and of the envelope of the speckle structure in a transverse cross section exhibits self-rotation of its path at a rate proportional to the square of the irregular ('grey') divergence. The bulk of the beam self-rotation takes place within a distance equal to its focal waist.
Kuzelev, M.V.; Rukhadze, A.A.; Sanadze, G.V.; Filippychev, D.S.
1983-02-01
When an electromagnetic wave is scattered by an electron beam, beat plasma oscillations are excited in the latter. However, if the reciprocal of the characteristic time for the amplitude of the beat wave to change is much less than the plasma frequency, there are no eigenoscillations in the beam. This type of scattering is called Compton scattering and in this case the beat wave causes modulation and bunching of the electron beam.(AIP)
Geometric Frustration with Disorder
NASA Astrophysics Data System (ADS)
Woo, Nayoon; Silevitch, Daniel M.; Rosenbaum, Thomas F.
2014-03-01
We study the effects of Nd doping on the geometrically-frustrated Heisenberg antiferromagnet Gadolinium Gallium Garnet (GGG), using linear and nonlinear ac magnetic susceptibility. Doping levels from 0.1 to 1 percent Nd alleviate the intrinsic frustration of pure GGG and elevate the ordering temperature compared to the pure material. We use nonlinear pump-probe magnetic susceptometry to examine cluster dynamics for both the pure and the doped series. At low frequency (~10 Hz), spectral hole burning is possible, indicating the presence of spin clusters with discrete energy levels largely decoupled from the overall spin bath. At kHz, we find a Fano resonance, revealing scattering pathways between spin cluster excitations and the bath. We trace the evolution of this resonance behavior as a function of dopant concentration.
Importance of beam-beam tune spread to collective beam-beam instability in hadron colliders.
Jin, Lihui; Shi, Jicong
2004-03-01
In hadron colliders, electron-beam compensation of beam-beam tune spread has been explored for a reduction of beam-beam effects. In this paper, effects of the tune-spread compensation on beam-beam instabilities were studied with a self-consistent beam-beam simulation in model lattices of Tevatron and Large Hodron Collider. It was found that the reduction of the tune spread with the electron-beam compensation could induce a coherent beam-beam instability. The merit of the compensation with different degrees of tune-spread reduction was evaluated based on beam-size growth. When two beams have a same betatron tune, the compensation could do more harm than good to the beams when only beam-beam effects are considered. If a tune split between two beams is large enough, the compensation with a small reduction of the tune spread could benefit beams as Landau damping suppresses the coherent beam-beam instability. The result indicates that nonlinear (nonintegrable) beam-beam effects could dominate beam dynamics and a reduction of beam-beam tune spread by introducing additional beam-beam interactions and reducing Landau damping may not improve the stability of beams. PMID:15089423
NSDL National Science Digital Library
NCTM Illuminations
2000-01-01
This tool allows you to learn about various geometric solids and their properties. You can manipulate each solid, seeing it from every angle. You can also color each shape to explore the number of faces, edges, and vertices. With that information, you are challenged to investigate the following question: For any polyhedron, what is the relationship between the number of faces, vertices, and edges?
Discrete Surface Modeling using Geometric Flows
Guoliang Xu; Qing Pan; Chandrajit L. Bajaj
2003-01-01
We use various nonlinear geometric partial dieren tial equations to ecien tly solve several surface modelling problems, including surface blending, N-sided hole lling and free-form surface tting. The nonlinear equations used include two second order o ws (mean curvature o w and average mean curvature o w), one fourth order o w (surface diusion o w) and a sixth order
Non-isothermal elastoviscoplastic analysis of planar curved beams
NASA Technical Reports Server (NTRS)
Simitses, G. J.; Carlson, R. L.; Riff, R.
1988-01-01
The development of a general mathematical model and solution methodologies, to examine the behavior of thin structural elements such as beams, rings, and arches, subjected to large nonisothermal elastoviscoplastic deformations is presented. Thus, geometric as well as material type nonlinearities of higher order are present in the analysis. For this purpose a complete true abinito rate theory of kinematics and kinetics for thin bodies, without any restriction on the magnitude of the transformation is presented. A previously formulated elasto-thermo-viscoplastic material constitutive law is employed in the analysis. The methodology is demonstrated through three different straight and curved beams problems.
Linearizing Intra-Train Beam-Beam Deflection Feedback
Smith, S.R.; /SLAC
2006-02-22
Beam-beam deflection feedback acting within the crossing time of a single bunch train may be needed to keep linear collider beams colliding at high luminosity. In a short-pulse machine such as the Next Linear Collider (NLC) this feedback must converge quickly to be useful. The non-linear nature of beam-beam deflection vs. beam-beam offset in these machines precludes obtaining both rapid convergence and a stable steady-state lock to beam offsets with a linear feedback algorithm. We show that a simply realizable programmable non-linear amplifier in the feedback loop can linearize the feedback loop, approximately compensating the beam-beam deflection non-linearity. Performance of a prototype non-linear amplifier is shown. Improvement of convergence and stability of the beam-beam feedback loop is simulated.
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.
Saberian, E.; Esfandyari-Kalejahi, A.; Rastkar-Ebrahimzadeh, A.; Afsari-Ghazi, M.
2013-03-15
The propagation of ion-acoustic (IA) solitons is studied in a plasma system, comprised of warm ions and superthermal (Kappa distributed) electrons in the presence of an electron-beam by using a hydrodynamic model. In the linear analysis, it is seen that increasing the superthermality lowers the phase speed of the IA waves. On the other hand, in a fully nonlinear investigation, the Mach number range and characteristics of IA solitons are analyzed, parametrically and numerically. It is found that the accessible region for the existence of IA solitons reduces with increasing the superthermality. However, IA solitons with both negative and positive polarities can coexist in the system. Additionally, solitary waves with both subsonic and supersonic speeds are predicted in the plasma, depending on the value of ion-temperature and the superthermality of electrons in the system. It is examined that there are upper critical values for beam parameters (i.e., density and velocity) after which, IA solitary waves could not propagate in the plasma. Furthermore, a typical interaction between IA waves and the electron-beam in the plasma is confirmed.
Nonlinear inelastic time-history analysis of truss structures
Huu-Tai Thai; Seung-Eock Kim
2011-01-01
This paper presents the nonlinear inelastic time-history analysis of truss structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on an updated Lagrangian formulation, while the material nonlinearity is captured by tracing an empirical stress–strain relationship in the elastoplastic range. The presented truss model is capable of capturing several failure modes of member such as buckling,
Geometric formulation of quantum mechanics
Hoshang Heydari
2015-03-01
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical and non-linear theory defined on a symplectic geometry. However, after invention of general relativity, we are convinced that geometry is physical and affect us in all scale. Hence the geometric formulation of quantum mechanics sought to give a unified picture of physical systems based on its underling geometrical structures, e.g., now, the states are represented by points of a symplectic manifold with a compatible Riemannian metric, the observable are real-valued functions on the manifold, and quantum evolution is governed by the symplectic flow that is generated by a Hamiltonian function. In this work we will give a compact introduction to main ideas of geometric formulation of quantum mechanics. We will provide the reader with the details of geometrical structures of both pure and mixed quantum states. We will also discuss and review some important applications of geometric quantum mechanics.
