NASA Astrophysics Data System (ADS)
Stojanović, Vladimir
2015-11-01
Geometrically nonlinear vibrations of a Timoshenko beam resting on a nonlinear Winkler and Pasternak elastic foundation with variable discontinuity are investigated in this paper. A p-version finite element method is developed for geometric nonlinear vibrations of a shear deformable beam resting on a nonlinear foundation with discontinuity. The elastic foundation has cubic nonlinearity with the shearing layer. In the study the p-element which comes from the use of explored special displacement shape functions for damaged beams is used and applied to a model with nonlinear foundation. The novelty of the present study lies in the easy generalisation of the approach of natural frequencies, general mode shapes (transverse and rotations of cross sections), and maximal deflections in nonlinear steady state vibrations of the shear deformable beam for any size and location of discontinuity of the nonlinear elastic support. A new set of nonlinear partial differential equations is developed, and they are solved in the time domain using the Newmark method for obtaining the amplitudes and deformed shapes of a beam in the steady state forced vibration regime. The present work consists of the comparison of the results with various stiffnesses of nonlinear elastic supports of the Winkler and Pasternak type.
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.
NASA Astrophysics Data System (ADS)
Rahmouni, A.; Beidouri, Z.; Benamar, R.
2013-09-01
The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the
NASA Astrophysics Data System (ADS)
Berczyński, Paweł; Kravtsov, Yury A.; Żeglinski, Grzegorz
2008-09-01
The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.
System level simulation of a micro resonant accelerometer with geometric nonlinear beams
NASA Astrophysics Data System (ADS)
Wenlong, Jiao; Weizheng, Yuan; Honglong, Chang
2015-10-01
Geometric nonlinear behaviors of micro resonators have attracted extensive attention of MEMS (micro-electro-mechanical systems) researchers, and MEMS transducers utilizing these behaviors have been widely researched and used due to the advantages of essentially digital output. Currently, the design of transducers with nonlinear behaviors is mainly performed by numerical method and rarely by system level design method. In this paper, the geometric nonlinear beam structure was modeled and established as a reusable library component by system level modeling and simulation method MuPEN (multi port element network). A resonant accelerometer was constructed and simulated using this model together with MuPEN reusable library. The AC (alternating current) analysis results of MuPEN model agreed well with the results of architect model and the experiment results shown in the existing reference. Therefore, we are convinced that the beam component based on MuPEN method is valid, and MEMS system level design method and related libraries can effectively model and simulate transducers with geometric nonlinear behaviors if appropriate system level components are available.
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.
NASA Astrophysics Data System (ADS)
Sarangi, S. K.; Ray, M. C.
2010-07-01
This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated composite beams using vertically reinforced 1-3 piezoelectric composite material as the material of the constraining layer of the ACLD treatment. A nonlinear finite element model has been developed for analyzing the ACLD of laminated symmetric and antisymmetric cross-ply and angle-ply composite beams integrated with such ACLD treatment. The von Kármán-type nonlinear strain-displacement relations and the first-order shear deformation theory are used for deriving this coupled electromechanical nonlinear finite element model. The Golla-Hughes-McTavish (GHM) method has been used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. The backbone curves of such a class of nonlinear systems are plotted to determine the excitation levels for causing geometrical nonlinearity. The numerical results reveal that the ACLD treatment significantly improves the damping characteristics of the cross-ply and antisymmetric angle-ply beams for suppressing the geometrically nonlinear transient vibrations of the beams.
NASA Astrophysics Data System (ADS)
Al-Qaisia, A. A.; Hamdan, M. N.
2013-09-01
This work presents an investigation on the effect of an initial geometric imperfection wavelength, amplitude and degree of localization on the in-plane nonlinear natural frequencies veering and mode localization of an elastic Euler-Bernoulli beam resting on a Winkler elastic foundation. The beam is assumed to be pinned-pinned with a linear torsional spring at one end. The effect of the axial force induced by mid-plane stretching is accounted for in the derivation of the mathematical model, due to its known importance and significant effect on the nonlinear dynamic behavior of the beam, as it was proved and presented in earlier investigations. The governing partial differential equation is discretized using the assumed mode method and the resulting nonlinear temporal equation was solved using the harmonic balance method to obtain results for the nonlinear natural frequencies and mode shapes. The results are presented in the form of characteristic curves which show the variations of the nonlinear natural frequencies of the first three modes of vibration, for a selected range of physical parameters like; torsional spring constant, elastic foundation stiffness and amplitude and wavelength of a localized and non-localized initial slack.
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.
Complex geometrical optics of nonlinear inhomogeneous fibres
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2011-03-01
This paper analyses the Gaussian beam (GB) evolution in nonlinear fibres with special attention given to the influence of the initial curvature of the wavefront and to the fibres' permittivity profile. The analysis is performed in the framework of paraxial complex geometrical optics (PCGO). This method reduces the problem of GB evolution in nonlinear and inhomogeneous media to the solution of ordinary differential equations, which can be easily solved either analytically or numerically. It is shown that the PCGO approach radically simplifies modelling of nonlinear phenomena in fibres as compared with standard methods of nonlinear optics such as the variational method approach and the method of moments. It is shown that the PCGO method readily supplies the solution of the nonlinear Schrödinger equation (NLS) for a self-focusing fibre with a focusing permittivity profile and provides a number of new results. The discussion on the interplay between the nonlinear (self-focusing and self-defocusing) and linear (focusing and defocusing) components of the total permittivity demonstrates the new possibilities to limit the collapse phenomenon in nonlinear fibres of Kerr type taking into account the effect of initial beam divergence.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2016-02-01
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less
Complex geometrical optics of inhomogeneous and nonlinear saturable media
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2013-05-01
The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing along curvilinear trajectory in smoothly inhomogeneous and nonlinear saturable media. CGO method reduces the problem of Gaussian beam propagation in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to the other methods of nonlinear optics such as: variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of the evolution of beam intensity and wave front cross-section along curvilinear central ray with torsion in weakly absorptive and nonlinear saturable graded-index fiber, where the effect of initial beam ellipticity is included into our description.
Stationary nonlinear Airy beams
Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.
2011-08-15
We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.
Geometrically nonlinear behavior of piezoelectric laminated plates
NASA Astrophysics Data System (ADS)
Rabinovitch, Oded
2005-08-01
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 the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.
Complex geometrical optics of Kerr type nonlinear media
NASA Astrophysics Data System (ADS)
Berczynski, P.; Kravtsov, Yu. A.; Sukhorukov, A. P.
2010-03-01
The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.
Geometrically nonlinear analysis of adhesively bonded joints
NASA Technical Reports Server (NTRS)
Dattaguru, B.; Everett, R. A., Jr.; Whitcomb, J. D.; Johnson, W. S.
1982-01-01
A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-relase rates (G1/G2) was found to be strongly affected by he adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements.
Precise formation of geometrically focused ion beams
Davydenko, V.I.; Ivanov, A.A.; Korepanov, S.A.; Kotelnikov, I.A.
2006-03-15
Geometrically focused intense neutral beams for plasma diagnostic consist of many elementary beams formed by a multiaperture ion-optical system and aimed at the focal point. In real conditions, some of the elementary beams may have increased angular divergence and/or deviate from the intended direction, thus diminishing the neutral beam density at the focus. Several improvements to the geometrical focusing are considered in the article including flattening of the plasma profile across the emission surface, using of quasi-Pierce electrodes at the beam periphery, and minimizing the deviation of the electrodes from the spherical form. Application of these measures to the neutral beam Russian diagnostic injector developed in Budker Institute of Nuclear Physics allows an increase of neutral beam current density in the focus by {approx}50%.