Incrementally small-deformation theory for nonlinear analysis of structural frames
Y. B. Yang; S. R. Kuo; Y. S. Wu
2002-01-01
An incrementally small-deformation theory that is physically self-explainable is presented for the large-displacement nonlinear analysis of structural frames. Strictly based on the assumption of small strains, small rotations, and small displacements within each incremental step, the elastic and geometric stiffness matrices for the beam element are derived from the force–displacement relations. Due consideration is taken of the 3D rotational behavior
Active vibration isolation with a MEMS device. Effects of nonlinearities on control efficiency
NASA Astrophysics Data System (ADS)
Meyer, Y.; Cumunel, G.
2015-08-01
This paper investigates piezoelectric and geometrical nonlinear effects on an active vibration isolation MEMS device. The objective is to study the impact of these nonlinearities on the vibration control efficiency. By confirming the importance of an accurate modeling of the microstructure, which is a laminated piezocomposite clamped–clamped beam in our example, we aim to develop high-performance active vibration isolation control. In this paper, the control law is an integral force feedback. The co-location condition is assumed because of the low device dimensions. First, a mathematical modeling is described and implemented into COMSOL Multiphysics software, with the governing equations of the beam taking into account geometric nonlinearities as well as piezoelectric nonlinearities. Then, active vibration control architecture is introduced. The active vibration control of the MEMS device is numerically implemented for different types of nonlinearity. The control performances of the classical linear structure are presented as a reference result. The impact of these nonlinearities on the control efficiency is presented and discussed.
NASA Astrophysics Data System (ADS)
Kirsanov, A. V.; Yarovoi, V. V.
1997-03-01
A study is reported of a system, making use of four-wave mixing with feedback (FWMF), for high-quality phase conjugation of speckle-inhomogeneous radiation. The system includes a hologram formed on the basis of nonlinearity of gain saturation. A theoretical analysis is made of selective capabilities of a 'short' hologram, whose length is less than the longitudinal correlation lengths of the 'write' waves used to form it. The statistical-average values of the parameters of modes in an FWMF cavity are determined. The experimental results obtained for a neodymium glass system show that the fidelity of phase conjugation of speckle beams with a divergence (5 — 25) ?diffr is 80%. The maximum energy of the phase-conjugated component is 0.35 J and the maximum energy reflection coefficient of an FWMF mirror is 20.
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.
NASA Astrophysics Data System (ADS)
Omohundro, Stephen M.
1990-06-01
Emergent computation in the form of geometric learning is central to the development of motor and perceptual systems in biological organisms and promises to have a similar impact on emerging technologies including robotics, vision, speech, and graphics. This paper examines some of the trade-offs involved in different implementation strategies, focusing on the tasks of learning discrete classifications and smooth nonlinear mappings. The trade-offs between local and global representations are discussed, a spectrum of distributed network implementations are examined, and an important source of computational inefficiency is identified. Efficient algorithms based on k-d trees and the Delaunay triangulation are presented and the relevance to biological networks is discussed. Finally, extensions of both the tasks and the implementations are given.
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.
Geometrical expression of excess entropy production.
Sagawa, Takahiro; Hayakawa, Hisao
2011-11-01
We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states. PMID:22181372
Parallel processors and nonlinear structural dynamics algorithms and software
NASA Technical Reports Server (NTRS)
Belytschko, Ted
1989-01-01
A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.
NASA Technical Reports Server (NTRS)
1976-01-01
A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Kuchik, Igor E.
2015-05-01
We develop an explicit solution of the problem describing collinear four-waves mixing in medium with cubic nonlinear response. This solution is carried out for a set of Schrödinger equations using plane wave approximation under phase matching of interacting waves. This solution allows to provide full analysis of four-wave interaction modes in dependence of the problem parameters. We have shown, in particular, an existence of bistable mode for energy conversion from pump waves to signal wave under certain conditions. In general case, there are greater than 10 various modes of four-wave interaction. Knowledge about these modes is very important for spectroscopic experiment results understanding using four-waves mixing because its result depends on them in a strong way. Analytical solution and developed modes can explain complicated regime of four-wave interaction which may appear at high intensity of interacting waves.
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2005-01-01
An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.
NASA Astrophysics Data System (ADS)
He, Jun; Wei, YanYu; Park, GunSik
2013-07-01
A W-band traveling-wave tube (TWT) with double-groove loaded folded waveguide structure (FWSWS) has been designed and numerically modelled. The nonlinear performance of such a TWT is investigated by a particle-in-cell code MAGIC3D. Simulation results indicate this TWT produces a saturated electromagnetic power of 170.2 W at 90 GHz, corresponding to 36.9 dB gain and 69.6 mm interaction distance. A comparison between the novel folded waveguide traveling-wave tube (FWTWT) and the conventional one is also carried out to verify the effect of groove loading on the large-signal performance of TWT. Within the same working conditions, the double groove-loaded FWTWT could obtain higher saturated output power and gain in a shorter interaction length. The maximum of output power and gain of this novel TWT is 58.6% and 10% higher than those of the conventional FWTWT, while the 3-dB bandwidth of TWT is reduced to 4 GHz. With the additional advantage of ease of fabrication based on micro-electro-mechanical systems (MEMS) technologies, the double-groove loaded FWSWS is suitable for a millimeter-wave TWT with high power capacity and gain.
NASA Astrophysics Data System (ADS)
Popa, Alexandru
2015-04-01
In a previous paper we proved a periodicity property of the Liénard-Wiechert equation in the case of the relativistic interaction between electromagnetic field and electron. This property predicts the existence of harmonics of the nonlinear Thomson scattered radiations in head on collisions between very intense laser beams and relativistic electron bunches. In this paper we present the properties of these radiations and show that our method for the calculation of the angular and spectral distributions of the backscattered radiations is in good agreement with the existing experimental data from literature. In the case of incident radiations having relativistic parameters of the order of few units and electron energies up to 100 MeV, our calculations predict the possibility of producing hard X-rays, having relatively high intensities, which are comparable to the intensities of the first harmonics, and energies higher than 1 MeV, using the current technology. Our theoretical model uses only one approximation, that of the neglecting of the radiative corrections.
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.
DISPERSIVE NONLINEAR GEOMETRIC OPTICS Phillipe DONNAT
Rauch, Jeffrey
is that the light forces the electrons in atoms and molecules to oscillate. The oscillating electrons emit light accurate approximate solutions to systems of hyperbolic partial differential equations which model short for the study of dispersion is wavelength ffl solutions of systems of partial differential operators in ffl
Modeling of delamination propagation in composite laminated beam structures
NASA Astrophysics Data System (ADS)
Harvey, C.; Wang, S.
2012-12-01
A numerical method is developed to predict delamination propagation in composite laminated beam structures under lateral and axial loads. Full geometrical nonlinearity is included in the development of beam elements and the interfaces are modeled with imaginary interface springs. The one step crack closure technique, a contact algorithm and tensor symmetrization are employed in the formulation. It is found that asymmetric composite beam elements suffer from membrane locking and this is completely solved in the work. Also, the mode partitioning results are different to those from the existing mode partition theory. A new theory is developed which shows the flaw in the existing theory and demonstrates the validity of the imaginary interface spring model. In general, excellent agreement with existing numerical and experimental results is observed.
Global Tracking Control Structures for Nonlinear Singularly Perturbed
Valasek, John
Singular Perturbation Theory Mathematical development Numerical Simulations Nonlinear six degree Literature Review Geometric Singular Perturbation Theory Mathematical Development & Stability Analysis Approach: Model-reduction via Geometric Singular Perturbation Theory Use coordinate transformation
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
Sandkuijl, Daaf; Cisek, Richard; Major, Arkady; Barzda, Virginijus
2010-01-01
We present a new laser system and nonlinear microscope, designed for differential nonlinear microscopy. The microscope features time-correlated single photon counting of multiphoton fluorescence generated by an alternating pulse-train of orthogonally polarized pulses. The generated nonlinear signal is separated using home-built electronics. Results are presented on fluorescence-detected nonlinear absorption linear anisotropy (FDNALA) of chloroplasts in Asparagus Sprengerii Regel and of Congo Red-stained cellulose. PMID:21258516
Transition from linear- to nonlinear-focusing regime in filamentation
NASA Astrophysics Data System (ADS)
Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin
2014-12-01
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.
Beam halo in high-intensity beams
Wangler, T.P.
1993-01-01
In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which in projection to the 2-D phase spaces results in a 2-component beam consisting of an inner core and a diffuse outer halo. The beam-halo is of concern for a next generation of cw, high-power proton linacs that could be applied to intense neutron generators for nuclear materials processing. The author describes what has been learned about beam halo and the evolution of space-charge dominated beams using numerical simulations of initial laminar beams in uniform linear focusing channels. Initial results are presented from a study of beam entropy for an intense space-charge dominated beam.
Beam halo in high-intensity beams
Wangler, T.P.
1993-06-01
In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which in projection to the 2-D phase spaces results in a 2-component beam consisting of an inner core and a diffuse outer halo. The beam-halo is of concern for a next generation of cw, high-power proton linacs that could be applied to intense neutron generators for nuclear materials processing. The author describes what has been learned about beam halo and the evolution of space-charge dominated beams using numerical simulations of initial laminar beams in uniform linear focusing channels. Initial results are presented from a study of beam entropy for an intense space-charge dominated beam.
Berry phase in nonlinear systems
Liu, J.; Fu, L. B. [Institute of Applied Physics and Computational Mathematics, Post Office Box 8009, Beijing 100088 (China) and Center for Applied Physics and Technology, Peking University, Beijing 100084 (China)
2010-05-15
The Berry phase acquired by an eigenstate that experienced a nonlinear adiabatic evolution is investigated thoroughly. The circuit integral of the Berry connection of the instantaneous eigenstate cannot account for the adiabatic geometric phase, while the Bogoliubov excitations around the eigenstates are found to be accumulated during the nonlinear adiabatic evolution and contribute a finite phase of geometric nature. A two-mode model is used to illustrate our theory. Our theory is applicable to Bose-Einstein condensate, nonlinear light propagation, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics.
On geometric factors for neutral particle analyzers
Stagner, L.; Heidbrink, W. W.
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
NASA Astrophysics Data System (ADS)
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.
Optimization of piezoelectric cantilever energy harvesters including non-linear effects
NASA Astrophysics Data System (ADS)
Patel, R.; McWilliam, S.; Popov, A. A.
2014-08-01
This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations.
Nonlinear springs with applications to flow regulation valves and mechanisms
Freeman, David Calvin
2008-01-01
This thesis focuses on the application of nonlinear springs for fluid flow control valves where geometric constraints, or fabrication technologies, limit the use of available solutions. Types of existing nonlinear springs ...
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.
Perturbation approach to dispersion curves calculation for nonlinear Lamb waves
NASA Astrophysics Data System (ADS)
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2015-05-01
Analysis of elastic wave propagation in nonlinear media has gained recent research attention due to the recognition of their amplitude-dependent behavior. This creates opportunities for increased accuracy of damage detection and localization, development of new structural monitoring strategies, and design of new structures with desirable acoustic behavior (e.g., amplitude-dependent frequency bandgaps, wave beaming, and filtering). This differs from more traditional nonlinear analysis approaches which target the prediction of higher harmonic growth. Of particular interest in this work is the analysis of amplitude-dependent shifts in Lamb wave dispersion curves. Typically, dispersion curves are calculated for nominally linear material parameters and geometrical features of a waveguide, even when the constitutive law is nonlinear. Instead, this work employs a Lindstedt - Poincare perturbation approach to calculate amplitude-dependent dispersion curves, and shifts thereof, for nonlinearly-elastic plates. As a result, a set of first order corrections to frequency (or equivalently wavenumber) are calculated. These corrections yield significant amplitude dependence in the spectral characteristics of the calculated waves, especially for high frequency waves, which differs fundamentally from linear analyses. Numerical simulations confirm the analytical shifts predicted. Recognition of this amplitude-dependence in Lamb wave dispersion may suggest, among other things, that the analysis of guided wave propagation phenomena within a fully nonlinear framework needs to revisit mode-mode energy flux and higher harmonics generation conditions.
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.
Collective beam-beam effects in hadron colliders
Shi; Yao
2000-07-01
Collective beam-beam effects in hadron colliders were studied with a strong-strong beam-beam simulation on the CERN Large Hadron Collider, including multipole field errors in the lattice and beam-beam interactions at two high-luminosity interaction points. It was found that the beam-beam interaction could result in two distinct dynamics for hadron beams: a slow beam-size growth and an unstable beam-centroid oscillation. The instability of the beam-centroid oscillation has typical characteristics of the chaotic transport, i. e., the amplitude increase of the oscillation consists of slow escape from the remnants of invariant manifolds and fast diffusion in fully developed chaotic regions. The simulation results indicate that there is a threshold of the beam-beam parameter below which no unstable beam-centroid motion was observed. The escape rate of the unstable beam-centroid motion, on the other hand, increases with the nonlinear field errors in the lattice. As the slow beam-size growth is strongly enhanced by the beam-centroid oscillation, an elimination of the centroid motion with feedback can effectively suppress the beam-size growth. No steady state of coherent beam-beam oscillation was observed. PMID:11088586
Geometrical method of decoupling
NASA Astrophysics Data System (ADS)
Baumgarten, C.
2012-12-01
The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E?, B?, and P?, which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of) transformations must be symplectic and hence canonical. When used iteratively, the decoupling algorithm can also be applied to n-dimensional systems and requires O(n2) iterations to converge to a given precision.
Coherent beam-beam effects in storage ring colliders
NASA Astrophysics Data System (ADS)
Jin, Lihui
In storage-ring colliders, it has been a first priority to achieve the highest possible luminosity in order to provide adequate physical data for research in high-energy and nuclear physics. The luminosity is usually limited by beam-beam effects especially in the case of high-intensity beams. Therefore understanding beam-beam effects is important to achieve high luminosity in storage-ring colliders. Theoretically, a complete understanding of beam-beam effects requires a relevant solution of the nonlinear Vlasov equation that describes the evolution of phase-space distributions of beam particles. Unfortunately no analytic method of solving the Vlasov equation in the relevant conditions of a storage-ring is currently available unless some approximations (linearization) are made. However those approximations can distort the genuine picture of the beam dynamics especially in the nonlinear regime (nonintegrable) of the Vlasov equation. On the other hand, the advance of computer technology and computational physics has made it possible to study beam-beam effects with numerical simulation in a scenario that is much closer to a real situation. A self-consistent beam-beam simulation code has therefore been developed using the particle-in-cell method. In the simulation, both head-on and long-range beam-beam interactions as well as multipole error fields in magnets of an accelerator can be included. The simulation results have been compared with the experiments in the HERA, which showed a remarkable agreement in the luminosity, emittance and coherent beam-beam tune shifts. In this dissertation, some important aspects of beam-beam effects were studied mainly by beam-beam simulations. Topics include the coherent beam-beam tune shift of the unsymmetrical beam-beam interaction, the coherent beam-beam instability of the strong-weak beam-beam interaction, the importance of the beam-beam tune spread to the coherent (collective) beam-beam instability and the wire compensation of long-range beam-beam interactions in the LHC.