Geometric non-linear hexahedral elements with rotational DOFs
NASA Astrophysics Data System (ADS)
Meftah, Kamel; Zouari, Wajdi; Sedira, Lakhdar; Ayad, Rezak
2016-01-01
This paper presents an extension of two recently published conforming and non conforming eight-node hexahedral finite elements, presenting rotational degrees of freedom in addition to the classical displacement ones, to analyze geometric nonlinear problems. Their formulations are based on the so-called space fiber rotation concept that considers virtual rotations of a nodal fiber within the element which enhances the displacement vector approximation. To demonstrate the efficiency and accuracy of the proposed finite elements, several beam and shell nonlinear assessment tests are presented and the obtained results are principally compared with the classical first-order and second-order hexahedral elements responses as well as other advanced elements from the literature. In particular, it is shown that the proposed elements allow a correct prediction of the studied structures nonlinear behaviors including snap-through and snap-back instabilities and the accuracy of the non conforming element is close to the classical 20-node hexahedral element.
A Geometric Theory of Nonlinear Morphoelastic Shells
NASA Astrophysics Data System (ADS)
Sadik, Souhayl; Angoshtari, Arzhang; Goriely, Alain; Yavari, Arash
2016-08-01
Many thin three-dimensional elastic bodies can be reduced to elastic shells: two-dimensional elastic bodies whose reference shape is not necessarily flat. More generally, morphoelastic shells are elastic shells that can remodel and grow in time. These idealized objects are suitable models for many physical, engineering, and biological systems. Here, we formulate a general geometric theory of nonlinear morphoelastic shells that describes both the evolution of the body shape, viewed as an orientable surface, as well as its intrinsic material properties such as its reference curvatures. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell, the so-called material manifold. Geometric quantities attached to the surface, such as the first and second fundamental forms, are obtained from the metric of the three-dimensional body and its evolution. The governing dynamical equations for the body are obtained from variational consideration by assuming that both fundamental forms on the material manifold are dynamical variables in a Lagrangian field theory. In the case where growth can be modeled by a Rayleigh potential, we also obtain the governing equations for growth in the form of kinetic equations coupling the evolution of the first and the second fundamental forms with the state of stress of the shell. We apply these ideas to obtain stress-free growth fields of a planar sheet, the time evolution of a morphoelastic circular cylindrical shell subject to time-dependent internal pressure, and the residual stress of a morphoelastic planar circular shell.
Nonlinearity of Pancharatnam's geometric phase in polarizing interferometers.
Hils, B; Dultz, W; Martienssen, W
1999-08-01
Earlier investigations show a time-variable nonlinear shift of the fringe pattern in a polarizing interferometer while rotating a polarizer at the exit. This effect was identified as Pancharatnam's geometrical phase and proposed for applications in interferometry and fast optical switching devices. A heterodyne analysis attributes moving fringes to a frequency difference between the interfering beams; thus changing fringe velocities point to a dynamic frequency development within the period of the uniformly rotating analyzer. This explanation offends the intuition and we undertake an experimental and theoretical investigation of the effect to solve the paradox. We determine, e.g., the complete frequency and mode spectrum of an arbitrary state of polarization P0 behind a rotating linear analyzer and behind a rotating arbitrary linear birefringent plate. We find that, in spite of a fast changing phase in the interferometer, no other (higher) frequency components appear in the spectral distribution of the intensity at the exit than the double of the rotary frequency of the analyzer: phase nonlinearities are compensated for by intensity changes. Only a phase-sensitive detector like an array of photodetectors is able to observe the nonlinearity of Pancharatnam's geometrical phase. A single detector only finds a sinusoidal intensity variation. Our insight into these relations leads us to two new applications of Pancharatnam's phase: supersensitivity of a polarizing double beam interferometer with a video camera acting as a phase detector and external tuning of a Fizeau interferometer. PMID:11970029
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.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.
2015-09-15
Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.
2015-09-15
Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less
Nonlinear combining of laser beams.
Lushnikov, Pavel M; Vladimirova, Natalia
2014-06-15
We propose to combine multiple laser beams into a single diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. Beams with total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with Kerr nonlinearity. Random fluctuations during propagation eventually trigger a strong self-focusing event and produce a diffraction-limited beam carrying the critical power. PMID:24978503
Gaussian beam evolution in nonlinear inhomogeneous plasma
NASA Astrophysics Data System (ADS)
Berczynski, P.; Kravtsov, Yu. A.; Tikhonchuk, V.; Tikhonchuk
2014-04-01
The method of nonlinear complex geometrical optics (NCGO) is proposed in this paper for description of the evolution of a spatially narrow Gaussian beam (GB) in an inhomogeneous nonlinear plasma. NCGO method deals with first-order ordinary differential equations for the complex curvature of the wave front and for GB amplitude and for second-order ordinary differential equation for GB width. Thus, NCGO simplifies the description of GB diffraction and self-focusing effects as compared to the known methods of plasma physics and this way it can be assumed to be attractive and comprehensive approach in problems of plasma heating by electromagnetic waves. Moreover, we demonstrate in this paper some regularity for nonlinear inhomogeneous plasma in the framework of which central ray of a GB is not subjected to nonlinear refraction within NCGO method boundary applicability. On the contrary, the beam width, wave front curvature, and GB amplitude are modified by diffraction and self-focusing processes. General properties of the beam propagation are illustrated with results of numerical modeling for two particular cases: GB diffraction and self-focusing along curvilinear trajectory with torsion in axially symmetric plasma column and GB reflection from nonlinear inhomogeneous plasma layer. We prove in this paper that NCGO is new effective method of plasma physics, which can be applied for improvement of ray tracing techniques and plasma diagnostics.
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-β 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.
Gaussian beam diffraction in inhomogeneous and logarithmically saturable nonlinear media
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2012-08-01
The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, PCGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous and nonlinear media as compared to the numerical and analytical methods of nonlinear optics. The power of PCGO method is presented on the example of Gaussian beam evolution in logarithmically saturable medium with either focusing and defocusing refractive profile. Besides, the influence of initial curvature of the wave front on GB evolution in nonlinear saturable medium is discussed in this paper.
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.
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.
Influence of geometric nonlinearities on skin-stiffener interface stresses
NASA Technical Reports Server (NTRS)
Cohen, D.; Hyer, M. W.
1988-01-01
A method for computing skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The results indicate that the inclusion of geometric nonlinearities is very important for an accurate determination of the interface stresses. Membrane flattening of the panel tends to reduce the tendency of the stiffener to separate.
Geometric and material nonlinear analysis of tensegrity structures
NASA Astrophysics Data System (ADS)
Tran, Hoang Chi; Lee, Jaehong
2011-12-01
A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations, while the material nonlinearity is treated through elastoplastic stress-strain relationship. The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method. A computer program is developed to predict the mechanical responses of tensegrity systems under tensile, compressive and flexural loadings. Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program. The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications. On the other hand, its bending strength capacity is not sensitive to the self-stress level.
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.; Chandrashekhara, K.; Chao, W. C.
1993-01-01
This final technical report contains three parts: Part 1 deals with the 2-D shell theory and its element formulation and applications. Part 2 deals with the 3-D degenerated element. These two parts constitute the two major tasks that were completed under the grant. Another related topic that was initiated during the present investigation is the development of a nonlinear material model. This topic is briefly discussed in Part 3. To make each part self-contained, conclusions and references are included in each part. In the interest of brevity, the discussions presented are relatively brief. The details and additional topics are described in the references cited.
User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures
NASA Technical Reports Server (NTRS)
Whitcomb, J. D.; Dattaguru, B.
1984-01-01
GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.
Auto-focusing accelerating hyper-geometric laser beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-02-01
We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is ‘sharply’ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory.
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.
Harnessing geometric and magnetic nonlinearities in phononic meta-plates
NASA Astrophysics Data System (ADS)
Bilal, Osama; Foehr, Andre; Daraio, Chiara
Owing to their physical realization, locally resonant metamaterials retain narrow subwavelength band gaps. Moreover, the fixed geometry and dimensions of the unit cell set a hardbound on the central frequency of the operational bandwidth. Real-time tunable metamaterials extend the range of applications and further enable the realization of new sensors, filters, and switches. Our work harnesses the interaction between geometric nonlinearity and nonlinear magnetic potentials to engineer frequency-agile subwavelength band gaps. The concept is general and applicable to various metamaterials systems. Both numerical simulations and experimental realization of the proposed concept will be presented.
Radiometric versus geometric, linear, and nonlinear vignetting coefficient.
Duma, Virgil-Florin
2009-11-10
We analyze the vignetting phenomenon both for optical systems with objects placed at finite distances and for systems with objects at infinity. Four of the possible definitions of the vignetting coefficient k, only two of them existing in the literature, are discussed. We propose two new definitions, i.e., a nonlinear geometric coefficient that is, in part, an analytical model of the vignetting characterization using optical software and a radiometric vignetting coefficient. The object space of each type of optical systems is studied first, defining its characteristic light circles and cones. Several simplifying assumptions are made for each of the two cases considered to derive analytical equations of the vignetting coefficient and thus to determine the best definition to be used. A geometric vignetting coefficient with two expressions, a linear classical and easy-to-use one and a nonlinear, that we propose for both types of systems is obtained. This nonlinear geometric vignetting coefficient proves to be more adequate in modeling the phenomenon, but it does not entirely fit the physical reality. We finally demonstrate that the radiometric vignetting coefficient we define and derive as a view factor for both types of optical systems is the most appropriate one. The half vignetting level, necessary in most optical design procedures to obtain a satisfactory illumination level in the image plane, is also discussed. PMID:19904336
Exact and geometrical optics energy trajectories in twisted beams
NASA Astrophysics Data System (ADS)
Berry, M. V.; McDonald, K. T.
2008-03-01
Energy trajectories, that is, integral curves of the Poynting (current) vector, are calculated for scalar Bessel and Laguerre-Gauss beams carrying orbital angular momentum. The trajectories for the exact waves are helices, winding on cylinders for Bessel beams and hyperboloidal surfaces for Laguerre-Gauss beams. In the geometrical optics approximations, the trajectories for both types of beam are overlapping families of straight skew rays lying on hyperboloidal surfaces; the envelopes of the hyperboloids are the caustics: a cylinder for Bessel beams and two hyperboloids for Laguerre-Gauss beams.
NASTRAN nonlinear vibration analysis of beam and frame structures
NASA Technical Reports Server (NTRS)
Mei, C.; Rogers, J. L., Jr.
1975-01-01
A capability for the nonlinear vibration analysis of beam and frame structures suitable for use with NASTRAN level 15.5 is described. The nonlinearity considered is due to the presence of axial loads induced by longitudinal end restraints and lateral displacements that are large compared to the beam height. A brief discussion is included of the mathematical analysis and the geometrical stiffness matrix for a prismatic beam (BAR) element. Also included are a brief discussion of the equivalent linearization iterative process used to determine the nonlinear frequency, the required modifications to subroutines DBAR and XMPLBD of the NASTRAN code, and the appropriate vibration capability, four example problems are presented. Comparisons with existing experimental and analytical results show that excellent accuracy is achieved with NASTRAN in all cases.
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.
Geometrically nonlinear analysis of layered composite plates and shells
NASA Technical Reports Server (NTRS)
Chao, W. C.; Reddy, J. N.
1983-01-01
A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion.
Numerical treatment of a geometrically nonlinear planar Cosserat shell model
NASA Astrophysics Data System (ADS)
Sander, Oliver; Neff, Patrizio; Bîrsan, Mircea
2016-05-01
We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton's method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2013-12-01
In this paper complex geometrical optics (CGO) is applied to spatiotemporal evolution of 2D Gaussian wavepackets in nonlinear media of Kerr type. Instead of solving the commonly accepted nonlinear Schrödinger equation (NLS), we propose equations of geometrical optics: a complex eikonal equation and a complex transport equation. The eikonal equation lets us derive immediately the ordinary differential equations for spatial and temporal widths, omitting in this way the complicated variational process used in nonlinear optics. Moreover, the obtained CGO equations for actual spatial and temporal widths happen to be identical to those obtained by the variational method approach. From the transport equation we obtain the first order ordinary differential equation for complex amplitude evolution and the conservation principle for energy flux in the packet cross-section. For the combined effect of diffraction, anomalous dispersion and nonlinear refraction, we observe three types of solution for temporal and spatial widths of the packet propagating in a nonlinear medium of Kerr type: the diffraction/dispersion widening, the stationary solution and the solution under the effect of the spatiotemporal collapse. Moreover, we discuss the evolution of the 2D Gaussian wavepacket in a nonlinear inhomogeneous waveguide and we present conditions for stable propagation without the collapse effect. Under these conditions the wavepacket asymptotically approaches stationary solutions when the parameters of the waveguide change over the propagation distance. The paper also discusses the influence of initial spatial and temporal chirps on Gaussian wavepacket evolution in nonlinear media of Kerr type and in nonlinear inhomogeneous waveguides. Moreover, we notice that the equations for temporal and spatial widths of the 2D wavepacket have the same structure as the equations for the evolution of the elliptical Gaussian beam. Thus, the description of the 2D spatiotemporal wavepacket can be
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 flap-lag axial equations of a rotating beam
NASA Technical Reports Server (NTRS)
Kaza, K. R. V.; Kvaternik, R. G.
1977-01-01
It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.
Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections
NASA Technical Reports Server (NTRS)
Atilgan, Ali R.; Hodges, Dewey H.
1991-01-01
A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.
NASA Astrophysics Data System (ADS)
Hu, Zhan; Zheng, Gangtie
2016-08-01
A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.
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
NASA Astrophysics Data System (ADS)
Song, Pengchao
Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) of the F-16 have provided good support to the long-standing hypothesis that this phenomenon involves a nonlinear structural damping. A potential mechanism for the appearance of nonlinearity in the damping are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is first on extending nonlinear reduced order modeling (ROM) methods to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An identification approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software. The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.