Nonlinear dynamic modeling of micromachined microwave switches
E. K. Chan; E. C. Kan; R. W. Dutton; P. M. Pinsky
1997-01-01
Nonlinear dynamic lumped models of micromachined microwave switches have been formulated and successfully applied to analyses of transient characteristics and geometrical scaling. Parameter extraction through electrical measurements is summarized. The results are compared to transient quasi-2D simulations
Multipole Compensation of Long-Range Beam-Beam Interactions
NASA Astrophysics Data System (ADS)
Shi, J.; Jin, L.; Kheawpum, O.
2003-12-01
In cases of multi-bunches operation in storage-ring colliders, serious long-range beam-beam effects could be due to many parasitic collisions that are localized inside interaction regions or/and distributed around the ring. To reduce the long-range beam-beam effects, the compensation of long-range beam-beam interaction with magnetic multipole correctors based on minimizations of nonlinearities in one-turn or sectional maps of a collider has been proposed. With LHC as a test model, the effectiveness of the multipole compensation of long-range beam-beam interactions was studied in terms of improvement of dynamic aperture and reduction of emittance growth. The study showed that both the local and global compensation of long-range beam-beam interactions with magnetic multipole correctors is very effective in increasing the dynamic aperture and improving the linearity of the phase-space region relevant to the beams.
Pescara benchmarks: nonlinear identification
NASA Astrophysics Data System (ADS)
Gandino, E.; Garibaldi, L.; Marchesiello, S.
2011-07-01
Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled "Monitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing", financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.
Discontinuous Buckling of Wide Beams and Metabeams
NASA Astrophysics Data System (ADS)
Coulais, Corentin; Overvelde, Johannes T. B.; Lubbers, Luuk A.; Bertoldi, Katia; van Hecke, Martin
2015-07-01
We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams—beams made from a mechanical metamaterial—exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally.
Discontinuous Buckling of Wide Beams and Metabeams.
Coulais, Corentin; Overvelde, Johannes T B; Lubbers, Luuk A; Bertoldi, Katia; van Hecke, Martin
2015-07-24
We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams-beams made from a mechanical metamaterial-exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally. PMID:26252687
Discontinuous Buckling of Wide Beams and Metabeams
Corentin Coulais; Johannes T. B. Overvelde; Luuk A. Lubbers; Katia Bertoldi; Martin van Hecke
2015-08-11
We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams ---beams made from a mechanical metamaterial--- exhibit discontinuous buckling, an unstable form of buckling where the post-buckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit increasingly negative post-buckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as $1\\%$ numerically and $5\\%$ experimentally.
Transverse Angular Momentum and Geometric Spin Hall Effect of Light
NASA Astrophysics Data System (ADS)
Aiello, Andrea; Lindlein, Norbert; Marquardt, Christoph; Leuchs, Gerd
2009-09-01
We present a novel fundamental phenomenon occurring when a polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam. This effect has a purely geometric nature and amounts to a polarization-dependent shift or split of the beam intensity distribution evaluated as the time-averaged flux of the Poynting vector across the plane of observation. We demonstrate that such a shift is unavoidable whenever the beam possesses a nonzero transverse angular momentum. This latter result has general validity and applies to arbitrary systems such as, e.g., electronic and atomic beams.
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
Reconciling Geometric Planners with
North Carolina at Chapel Hill, University of
Search #12;#12;Manipulation #12;Manipulation Perception Systems Navigation Learning Parallelism Control 3;#12;#12;#12;Physical Manipulation Geometric Search Manipulation Perception Systems Navigation Learning Parallelism-away Sweep #12;Physical Manipulation Geometric Search Manipulation Perception Systems Navigation Learning
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
NASA Astrophysics Data System (ADS)
Davidson, Ronald C.; Qin, Hong; Lee, W. Wei-Li
1999-11-01
This paper considers an intense nonneutral ion beam propagating in the z-direction through a periodic focusing quadrupole field with transverse focusing force, F_foc=-? _q(s)(xhat e_x-yhat e_y), on the beam ions. Here, (?_q(s+S)=?_q(s) ) is the oscillatory focusing coefficient with period (S=const.) A third-order Hamiltonian averaging technique using a canonical transformation is employed to transform away the rapidly oscillating terms. This leads to a Hamiltonian, \\cal H(tilde X,tilde Y,tilde X',tilde Y',s)=(1/2)(tilde X'^2+tilde Y'^2)+(1/2)? _fq(tilde X^2+tilde Y^2)+? (tilde X,tilde Y,s), in the transformed variables (tilde X,tilde Y,tilde X',tilde Y'), where the focusing coefficient ? _fq is constant, and many solutions and properties of the nonlinear Vlasov-Maxwell system are well known. When known equilibrium solutions in the transformed variables are transformed back to the laboratory fame, they generate approximate periodically-focused solutions which are much more general than the Kapchinskij-Vladimirskij equilibrium. A wide range of intense beam equilibrium and stability properties are presented using this newly developed Hamiltonian averaging technique.
Makov, Yu N; Sánchez-Morcillo, V J; Camarena, F; Espinosa, V
2008-12-01
A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f=1 MHz, aperture radius a=1.5 cm and geometrical focal distance R=11.7 cm, corresponding to a Fresnel number N(F)=1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions. PMID:18442837
Astrometry without Geometric Distortion
NASA Astrophysics Data System (ADS)
Peng, Qingyu; Wang, Na; Peng, Huanwen; Zhang, Qingfeng; Li, Zhan
2015-08-01
Geometric distortion often exists in an astronomical CCD image even though a long focal length telescope is used. Two algorithms are developed to solve the pattern of geometric distortion and are tested based on many dithering CCD images observed at Yunnan Observatory using the 1 m telescope and 2.4 m telescope. Our results have shown that the astrometry for some moving targets such as an asteroid (Apophis) or a planetary natural satellite (Phoebe) is improved significantly after removing the geometric distortion in each CCD image. The algorithms can be also extended to applying to other telescopes for the purpose of precise astrometry or the check of positional propriety of a telescope.
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.
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-07-15
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. PMID:26076671
Polarimetric measurements of single-photon geometric phases
NASA Astrophysics Data System (ADS)
Ortíz, O.; Yugra, Y.; Rosario, A.; Sihuincha, J. C.; Loredo, J. C.; Andrés, M. V.; De Zela, F.
2014-01-01
We report polarimetric measurements of geometric phases that are generated by evolving polarized photons along nongeodesic trajectories on the Poincaré sphere. The core of our polarimetric array consists of seven wave plates that are traversed by a single-photon beam. With this array, any SU(2) transformation can be realized. By exploiting the gauge invariance of geometric phases under U(1) local transformations, we nullify the dynamical contribution to the total phase, thereby making the latter coincide with the geometric phase. We demonstrate our arrangement to be insensitive to various sources of noise entering it. This makes the single-beam, polarimetric array a promising, versatile tool for testing robustness of geometric phases against noise.
On solving certain nonlinear acoustics problems
NASA Astrophysics Data System (ADS)
Rubina, L. I.; Ul'yanov, O. N.
2015-09-01
Previously the authors developed a geometric method for studying and solving nonlinear equations and systems of equations with partial derivatives. This method is used in this paper to obtain a series of exact solutions to certain nonlinear acoustics equations, as well as to reduce the system of Euler equations to systems of common differential equations.
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. Szulerecka, A.; Pedrak, A.
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.
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
Hierarchies of Geometric Entanglement
M. Blasone; F. Dell'Anno; S. De Siena; F. Illuminati
2008-05-28
We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows to discriminate among the different contributions. The extended measures are applied to the study of entanglement in different classes of $N$-qubit pure states. These classes include $W$ and $GHZ$ states, and their symmetric superpositions; symmetric multi-magnon states; cluster states; and, finally, asymmetric generalized $W$-like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between $GHZ$ and $W$ states, clarifying the original result of Wei and Goldbart that $W$ states possess a larger global entanglement than $GHZ$ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.
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.
Development of solution techniques for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Vos, R. G.; Andrews, J. S.
1974-01-01
Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.
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.
A geometric representation scheme suitable for shape optimization
NASA Technical Reports Server (NTRS)
Tortorelli, Daniel A.
1990-01-01
A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.
Comparison of beam-position-transfer functions using circular beam-position monitors
J. D. Gilpatrick
1997-01-01
A cylindrical beam-position monitor (BPM) used in many accelerator facilities has four electrodes on which beam-image currents induce bunched-beam signals. These probe-electrode signals are geometrically configured to provide beam-position information about two orthogonal axes. An electronic processor performs a mathematical transfer function (TF) on these BPM-electrode signals to produce output signals whose time-varying amplitude is proportional to the beam's vertical
Decentralized nonlinear optimal excitation control
Lu, Q.; Sun, Y. [Tsinghua Univ., Beijing (China). Dept. of Electrical Engineering] [Tsinghua Univ., Beijing (China). Dept. of Electrical Engineering; Xu, Z.; Mochizuki, T. [Kyushu Inst. of Tech., Kitakyushu (Japan). Dept. of Electrical Engineering] [Kyushu Inst. of Tech., Kitakyushu (Japan). Dept. of Electrical Engineering
1996-11-01
A design method to lay emphasis on differential geometric approach for decentralized nonlinear optimal excitation control of multimachine systems is suggested in this paper. The control law achieved is implemented via purely local measurements. Moreover, it is independent of the parameters of power networks. Simulations are performed on a six-machine system. It has been demonstrated that the nonlinear optimal excitation control could adapt to the conditions under large disturbances. Besides, this paper has verified that the optimal control in the sense of LQR principle for the linearized system is equivalent to an optimal control in the sense of a quasi-quadratic performance index for the primitive nonlinear control system.
Nonlinear vibrations of moderately thick orthotropic shallow spherical shells
M. Sathyamoorthy
1995-01-01
This paper deals with the effects of large amplitude on the flexural vibrations of shallow spherical shells. A shallow shell theory is presented for the geometrically nonlinear dynamic analysis of moderately thick orthotropic spherical shells. Transverse shear deformation and rotatory inertia effects are incorporated into the nonlinear equations of motion by means of tracing constants. The coupled set of nonlinear
Nonlinear aerostatic stability analysis of Jiang Yin suspension bridge
Jin Cheng; Jian-Jing Jiang; Ru-Cheng Xiao; Hai-Fan Xiang
2002-01-01
A nonlinear aerostatic stability analysis of the Jiang Yin suspension bridge over the Yangtse River in China is carried out in this paper. We propose a new nonlinear method to analyze aerostatic stability of suspension bridges, based on both the three components of wind loads and geometric nonlinearity. A computer program NASAB, based on the proposed method, has been developed.
NASA Technical Reports Server (NTRS)
Simitses, George J.; Carlson, Robert L.; Riff, Richard
1991-01-01
The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.
The hyperbolic geometric flow on Riemann surfaces
Liu, De-Xing; Xu, De-Liang
2007-01-01
In this paper the authors study the hyperbolic geometric flow on Riemann surfaces. This new nonlinear geometric evolution equation was recently introduced by the first two authors motivated by Einstein equation and Hamilton's Ricci flow. We prove that, for any given initial metric on ${\\mathbb{R}}^{2}$ in certain class of metrics, one can always choose suitable initial velocity symmetric tensor such that the solution exists for all time, and the scalar curvature corresponding to the solution metric $g_{ij}$ keeps uniformly bounded for all time. If the initial velocity tensor does not satisfy the condition, then the solution blows up at a finite time, and the scalar curvature $R(t,x)$ goes to positive infinity as $(t,x)$ tends to the blowup points, and a flow with surgery has to be considered. The authors attempt to show that, comparing to Ricci flow, the hyperbolic geometric flow has the following advantage: the surgery technique may be replaced by choosing suitable initial velocity tensor. Some geometric pro...
Wave Function as Geometric Entity
NASA Astrophysics Data System (ADS)
Lev, Bohdan I.
A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. Interference of electrons whose wave functions are represented by geometric entities is considered. New experiments concerning the geometric nature of electrons are proposed.
Geometric reconstruction methods for electron tomography
Andreas Alpers; Richard J. Gardner; Stefan König; Robert S. Pennington; Chris B. Boothroyd; Lothar Houben; Rafal E. Dunin-Borkowski; Kees Joost Batenburg
2013-02-06
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and nonlinear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full $180^\\circ$ tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire.
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.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly. PMID:25507310
Inflation from geometrical tachyons
Thomas, Steven; Ward, John [Department of Physics, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom)
2005-10-15
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Inflation from Geometrical Tachyons
Steven Thomas; John Ward
2005-10-04
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS $D3$-brane in the background geometry due to $k$ parallel $NS$5-branes arranged around a ring of radius $R $. Due to the fact that the mass of this geometrical tachyon field is $\\sqrt{2/k} $ times smaller than the corresponding open-string tachyon mass, we find that the slow roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly. PMID:25420326
Inflation from geometrical tachyons
NASA Astrophysics Data System (ADS)
Thomas, Steven; Ward, John
2005-10-01
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is 2/k times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Prediction of angle beam ultrasonic testing signals using multi-Gaussian beams
NASA Astrophysics Data System (ADS)
Kim, Hak-Joon; Song, Sung-Jin
2002-05-01
Interpretation of angle beam ultrasonic testing (UT) signals from welded joints is quite often very difficult due to the presence of non-relevant signals from geometrical reflectors. To provide the necessary information for the reliable interpretation of UT signals, quantitative prediction of geometrical reflection signals is strongly desired. To address such a need, a systematic way is proposed using multi-Gaussian beams, and its performance is demonstrated by predicting angle beam UT signals from geometrical reflectors such as corners and counter bores were predicted with initial experimental validation.