Nonlinear instability and reliability analysis of composite laminated beams
NASA Astrophysics Data System (ADS)
Fereidooni, Alireza
The wide range of high performance engineering applications of composite laminated structures demands a proper understanding of their dynamics performance. Due to the complexity and nonlinear behaviour of such structures, developing a mathematical model to determine the dynamic instability boundaries is indispensable and challenging. The aim of this research is to investigate the dynamic behaviour of shear deformable composite laminated beams subjected to varying time conservative and nonconservative loads. The dynamic instability behaviour of non-conservative and conservative system are dissimilar. In case of conservative loading, the instability region intersects the loading axis, but in case of non-conservative loads the region will be increased with loading increases. The extended Hamilton's principle and the first order shear deformation theory are employed in this investigation to establish the integral form of the equation of motion of the beam. A five node beam model is presented to descritize the integral form of the governing equations. The model has the capability to capture the dynamic effects of the transverse shear stress, warping, and bending-twisting, bending-stretching, and stretching-twisting couplings. Also, the geometric and loading nonlinearities are included in the equation of system. The beam model incorporates, in a full form, the non-classical effects of warping on stability and dynamic response of symmetrical and unsymmetrical composite beams. In case of nonlinear elasticity, the resonance curves are bent toward the increasing exciting frequencies. The response of the stable beam is pure periodic and follow the loading frequency. When the beam is asymptotically stable the response of the beam is aperiodic and does not follow the loading frequency. In unstable state of the beam response frequency increases with time and is higher than the loading frequency, also the amplitude of the beam will increases, end to beam failure. The amplitude of
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.
NASA Astrophysics Data System (ADS)
Yang, J.; Yan, T.
2010-06-01
This paper investigates the nonlinear dynamic frequency response of a Timoshenko beam made of functionally graded materials (FGMs) with an open edge crack. The beam is clamped and subjected to an axial parametric excitation consisting of a static compressive force and a harmonic excitation force. Theoretical formulations are based on Timoshenko shear deformable beam theory, von Karman type geometric nonlinearity and rotational spring model. Hamilton's principle is used to derive the nonlinear partial differential equations which are transformed into nonlinear ordinary differential equation by using the Least Squares method and Galerkin technique. The nonlinear natural frequencies and excitation frequency-amplitude response curves are obtained by employing Runge-Kutta method and multiple scale method, respectively. A parametric study is conducted to study the effects of material property distribution, crack depth, crack location, excitation frequency, and slenderness ratio on the nonlinear dynamic characteristics of parametrically excited, cracked FGM Timoshenko beams.
gpICA: A Novel Nonlinear ICA Algorithm Using Geometric Linearization
NASA Astrophysics Data System (ADS)
Nguyen, Thang Viet; Patra, Jagdish Chandra; Emmanuel, Sabu
2006-12-01
A new geometric approach for nonlinear independent component analysis (ICA) is presented in this paper. Nonlinear environment is modeled by the popular post nonlinear (PNL) scheme. To eliminate the nonlinearity in the observed signals, a novel linearizing method named as geometric post nonlinear ICA (gpICA) is introduced. Thereafter, a basic linear ICA is applied on these linearized signals to estimate the unknown sources. The proposed method is motivated by the fact that in a multidimensional space, a nonlinear mixture is represented by a nonlinear surface while a linear mixture is represented by a plane, a special form of the surface. Therefore, by geometrically transforming the surface representing a nonlinear mixture into a plane, the mixture can be linearized. Through simulations on different data sets, superior performance of gpICA algorithm has been shown with respect to other algorithms.
Beams on nonlinear elastic foundation
Lukkassen, Dag; Meidell, Annette
2014-12-10
In order to determination vertical deflections and rail bending moments the Winkler model (1867) is often used. This linear model neglects several conditions. For example, by using experimental results, it has been observed that there is a substantial increase in the maximum rail deflection and rail bending moment when considering the nonlinearity of the track support system. A deeper mathematical analysis of the models is necessary in order to obtain better methods for more accurate numerical solutions in the determination of deflections and rail bending moments. This paper is intended to be a small step in this direction.
Thermo-electro-mechanical postbuckling of piezoelectric FG-CNTRC beams with geometric imperfections
NASA Astrophysics Data System (ADS)
Wu, Helong; Kitipornchai, Sritawat; Yang, Jie
2016-09-01
This paper presents thermo-electro-mechanical postbuckling analysis of geometrically imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) hybrid beams that are integrated with surface-bonded piezoelectric actuators. The material properties of FG-CNTRCs are assumed to be temperature-dependent and graded in the thickness direction. By using a generic imperfection function, various possible imperfections with different shapes and locations in the beam are considered. The theoretical formulations are based on the first-order shear deformation beam theory with von-Kármán nonlinearity. A differential quadrature approximation based iteration process is employed to obtain the postbuckling equilibrium path of piezoelectric FG-CNTRC hybrid beams under thermo-electro-mechanical loading. Parametric studies are conducted to examine the effect of geometric imperfection, distribution pattern and volume fraction of carbon nanotubes, temperature rise, actuator voltage, beam geometry and boundary conditions on the thermo-electro-mechanical postbuckling behaviour. The results show that the thermo-electro-mechanical postbuckling is considerably affected by the imperfection mode, half-wave number, location and amplitude, as well as the temperature rise and boundary conditions. The effect of applied actuator voltage is much less pronounced but tends to be relatively more noticeable as the slenderness ratio increases.
NASA Astrophysics Data System (ADS)
HARRAS, B.; BENAMAR, R.; WHITE, R. G.
2002-04-01
The geometrically non-linear free vibration of thin composite laminated plates is investigated by using a theoretical model based on Hamilton's principle and spectral analysis previously applied to obtain the non-linear mode shapes and resonance frequencies of thin straight structures, such as beams, plates and shells (Benamar et al. 1991Journal of Sound and Vibration149 , 179-195; 1993, 164, 295-316; 1990 Proceedings of the Fourth International Conference on Recent Advances in Structural Dynamics, Southampton; Moussaoui et al. 2000 Journal of Sound and Vibration232, 917-943 [1-4]). The von Kármán non-linear strain-displacement relationships have been employed. In the formulation, the transverse displacement W of the plate mid-plane has been taken into account and the in-plane displacements U and V have been neglected in the non-linear strain energy expressions. This assumption, quite often made in the literature has been adopted in reference [2] and (El Kadiri et al. 1999 Journal of Sound and Vibration228, 333-358 [5]), in the isotropic case and has been mentioned here because the results obtained have been found to be in very good agreement with those based on the hierarchical finite element method (HFEM). In a previous study, it was assumed, based on the analogy with the isotropic case, that the fundamental carbon fibre reinforced plastic (CFRP) plate non-linear mode shape could be well estimated, by using nine plate functions, obtained as products of clamped-clamped beam functions in the x and y directions, symmetric in both the length U001and width directions [3]. In the present work, a convergence study has been performed and has shown that, although such an assumption may yield a good estimate for the non-linear resonance frequency, 18 plate functions should be taken into account instead of nine in the first non-linear mode shape and associated bending stress patterns calculations. This allows the anisotropy induced by the fibre orientations to be taken
A geometric calibration method for cone beam CT systems
Yang, Kai; Kwan, Alexander L. C.; Miller, DeWitt F.; Boone, John M.
2006-06-15
Cone beam CT systems are being deployed in large numbers for small animal imaging, dental imaging, and other specialty applications. A new high-precision method for cone beam CT system calibration is presented in this paper. It uses multiple projection images acquired from rotating point-like objects (metal ball bearings) and the angle information generated from the rotating gantry system is also used. It is assumed that the whole system has a mechanically stable rotation center and that the detector does not have severe out-of-plane rotation (<2 deg.). Simple geometrical relationships between the orbital paths of individual BBs and five system parameters were derived. Computer simulations were employed to validate the accuracy of this method in the presence of noise. Equal or higher accuracy was achieved compared with previous methods. This method was implemented for the geometrical calibration of both a micro CT scanner and a breast CT scanner. The reconstructed tomographic images demonstrated that the proposed method is robust and easy to implement with high precision.