Software for free-space beam propagation
Thomas J. Bruegge; Matthew P. Rimmer; James D. Targove
1999-01-01
Software has been developed to propagate uniform or non- uniform beams through an optical system using diffraction techniques. The optical system can be divided into regions where geometrical ray tracing is appropriate and regions where diffraction propagation is necessary. This combines the accuracy of diffraction propagation with the speed of geometrical ray tracing to obtain accurate diffraction analyses at any
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
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.
Aerospace plane guidance using geometric control theory
NASA Technical Reports Server (NTRS)
Van Buren, Mark A.; Mease, Kenneth D.
1990-01-01
A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.
Nonlinear vibrational microscopy
Holtom, Gary R. (Richland, WA); Xie, Xiaoliang Sunney (Richland, WA); Zumbusch, Andreas (Munchen, DE)
2000-01-01
The present invention is a method and apparatus for microscopic vibrational imaging using coherent Anti-Stokes Raman Scattering or Sum Frequency Generation. Microscopic imaging with a vibrational spectroscopic contrast is achieved by generating signals in a nonlinear optical process and spatially resolved detection of the signals. The spatial resolution is attained by minimizing the spot size of the optical interrogation beams on the sample. Minimizing the spot size relies upon a. directing at least two substantially co-axial laser beams (interrogation beams) through a microscope objective providing a focal spot on the sample; b. collecting a signal beam together with a residual beam from the at least two co-axial laser beams after passing through the sample; c. removing the residual beam; and d. detecting the signal beam thereby creating said pixel. The method has significantly higher spatial resolution then IR microscopy and higher sensitivity than spontaneous Raman microscopy with much lower average excitation powers. CARS and SFG microscopy does not rely on the presence of fluorophores, but retains the resolution and three-dimensional sectioning capability of confocal and two-photon fluorescence microscopy. Complementary to these techniques, CARS and SFG microscopy provides a contrast mechanism based on vibrational spectroscopy. This vibrational contrast mechanism, combined with an unprecedented high sensitivity at a tolerable laser power level, provides a new approach for microscopic investigations of chemical and biological samples.
Arbitrary accelerating micron-scale caustic beams in two and three dimensions
NASA Astrophysics Data System (ADS)
Froehly, L.; Courvoisier, F.; Mathis, A.; Jacquot, M.; Furfaro, L.; Giust, R.; Lacourt, P. A.; Dudley, J. M.
2011-08-01
We generate arbitrary convex accelerating beams by direct application of an appropriate spatial phase profile on an incident Gaussian beam. The spatial phase calculation exploits the geometrical properties of optical caustics and the Legendre transform. Using this technique, accelerating sheet caustic beams with parabolic profiles (i.e. Airy beams), as well as quartic and logarithmic profiles are experimentally synthesized from an incident Gaussian beam, and we show compatibility with material processing applications using an imaging system to reduce the main intensity lobe at the caustic to sub-10 micron transverse dimension. By applying additional and rotational spatial phase, we generate caustic-bounded sheet and volume beams, which both show evidence of the recently predicted effect of abrupt autofocussing. In addition, an engineered accelerating profile with femtosecond pulses is applied to generate a curved zone of refractive index modification in glass. These latter results provide proof of principle demonstration of how this technique may yield new degrees of freedom in both nonlinear optics and femtosecond micromachining.
NASA Astrophysics Data System (ADS)
Zhu, Y.; Zhang, Y. X.
2010-08-01
A simple and shear-flexible rectangular composite layered plate element and nonlinear finite element analysis procedures are developed in this paper for nonlinear analysis of fiber reinforced plastic (FRP)-reinforced concrete slabs. The composite layered plate element is constructed based on Mindlin-Reissner plate theory and Timoshenko’s composite beam functions, and transverse shear effects and membrane-bending coupling effects are accounted for. Both geometric nonlinearity and material nonlinearity of the materials, which incorporates tension, compression, tension stiffening and cracking of the concrete, are included in the new model. The developed element and the nonlinear finite element analysis procedures are validated by comparing the computed numerical results of numerical examples with those obtained from experimental investigations and from the commercial finite element analysis package ABAQUS. The element is then employed to investigate the nonlinear structural behavior and the cracking progress of a clamped two-way FRP-reinforced concrete slab. The influences of reinforcement with different materials, ratio and layout in tension or compressive regions on structural behavior of the clamped slabs are investigated by parametric studies.
High current beam transport with multiple beam arrays
Kim, C.H.
1985-05-01
Highlights of recent experimental and theoretical research progress on the high current beam transport of single and multiple beams by the Heavy Ion Fusion Accelerator Research (HIFAR) group at the Lawrence Berkeley Laboratory (LBL) are presented. In the single beam transport experiment (SBTE), stability boundaries and the emittance growth of a space charge dominated beam in a long quadrupole transport channel were measured and compared with theory and computer simulations. Also, a multiple beam ion induction linac (MBE-4) is being constructed at LBL which will permit study of multiple beam transport arrays, and acceleration and bunch length compression of individually focused beamlets. Various design considerations of MBE-4 regarding scaling laws, nonlinear effects, misalignments, and transverse and longitudinal space charge effects are summarized. Some aspects of longitudinal beam dynamics including schemes to generate the accelerating voltage waveforms and to amplify beam current are also discussed.
Lin, Ming C.
Geometric Sound Propagation Micah Taylor #12;Sound propagation Given a sound source in a scene arrive at the listener #12;Sound propagation Sound travels slow 344 m/s Specular reflections Perfect reflection Diffraction Sounds `bends' around corners #12;Sound propagation Doppler effect Change in frequency
1500 System Geometric Dictionary.
ERIC Educational Resources Information Center
Peloquin, Paul V.
A general description is provided of the "geometric dictionary," a graphic display aid, used by the Computer-Assisted Instruction Laboratory at the Pennsylvania State University. The purpose of the description is to enable the reader to duplicate and use the dictionary on any cathode ray tube terminal of the IBM 1500 system. The major advantages…
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…
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…
Driven geometric phase gates with trapped ions
NASA Astrophysics Data System (ADS)
Lemmer, A.; Bermudez, A.; Plenio, M. B.
2013-08-01
We describe a hybrid laser-microwave scheme to implement two-qubit geometric phase gates in crystals of trapped ions. The proposed gates can attain errors below the fault-tolerance threshold in the presence of thermal, dephasing, laser-phase and microwave-intensity noise. Moreover, our proposal is technically less demanding than previous schemes, since it does not require a laser arrangement with interferometric stability. The laser beams are tuned close to a single vibrational sideband to entangle the qubits, while strong microwave drivings provide the geometric character to the gate, and thus protect the qubits from these different sources of noise. A thorough analytic and numerical study of the performance of these gates in realistic noisy regimes is presented.
NONLINEAR SYSTEM IDENTIFICATION OF A MOORED STRUCTURAL SYSTEM S. Narayanan and S.C.S. Yim
Yim, Solomon C.
NONLINEAR SYSTEM IDENTIFICATION OF A MOORED STRUCTURAL SYSTEM S. Narayanan and S.C.S. Yim Ocean the practical application of a multiple- input/single-output nonlinear system identification technique on ocean structural systems. An ocean structure exhibiting nonlinear behavior due to geometric nonlinearity of mooring
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.