Active suppression of nonlinear composite beam vibrations by selected control algorithms
NASA Astrophysics Data System (ADS)
Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal
2011-05-01
This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.
Beam-Plasma Interaction and Nonlinear Effects
Yoon, Peter H.
2009-11-10
This paper presents a survey of perturbative nonlinear plasma theory known as the weak turbulence theory. After the basic concepts and methodology of the weak turbulence theory are outlined in sufficient detail, numerical solutions of the weak turbulence theory obtained in the context of the beam-plasma interaction are compared against particle-in-cell (PIC) numerical simulations. It is demonstrated that theory and PIC simulation are in excellent agreement.
Nonlinear wave scattering and electron beam relaxation
NASA Technical Reports Server (NTRS)
Muschietti, L.; Dum, C. T.
1991-01-01
The role played by nonlinear scattering during the relaxation of a warm electron beam is investigated through a numerical code based on kinetic equations. The code encompasses the quasi-linear wave-electron interaction and wave-wave scattering off ion clouds. Ions with velocities 2 nu sub i (nu sub i being the ion thermal velocity) are found to be the most efficient for scattering the Langmuir waves off their polarization clouds. The transfer rate of the spectrum out of resonance with the beam is larger by a factor 3 compared to usual estimates. The changes produced in the dispersion relation by the presence of the beam electrons dramatically alter the characteristics of the secondary spectrum. In a late phase the classic condensate K of about 0 is depleted, with the formation of a new condensate in resonance with the flat-topped beam distribution, which follows from the fact that the mere presence of the beam electrons creates a minimum in the frequency-wave-number relation. For strong and slow beams, the predictions of the code are found to be in excellent agreement with the results of the particle simulation if a dispersion relation that includes the beam is used.
Nonlinear bending models for beams and plates
Antipov, Y. A.
2014-01-01
A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler–Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960
Geometric beam coupling impedance of LHC secondary collimators
NASA Astrophysics Data System (ADS)
Frasciello, Oscar; Tomassini, Sandro; Zobov, Mikhail; Salvant, Benoit; Grudiev, Alexej; Mounet, Nicolas
2016-02-01
The High Luminosity LHC project is aimed at increasing the LHC luminosity by an order of magnitude. One of the key ingredients to achieve the luminosity goal is the beam intensity increase. In order to keep beam instabilities under control and to avoid excessive power losses a careful design of new vacuum chamber components and an improvement of the present LHC impedance model are required. Collimators are among the major impedance contributors. Measurements with beam have revealed that the betatron coherent tune shifts were higher by about a factor of 2 with respect to the theoretical predictions based on the LHC impedance model up to 2012. In that model the resistive wall impedance has been considered as the dominating impedance contribution for collimators. By carefully simulating also their geometric impedance we have contributed to the update of the LHC impedance model, reaching also a better agreement between the measured and simulated betatron tune shifts. During the just ended LHC Long Shutdown I (LSI), TCS/TCT collimators were replaced by new devices embedding BPMs and TT2-111R ferrite blocks. We present here preliminary estimations of their broad-band impedance, showing that an increase of about 20% is expected in the kick factors with respect to previous collimators without BPMs.
Geometric phase in cavity QED containing a nonlinear optical medium and a quantum well
NASA Astrophysics Data System (ADS)
Mohamed, A.-B. A.; Eleuch, H.
2015-11-01
The geometric phase (GP) in cavity QED filled with a nonlinear medium and containing a quantum well is analyzed. We observe collapses and revivals. The optical nonlinearity leads to high frequency oscillations of the GP. The GP is very sensitive not only to the dissipation rates but also to the amplitude of the laser pump.
The beam equation with nonlinear memory
NASA Astrophysics Data System (ADS)
D'Abbicco, Marcello; Lucente, Sandra
2016-06-01
In this paper, we study the critical exponent for the beam equation with nonlinear memory, i.e., {u_{tt}+Δ^2u = F(t, u)}, where F = intlimits0tf(t - s)N(u)(s, x) {d}s, quad N(u)≈ |u|^p. For suitable f and p, we prove the existence of local-in-time solutions and small data global solutions to the Cauchy problem, in homogeneous and nonhomogeneous Sobolev spaces. In some cases, we prove that the local solution cannot be extended to a global one. We also consider the limit case of power nonlinearity, i.e., {F = N(u)}.
A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
NASA Astrophysics Data System (ADS)
Ortigosa, Rogelio; Gil, Antonio J.; Bonet, Javier; Hesch, Christian
2016-02-01
In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55-70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney-Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.
Beam stability & nonlinear dynamics. Formal report
Parsa, Z.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations
NASA Technical Reports Server (NTRS)
Hodges, D. H.
1985-01-01
Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.
NASA Astrophysics Data System (ADS)
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
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.
Nonlinear dynamics of magnetically coupled beams for multi-modal vibration energy harvesting
NASA Astrophysics Data System (ADS)
Abed, I.; Kacem, N.; Bouhaddi, N.; Bouazizi, M. L.
2016-04-01
We investigate the nonlinear dynamics of magnetically coupled beams for multi-modal vibration energy harvesting. A multi-physics model for the proposed device is developed taking into account geometric and magnetic nonlinearities. The coupled nonlinear equations of motion are solved using the Galerkin discretization coupled with the harmonic balance method and the asymptotic numerical method. Several numerical simulations have been performed showing that the expected performances of the proposed vibration energy harvester are significantly promising with up to 130 % in term of bandwidth and up to 60 μWcm-3g-2 in term of normalized harvested power.
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.
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.
An integrated approach to the synthesis of geometrically non-linear structures
NASA Technical Reports Server (NTRS)
Smaoui, H.; Schmit, L. A.
1988-01-01
An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.
Geometrically nonlinear bending analysis of laminated composite plate
NASA Astrophysics Data System (ADS)
Dash, Padmanav; Singh, B. N.
2010-10-01
In this work, a transverse bending of shear deformable laminated composite plates in Green-Lagrange sense accounting for the transverse shear and large rotations are presented. Governing equations are developed in the framework of higher order shear deformation theory. All higher order terms arising from nonlinear strain-displacement relations are included in the formulation. The present plate theory satisfies zero transverse shear strains conditions at the top and bottom surfaces of the plate in von-Karman sense. A C0 isoparametric finite element is developed for the present nonlinear model. Numerical results for the laminated composite plates of orthotropic materials with different system parameters and boundary conditions are found out. The results are also compared with those available in the literature. Some new results with different parameters are also presented.
Geometrically nonlinear vibrations of rectangular plates carrying a concentrated mass
NASA Astrophysics Data System (ADS)
Amabili, M.
2010-10-01
Nonlinear forced vibrations of rectangular plates carrying a central concentrated mass are studied. The plate is assumed to have immovable edges and rotational springs; numerical results are presented for clamped plates. The Von Kármán nonlinear plate theory is used, but in-plane inertia in both the plate and the mass is retrained. The problem is discretized into a multi-degree-of-freedom (dof) system by using an energy approach and Lagrange equations taking damping into account. A pseudo-arclength continuation method is used in order to obtain numerical solutions. Results are presented as both (i) frequency-amplitude curves and (ii) time domain responses. The effect of gravity and the effect of the consequent initial plate deflection are also investigated.