Geometrical aspects of quantum spaces
Ho, P.M. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
NASA Astrophysics Data System (ADS)
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: ?SR measurements on single crystals Oren Ofer, Amit Keren, Jess H Brewer, Tianheng H Han and Young S Lee Classical topological order in kagome ice Andrew J Macdonald, Peter C W Holdsworth and Roger G Melko Magnetic phase diagrams of classical triangular and kagome antiferromagnets M V Gvozdikova, P-E Melchy and M E Zhitomirsky The ordering of XY spin glasses Hikaru Kawamura Dynamic and thermodynamic properties of the generalized diamond chain model for azurite Andreas Honecker, Shijie Hu, Robert Peters and Johannes Richter Classical height models with topological order Christopher L Henley A search for disorder in the spin glass double perovskites Sr2CaReO6 and Sr2MgReO6 using neutron diffraction and neutron pair distribution function analysis J E Greedan, Shahab Derakhshan, F Ramezanipour, J Siewenie and Th Proffen Order and disorder in the local and long-range structure of the spin-glass pyrochlore, Tb2Mo2O7 Yu Jiang, Ashfia Huq, Corwin H Booth, Georg Ehlers, John E Greedan and Jason S Gardner The magnetic phase diagram of Gd2Sn2O7 R S Freitas and J S Gardner Calculation of the expected zero-field muon relaxation rate in the geometrically frustrated rare earth pyrochlore Gd2Sn2O7 antiferromagnet P A McClarty, J N Cosman, A G Del Maestro and M J P Gingras Magnetic frustration in the disordered pyrochlore Yb2GaSbO7 J A Hodges, P Dalmas de Réotier, A Yaouanc, P C M Gubbens, P J C King and C Baines Titanium pyrochlore magnets: how much can be learned from magnetization measurements? O A Petrenko, M R Lees and G Balakrishnan Local susceptibility of the Yb2Ti2O7 rare earth pyrochlore computed from a Hamiltonian with anisotropic exchange J D Thompson, P A McClarty and M J P Gingras Slow and static spin correlations in Dy2 + xTi2 - xO7 - ? J S Gardner, G Ehlers, P Fouquet, B Farago and J R Stewart The spin ice Ho2Ti2O7 versus the spin liquid Tb2Ti2O7: field-induced magnetic structures A P Sazonov, A Gukasov and I Mirebeau Magnetic monopole dynamics in spin ice L D C Jaubert and P C W Holdsworth
NASA Astrophysics Data System (ADS)
Lugiato, Luigi; Prati, Franco; Brambilla, Massimo
2015-03-01
Preface; Part I. Models, Propagation, Steady-State Phenomena: 1. Rate equation model for the laser; 2. Interaction of a system of two-level atoms with the electromagnetic field; 3. The Maxwell–Bloch equations; 4. Inclusion of the irreversible processes in the atomic equations; 5. Linear and nonlinear propagation in irreversible Maxwell–Bloch equations; 6. Optical nonlinearities: materials with quadratic nonlinearities; 7. Optical nonlinearities: materials with cubic nonlinearities; 8. Optical resonators: the planar ring cavity, empty cavity, linear cavity; 9. Nonlinear active ring cavity: the ring laser, stationary states; 10. The adiabatic elimination principle; 11. Nonlinear passive ring cavity: optical bistability; 12. Modal equations for the ring cavity: the single-mode model; 13. Single- and two-mode models; 14. Nonlinear dynamics in Fabry–Perot cavities; 15. Inhomogeneous broadening; 16. The semiconductor laser; 17. Laser without inversion and the effects of atomic coherence; Part II. Dynamical Phenomena, Instabilities, Chaos: 18. Some general aspects in nonlinear dissipative dynamical systems; 19. Special limits in the single-mode model; 20. The linear stability analysis of Maxwell–Bloch equations; 21. Adiabatic elimination in the complete Maxwell–Bloch equations; 22. Dynamical aspects in the laser; 23. Single- and multi-mode operation in inhomogeneously broadened lasers; 24. Dynamical aspects in optical bistability; 25. Self-pulsing in other optical systems; Part III. Transverse Optical Patterns: 26. Gaussian beams and modes of cavities with spherical mirrors; 27. General features about optical pattern formation in planar cavities; 28. The LL model; 29. Spatial patterns in cavities with spherical mirrors; 30. Cavity solitons; Appendixes; References; Index.
Ion-beam Plasma Neutralization Interaction Images
Igor D. Kaganovich; Edward Startsev; S. Klasky; Ronald C. Davidson
2002-04-09
Neutralization of the ion beam charge and current is an important scientific issue for many practical applications. The process of ion beam charge and current neutralization is complex because the excitation of nonlinear plasma waves may occur. Computer simulation images of plasma neutralization of the ion beam pulse are presented.
Geometric diffusion of quantum trajectories
NASA Astrophysics Data System (ADS)
Yang, Fan; Liu, Ren-Bao
2015-07-01
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.
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
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.
MESHLESS GEOMETRIC SUBDIVISION Carsten Moenning
MESHLESS GEOMETRIC SUBDIVISION By Carsten Moenning Facundo M´emoli Guillermo Sapiro Nira Dyn0436 Phone: 612/624-6066 Fax: 612/626-7370 URL: http://www.ima.umn.edu #12;Meshless Geometric Subdivision by introducing the notion of meshless, or point cloud, geometric subdivision. Our meshless subdivision approach
Multigrid Geometric Active Contour Models
George Papandreou; Petros Maragos
2007-01-01
ó Geometric active contour models are very popular PDE tools in image analysis and computer vision. We present a new multigrid algorithm for the fast evolution of level set- based geometric active contours and compare it with other established numerical schemes. We overcome the main bottleneck associated with most numerical implementations of geometric active contours, namely the need for very
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.
A geometric definition of mass
NASA Astrophysics Data System (ADS)
González-Martin, Gustavo
1994-12-01
An invariant definition of mass is given, within the context of a geometric unified theory, in terms of the geometric connection and the matter current. This geometric mass corresponds to the concept of self energy and leads to the mass parameter in Dirac's equation.
Limits: Geometric and Harmonic Series
NSDL National Science Digital Library
Illuminations National Council of Teachers of Mathematics
2010-05-26
A geometric series is a sum of numbers such that the ratio between consecutive terms is constant. For instance, 1/2 + 1/4 + 1/8 + … is a geometric series. In this resource you can set up various geometric series and see a visual representation of the successive terms and the corresponding sum of those terms.
Program for analysis of nonlinear equilibrium and stability (PANES)
NASA Technical Reports Server (NTRS)
Vos, R. G.
1975-01-01
PANES utilizes improved techniques for analysis of structures with material and geometric nonlinearities, including limit point and bifurcations behavior which occurs in buckling and collapse problems. Incremental loading, Newton-Raphson iteration, and higher order methods are used in program.
Causal And Geometric Relations
Shrader, Douglas W. Jr.