Focused optical and acoustic beams in media with nonlinear absorption
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Sukhorukov, A. A.
1996-11-01
Optical and acoustic beams are known to be useful for medical and biological applications, such as diagnostics, surgery, etc. At high intensities both nonlinear lens effects and nonlinear absorption can be significant for the beams. The nonlinear absorption arises due to two-photon optical processes or acoustic shock wave formation. The present work is devoted to the theoretical description of nonlinear beam propagation and focal spot formation taking into account the competition between focusing, diffraction and absorption. We derived a new nonlinear integro- differential equation describing the spatial evolution of the beam width. The general analytical solution of this equation is obtained for arbitrary boundary conditions. The simple formulas are derived for the angle divergence in the far field, as well as for beam width at nonlinear waist. The results of the analysis of these key parameters in different situations are presented.
Geometrical Nonlinear Analysis of Composite Structures by Zigzag Theory—A Review
NASA Astrophysics Data System (ADS)
Shirbhate, N. J.; Tungikar, V. B.
2010-10-01
Advances in manufacturing technologies of composites leads to its uses as main load carrying structures which essentially need to be thick structures. Thus it is becoming increasingly important to predict accurately interlaminar variations of stresses and displacements along thickness of the composites. A review of the recent development of finite element methods for geometrical nonlinear analysis of composite structures specifically using zigzag theory is presented in this paper. The literature review is devoted to the recently developed finite elements, theories based on zigzag function for carrying out geometrical nonlinear analysis of composite structures. The future research is summarized finally.
Donko, Z.; Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D.
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.
Multiple-mode nonlinear free and forced vibrations of beams using finite element method
NASA Technical Reports Server (NTRS)
Mei, Chuh; Decha-Umphai, Kamolphan
1987-01-01
Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.
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 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.
NASA Astrophysics Data System (ADS)
Nanda, Namita; Bandyopadhyay, J. N.
2009-08-01
The nonlinear transient response of composite shells with/without cutouts and initial geometric imperfection is investigated using the finite element method. The present formulation considers doubly curved shells incorporating von Kármán type nonlinear strains into the first order shear deformation theory. The analysis is carried out using quadratic C0 eight-noded isoparametric element. The governing nonlinear equations are solved by using the Newmark average acceleration method in the time integration in conjunction with modified Newton-Raphson iteration scheme. The validity of the model is demonstrated by comparing the present results with those available in the literature. Parametric studies are carried out varying the radius of curvature to width ratio and amplitude of initial geometric imperfection of laminated composite cylindrical, spherical and hyperbolic paraboloid shells with/without cutouts.
NASA Technical Reports Server (NTRS)
Mangalgiri, P. D.; Prabhakaran, R.
1986-01-01
An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.
NASA Astrophysics Data System (ADS)
Collin, E.; Bunkov, Yu. M.; Godfrin, H.
2010-12-01
We report on low-temperature measurements performed on microelectromechanical systems driven deeply into the nonlinear regime. The materials are kept in their elastic domain while the observed nonlinearity is purely of geometrical origin. Two techniques are used, harmonic drive and free decay. For each case, we present an analytic theory fitting the data. The harmonic drive is fit with a modified Lorentzian line shape obtained from an extended version of Landau and Lifshitz’s nonlinear theory. The evolution in the time domain is fit with an amplitude-dependent frequency decaying function derived from the Lindstedt-Poincaré theory of nonlinear differential equations. The technique is perfectly generic and can be straightforwardly adapted to any mechanical device made of ideally elastic constituents, and which can be reduced to a single degree of freedom, for an experimental definition of its nonlinear dynamics equation.
Necklace beam generation in nonlinear colloidal engineered media.
Silahli, Salih Z; Walasik, Wiktor; Litchinitser, Natalia M
2015-12-15
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, rogue waves, and ring (or necklace) beam formation. To date, a majority of studies of these phenomena have focused on light-matter interactions in self-focusing Kerr media existing in nature. However, a large and tunable nonlinear response of a colloidal suspension can be tailored at will by judiciously engineering the optical polarizability. Here, we analytically and numerically show the possibility of necklace beam generation originating from spatial modulational instability of vortex beams in engineered soft-matter nonlinear media with different types of exponential nonlinearity. PMID:26670494
Nonlinear plasma and beam physics in plasma wake-fields
Rosenzweig, J.B.
1990-02-12
In experimental studies of the Plasma Wake-field Accelerator performed to date at the Argonne Advanced Accelerator Test Facility, significant nonlinearities in both plasma and beam behavior have been observed. The plasma waves driven in the wake of the intense driving beam in these experiments exhibit three-dimensional nonlinear behavior which has as yet no quantitative theoretical explanation. This nonlinearity is due in part to the self-pinching of the driving beam in the plasma, as the denser self-focused beam can excite larger amplitude plasma waves. The self-pinching is a process with interesting nonlinear aspects: the initial evolution of the beam envelope and the subsequent approach to Bennett equilibrium through phase mixing. 35 refs., 10 figs.
The effect of electron beam geometric deformation errors on the small-signal characteristic of ECRM
NASA Astrophysics Data System (ADS)
Yongjian, Yu
1993-08-01
In this paper is studied the effect of electron beam geometric deformation errors on the small — signal characteristics of the TE{mn/o} mode Electron Cyclotron Resonance Maser (ECRM), based on the elliptically cross—sectional e—beam deformation model. As an example, the effect of small geometric deformation errors on the TE{01/o} mode fundamental ECRM coupling coefficient is quantitatively shown.
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 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.
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.; Hodges, Dewey H.
1987-01-01
The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyze 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 deformation. The correlation is excellent in all cases.
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.
Nonlinear dynamics of inhomogeneous mismatched charged particle beams
Nunes, R. P.; Rizzato, F. B.
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.
NASA Astrophysics Data System (ADS)
Berczynski, P.
2013-09-01
The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear Kerr type and saturable fibres. CGO reduces the problem of Gaussian beam evolution in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to other methods of nonlinear optics such as variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of Gaussian beam propagation in saturable fibres with either focusing and defocusing refractive profiles. Besides, the influence of initial curvature of the wave front, phenomenon of weak absorption and effect of either transverse and longitudinal inhomogeneity on GB propagation in nonlinear fibres is discussed in this paper.
Beam width evolution of astigmatic hollow Gaussian beams in highly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Yang, Zhen-Feng; Jiang, Xue-Song; Yang, Zhen-Jun; Li, Jian-Xing; Zhang, Shu-Min
We investigate the beam width evolution of astigmatic hollow Gaussian beams propagating in highly nonlocal nonlinear media. The input-power-induced different evolutions of the beam width are illustrated: (i) the beam widths in two transverse directions are compressed or broadened at the same time; (ii) the beam width in one transverse direction keeps invariant, and the other is compressed or broadened; (iii) furthermore, the beam width in one transverse direction is compressed, whereas it in the other transverse direction is broadened.
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.
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.
Nonlinear analysis of cantilever shape memory alloy beams of variable cross section
NASA Astrophysics Data System (ADS)
Ashiqur Rahman, Muhammad; Arefin Kowser, Muhammad
2007-04-01
Cantilever beams, made of shape memory alloy (SMA), undergo much larger deflection in comparison to those made of other materials. Again, cantilever beams with reducing cross section along the span show much larger deflections compared to those of constant cross section beams. Analysis was conducted for such a cantilever beam with reducing cross-sectional area made of SMA, taking into account its highly nonlinear stress-strain curves. A computer code in C has been developed using the Runge-Kutta technique for the purpose of simulation. For rigorous analysis, the true stress-strain curves in tension as well as in compression have been used for the study. Moment-curvature and reduced modulus-curvature relations are obtained from the nonlinear stress-strain relations for different sections of the beam and used in the simulation. It is seen that load-deflection curves are initially linear but nonlinear and convex upward at a high load. Furthermore, the compressive stress in the beam is significantly higher than the tensile stress because of asymmetry. Interestingly, for the different cases considered, it is found that part of the SMA beam material may remain in the parent austenite phase, mixed phase or in the stress-induced martensitic phase. Importantly, it is found that more material can be removed from an SMA beam of uniform strength, originally designed without considering geometric nonlinearity and the effect of end-shortening. Comparison of the numerical results with the available theory shows very good agreement, verifying the soundness of the entire numerical simulation scheme.
NASA Astrophysics Data System (ADS)
Farokhi, Hamed; Ghayesh, Mergen H.
2016-06-01
This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory, the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff's hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct time-integration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed. Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.
NASA Astrophysics Data System (ADS)
Farokhi, Hamed; Ghayesh, Mergen H.
2015-12-01
This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory, the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff's hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct time-integration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed. Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.
Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations
NASA Technical Reports Server (NTRS)
Tessler, Alexander; Sleight, David W.
2006-01-01
Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.
Geometrically non-linear vibration of spinning structures by finite element method
NASA Astrophysics Data System (ADS)
Leung, A. Y. T.; Fung, T. C.
1990-05-01
The geometrically non-linear steady state vibration of spinning structures is studied. Full flap-lag-torsional gyroscopic coupling effects are considered. The non-linearity arises mainly from the non-linear axial strain-displacement relation. The equations of motion are derived from Lagrangian equations. Spatial discretization is achieved by the finite element method and steady state nodal displacements are expanded into Fourier series. The harmonic balance method gives a set of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The non-linear algebraic equations are solved by a Newtonian algorithm iteratively. The importance of the conditions of completeness and balanceability in choosing the number of harmonic terms to be used is discussed. General frame structures with arbitrary orientation in a rotating frame can be investigated by the present method. Rotating blades and shafts are treated as special cases. Examples of a rotating ring with different orientations are given. The non-linear amplitude-frequency relation can be constructed parametrically.
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.
Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations
NASA Astrophysics Data System (ADS)
Sotoudeh, Zahra
2011-07-01
Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.
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
Spatially varying geometric phase in classically entangled vector beams of light
NASA Astrophysics Data System (ADS)
King-Smith, Andrew; Leary, Cody
We present theoretical results describing a spatially varying geometric (Pancharatnam) phase present in vector modes of light, in which the polarization and transverse spatial mode degrees of freedom exhibit classical entanglement. We propose an experimental setup capable of characterizing this effect, in which a vector mode propagates through a Mach-Zehnder interferometer with a birefringent phase retarder present in one arm. Since the polarization state of a classically entangled light beam exhibits spatial variation across the transverse mode profile, the phase retarder gives rise to a spatially varying geometric phase in the beam propagating through it. When recombined with the reference beam from the other interferometer arm, the presence of the geometric phase is exhibited in the resulting interference pattern. We acknowledge funding from the Research Corporation for Science Advancement by means of a Cottrell College Science Award.
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.
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
NASA Technical Reports Server (NTRS)
Qin, Zhanming; Hasanyan, Davresh; Librescu, Liviu; Ambur, Damodar R.
2005-01-01
In Part 1 of this paper, the governing equations of geometrically nonlinear, anisotropic composite plates incorporating magneto-thermo-elastic effects have been derived. In order to gain insight into the implications of a number of geometrical and physical features of the system. three special cases are investigated: (i) free vibration of a plate strip immersed in a transversal magnetic field; (ii) free vibration of the plate strip immersed in an axial magnetic field; (iii) magneto-elastic wave propagations of an infinite plate. Within each of these cases, a prescribed uniform thermal field is considered. Special coupling characteristics between the magnetic and elastic fields are put into evidence. Extensive numerical investigations are conducted and pertinent conclusions which highlight the various effects induced by the magneto-elastic couplings and the finite electroconductivity, are outlined.
Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity
NASA Astrophysics Data System (ADS)
Bekhoucha, F.; Rechak, S.; Duigou, L.; Cadou, J. M.
2016-09-01
In this paper, we study the bending nonlinear free vibrations of a centrifugally stiffened beam with uniform cross-section and constant angular velocity. The nonlinear intrinsic equations of motion used here are geometrically exact and specific to beams exhibiting large amplitude displacements and rotations associated with small strains. Based on the Timoshenko beam model, these equations are derived from Hamilton's principle, in which the warping is considered. All coupling terms are considered including Coriolis terms. The studied beams are isotropic with clamped-free boundary conditions. By combining the Galerkin method with the harmonic balance method, the equations of motion are converted into a quadratic function treated with a continuation method: the Asymptotic Numerical Method, where the generalized displacement vector is presented as a series expansion. While analysing the effect of the angular velocity, we determine the amplitude versus frequency variations which are plotted as backbone curves. Considering the first lagging and flapping modes, the changes in beam behaviour from hardening to softening are investigated and identified as a function of the angular velocity and the effect of shear. Particular attention is paid to high angular velocities for both Euler-Bernoulli and Timoshenko beams and the natural frequencies so obtained are compared with the results available in the literature.
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 representation of Gaussian beams propagating through complex paraxial optical systems.
Andrews, L C; Miller, W B; Ricklin, J C
1993-10-20
Geometric relations are used to study the propagation environment of a Gaussian beam wave propagating through a complex paraxial optical system characterized by an ABCD ray matrix in two naturally linked complex planes. In the plane defined by beam transmitter parameters Ω(o) and Ω, the propagation path is described by a ray line similar to the ray line in the y? diagram method, whereas the path in the plane of beam receiver parameters θ and Λ is described by a circular arc. In either plane the amplitude, phase, spot size, and radius of curvature of the Gaussian beam are directly related to the modulus and argument of the complex number designating a particular transverse plane along the propagation path. These beam parameters also lead to simple geometric relations for locating the beam waist, Rayleigh range, focal plane, and sister planes, which share the same radius of curvature but have opposite signs. Combined with the paraxial wave propagation technique based on a Huygens-Fresnel integral and complex ABCD ay matrices, this geometric approach provides a new and powerful method for the analysis and design of laser systems. PMID:20856413
Finite rotation and nonlinear beam kinematics
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.
1987-01-01
Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.
Ion beam analysis based on cellular nonlinear networks
NASA Astrophysics Data System (ADS)
Senger, V.; Tetzlaff, R.; Reichau, H.; Ratzinger, U.
2011-07-01
The development of a non- destructive measurement method for ion beam parameters has been treated in various projects. Although results are promising, the high complexity of beam dynamics has made it impossible to implement a real time process control up to now. In this paper we will propose analysing methods based on the dynamics of Cellular Nonlinear Networks (CNN) that can be implemented on pixel parallel CNN based architectures and yield satisfying results even at low resolutions.
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.
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.