CAUSAL AND GEOMETRIC RELATIONS* Douglas W. Shrader, Jr. Is space curved? The discovery of Non-Euclidean geometries inspired several attempts to determine empirically the topology of physical space. Hans Reichenbach recognized that a number... of causal principles are presupposed in these experiments and suggested that, for geometry to be an empirical matter, we have to intro duce the requirement that no causal relations are vio lated (that there are no causal anomalies). Though objectionable...
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.
Observation of the Geometric Spin Hall Effect of Light
NASA Astrophysics Data System (ADS)
Korger, Jan; Aiello, Andrea; Chille, Vanessa; Banzer, Peter; Wittmann, Christoffer; Lindlein, Norbert; Marquardt, Christoph; Leuchs, Gerd
2014-03-01
The spin Hall effect of light (SHEL) is the photonic analogue of the spin Hall effect occurring for charge carriers in solid-state systems. This intriguing phenomenon manifests itself when a light beam refracts at an air-glass interface (conventional SHEL) or when it is projected onto an oblique plane, the latter effect being known as the geometric SHEL. It amounts to a polarization-dependent displacement perpendicular to the plane of incidence. In this work, we experimentally investigate the geometric SHEL for a light beam transmitted across an oblique polarizer. We find that the spatial intensity distribution of the transmitted beam depends on the incident state of polarization and its centroid undergoes a positional displacement exceeding one wavelength. This novel phenomenon is virtually independent from the material properties of the polarizer and, thus, reveals universal features of spin-orbit coupling.
Boyd, R.W. (Rochester Univ., NY (United States). Inst. of Optics)
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics.
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.
NASA Astrophysics Data System (ADS)
Silina, Kseniya G.; Kikot, Irina P.; Manevitch, Leonid I.
2015-03-01
We present analytical and numerical studies of nonstationary resonance processes in a system with four degrees of freedom. The system under consideration can be considered as one of the simplest geometrically nonlinear discrete models of an elastic beam supported by nonlinear elastic grounding support. Two symmetrically distributed discrete masses reflect the inertial properties of the beam, two angular springs simulate its bending stiffness. The longitudinal springs, as is usual in systems of oscillators, reflect the tensile stiffness and two transversal springs simulate the reaction of grounding support. Dealing with low-energy dynamics, we singled out the equations of transversal motion corresponding to the approximation of two coupled oscillators with nonlocal nonlinearity in elastic forces. We have analyzed this model using the concept of limiting phase trajectories (LPT). LPT's concept was recently developed to study the nonstationary resonance dynamics. An analytical description of intensive interparticle energy exchange was obtained in terms of nonsmooth functions, which is consistent with numerical results. We have identified two dynamic transitions the first of which corresponds to the instability of out-of-phase normal mode and the second one is a transition from the intense energy exchange to the energy localization on the initially excited oscillator. Special attention was paid to the influence of bending stiffness on the conditions that ensure the implementation of each of the dynamic transitions.
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
What Makes a Beam Shaping Problem Difficult?
ROMERO,LOUIS; DICKEY,FRED M.
2000-07-19
The authors have discussed the three factors that they believe are the most important in determining the difficulty of a beam shaping problem: scaling, smoothness, and coherence. The arguments have been almost completely based on considering how these factors influence beam shaping lenses that were designed using geometrical optics. However, they believe that these factors control the difficulty of beam shaping problems even if one does not base ones design strategy on geometrical optics. For example, they have shown that a lens designed using geometrical optics will not work well unless {beta} is large. However, they have also shown that if {beta} is small the uncertainty principle shows that it is impossible to do a good job of beam shaping no matter how one designs ones lens.
Representing geometrical knowledge.
Anderson, J A
1997-01-01
This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic. PMID:9304680
Controlling Second Harmonic Efficiency of Laser Beam Interactions
NASA Technical Reports Server (NTRS)
Barnes, Norman P. (Inventor); Walsh, Brian M. (Inventor); Reichle, Donald J. (Inventor)
2011-01-01
A method is provided for controlling second harmonic efficiency of laser beam interactions. A laser system generates two laser beams (e.g., a laser beam with two polarizations) for incidence on a nonlinear crystal having a preferred direction of propagation. Prior to incidence on the crystal, the beams are optically processed based on the crystal's beam separation characteristics to thereby control a position in the crystal along the preferred direction of propagation at which the beams interact.
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.
Regular and chaotic oscillations of a Timoshenko beam subjected to mechanical and thermal loadings
NASA Astrophysics Data System (ADS)
Warminska, Anna; Manoach, Emil; Warminski, Jerzy; Samborski, Sylwester
2015-09-01
Dynamics of a Timoshenko beam under an influence of mechanical and thermal loadings is analysed in this paper. Nonlinear geometrical terms and a nonuniform heat distribution are taken into account in the considered model. The mathematical model is represented by a set of partial differential equations (PDEs) which takes into account thermal and mechanical loadings. The problem is simplified to two PDEs and then reduced to ordinary differential equations (ODEs) by means of the Galerkin method taking into account three modes of a linear Timoshenko beam. Correctness of the analytical model is verified by a finite element method. Then, the nonlinear model is studied numerically by a continuation method or by a direct numerical integration of ODEs. An effect of the temperature distribution on the resonance near the first natural frequency and on stability of the solutions is presented. The increase of mechanical loading results in hardening of the resonance curve. Thermal loading may stabilise the beam dynamics when the temperature is decreased. The elevated temperature may transit dynamics from regular to chaotic oscillations.
Wang Shaomin; Lu Xuanhui; Lin Qiang; Zhao Daomu; Li Kang; Zhu Jingmin [Hangzhou Univ. (China). Dept. of Physics
1996-12-31
A new suggestion that there is a phase jump of {pi} in the boundary wave is put forward in this paper. This suggestion may be a supplement of Huygens-Fresnel principle. Based on this new suggestion, a series of new beams was invented, both outside and inside the laser cavity. Especially, a new CO{sub 2} laser with equivalent beam quality factor M{sub e}{sup 2} < 1 is achieved. It can be considered as the result of some controllable nonlinear self-focusing, and the physical background of deformed quantum mechanics.
Independent component analysis for beam measurement
NASA Astrophysics Data System (ADS)
Pang, Xiaoying
Independent component analysis (ICA) has been used for data mining in many branches of science. In beam physics, ICA can be applied to analyze the turn-by-turn beam position monitor (BPM) data of the transverse beam motion. Transverse beam motion consists of both linear betatron motion and the nonlinear motions which can be excited by higher order nonlinear magnetic elements. The diagnosis of the linear betatron motion has been developed by other methods like the model independent analysis (MIA) which is essentially built upon the principal component analysis (PCA). However, the detection and analysis of the nonlinear optics of an accelerator has never been effectively addressed. With the introduction of the ICA method which is inherently superior over the other traditional multivariate statistical methods like PCA or factor analysis, one can gain better accuracy in the linear betatron motion analysis and make the nonlinear optics diagnosis feasible. The narrow-band filtering of ICA provides us with accurate interpretation of both the linear and nonlinear betatron motions, especially the x2nu motion as we show in this thesis. For linear betatron oscillation, ICA can extract the betatron amplitude function and phase advance with high precision. For the nonlinear motion, the x 2nu motion uncovered by ICA agrees very well the analytical result derived from the Hill's equation. Based upon the study of both linear and nonlinear optics using ICA method, we finally propose two methods of beam-based measurement of the higher order nonlinear magnetic elements.
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.