Generation of equal-intensity coherent optical beams by binary geometrical phase on metasurface
NASA Astrophysics Data System (ADS)
Wang, Zheng-Han; Jiang, Shang-Chi; Xiong, Xiang; Peng, Ru-Wen; Wang, Mu
2016-06-01
We report here the design and realization of a broadband, equal-intensity optical beam splitter with a dispersion-free binary geometric phase on a metasurface with unit cell consisting of two mirror-symmetric elements. We demonstrate experimentally that two identical beams can be efficiently generated with incidence of any polarization. The efficiency of the device reaches 80% at 1120 nm and keeps larger than 70% in the range of 1000-1400 nm. We suggest that this approach for generating identical, coherent beams have wide applications in diffraction optics and in entangled photon light source for quantum communication.
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
Gaussian beam diffraction in inhomogeneous media: solution in frame of complex geometrical optics
NASA Astrophysics Data System (ADS)
Kravtsov, Yu. A.; Berczynski, P.
2005-09-01
The method of paraxial complex geometrical optics is presented to describe Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like media. The method modifies and specifies the results by Babic' (1968), Kirpichnikova (1971), Cerveny, Popov, Psencik (1982), Cerveny (1983, 2001), Timofeev (1995) and Pereverzev (1996) as applied to the optical problems. The method of paraxial complex geometrical optics reduces the problem of Gaussian beam diffraction in inhomogeneous media to the solution of the system of the ordinary differential equations of first order, which can be readily calculated numerically by the Runge-Kutta method. Thereby the paraxial complex geometrical optics radically simplifies description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. By the way of example the known analytical solution for Gaussianbeam diffraction both in a free space and in lens-like medium (Bornatici, Maj 2003) are presented. It is pointed out, that the method of paraxial complex geometrical optics turns out to be equivalent to the solutions of the abridged parabolic wave equation.
NASA Technical Reports Server (NTRS)
Norwood, D. S.; Shuart, Mark J.; Herakovich, Carl T.
1991-01-01
An analytical study of interlaminar stresses in unsymmetrically laminated plates is presented. The study examines the linear elastic, large deflection response of square laminated composite plates subjected to uniform thermal loading. Both cross-ply and angle-ply, symmetric and unsymmetric, laminates are examined to evaluate the effects of mismatch between adjacent layers in elastic constants and coefficients of thermal expansion. A geometrically nonlinear kinematic description is used to predict the large out-of-plane (transverse) deflections. The nonlinear, three-dimensional boundary value problems are formulated from elasticity theory and approximate solutions are determined using the finite element method. A global/local analysis procedure is used to obtain improved free edge stress predictions. For the laminates and loading conditions considered, the results indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses. These deflections also reduce interlaminar normal stresses in some laminates and increase these stresses for others. The results indicate that as the out-of-plane deflections become large, the differences in interlaminar stress predictions between linear and nonlinear theory can become quite large.
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.
Nonlinear transmission line based electron beam driver
NASA Astrophysics Data System (ADS)
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.
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; Allen-Flowers, Jordan
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.
Nonlinear dynamics of optical absorption of intense beams
NASA Astrophysics Data System (ADS)
Corbett, D.; van Oosten, C. L.; Warner, M.
2008-07-01
On traversing materials with absorbing dyes, weak optical beams decay exponentially (a Beer profile), while intense beams develop in time a profile that is spatially linear until at great depth it becomes spatially exponential. This anomalous, deep penetration, due to photobleaching of surface layers, is important for heavy dye loading and intense beams, for instance in photo-actuation. We address the problem of the evolution in time from initial Beer’s Law to a finally deeply-penetrating optical profile in dyes. Our largely analytic solution of the coupled, nonlinear, partial differential equations governing the spatiotemporal decay of the Poynting flux and the nonlinear population dynamics of the photo-active molecules under intense irradiation has application to optomechanical devices.
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.
View-dependent geometric calibration for offset flat-panel cone beam computed tomography systems
NASA Astrophysics Data System (ADS)
Nguyen, Van-Giang
2016-04-01
Geometric parameters that define the geometry of imaging systems are crucial for image reconstruction and image quality in x-ray computed tomography (CT). The problem of determining geometric parameters for an offset flat-panel cone beam CT (CBCT) system, a recently introduced modality with a large field of view, with the assumption of an unstable mechanism and geometric parameters that vary in each view, is considered. To accurately and rapidly find the geometric parameters for each projection view, we use the projection matrix method and design a dedicated phantom that is partially visible in all projection views. The phantom consists of balls distributed symmetrically in a cylinder to ensure the inclusion of the phantom in all views, and a large portion of the phantom is covered in the projection image. To efficiently use calibrated geometric information in the reconstruction process and get rid of approximation errors, instead of decomposing the projection matrix into actual geometric parameters that are manually corrected before being used in reconstruction, as in conventional methods, we directly use the projection matrix and its pseudo-inverse in projection and backprojection operations of reconstruction algorithms. The experiments illustrate the efficacy of the proposed method with a real offset flat-panel CBCT system in dental imaging.
NASA Astrophysics Data System (ADS)
Passalacqua, Paola; Do Trung, Tien; Foufoula-Georgiou, Efi; Sapiro, Guillermo; Dietrich, William E.
2010-03-01
A geometric framework for the automatic extraction of channels and channel networks from high-resolution digital elevation data is introduced in this paper. The proposed approach incorporates nonlinear diffusion for the preprocessing of the data, both to remove noise and to enhance features that are critical to the network extraction. Following this preprocessing, channels are defined as curves of minimal effort, or geodesics, where the effort is measured on the basis of fundamental geomorphological characteristics such as flow accumulation area and isoheight contours curvature. The merits of the proposed methodology, and especially the computational efficiency and accurate localization of the extracted channels, are demonstrated using light detection and ranging (lidar) data of the Skunk Creek, a tributary of the South Fork Eel River basin in northern California.
Geometric Nonlinear Analysis of Self-Anchored Cable-Stayed Suspension Bridges
Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang
2013-01-01
Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed. PMID:24282388
Geometric nonlinear analysis of self-anchored cable-stayed suspension bridges.
Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang
2013-01-01
Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed. PMID:24282388
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.
Douglas, David R.
2012-01-10
A method of using off-axis particle beam injection in energy-recovering linear accelerators that increases operational efficiency while eliminating the need to merge the high energy re-circulating beam with an injected low energy beam. In this arrangement, the high energy re-circulating beam and the low energy beam are manipulated such that they are within a predetermined distance from one another and then the two immerged beams are injected into the linac and propagated through the system. The configuration permits injection without geometric beam merging as well as decelerated beam extraction without the use of typical beamline elements.
NASA Astrophysics Data System (ADS)
Bekhoucha, Ferhat; Rechak, Said; Duigou, Laëtitia; Cadou, Jean-Marc
2015-05-01
This paper deals with the computation of backbone curves bifurcated from a Hopf bifurcation point in the framework of nonlinear free vibrations of a rotating flexible beams. The intrinsic and geometrical equations of motion for anisotropic beams subjected to large displacements are used and transformed with Galerkin and harmonic balance methods to one quadratic algebraic equation involving one parameter, the pulsation. The latter is treated with the asymptotic numerical method using Padé approximants. An algorithm, equivalent to the Lyapunov-Schmidt reduction is proposed, to compute the bifurcated branches accurately from a Hopf bifurcation point, with singularity of co-rank 2, related to a conservative and gyroscopic dynamical system steady state, toward a nonlinear periodic state. Numerical tests dealing with clamped, isotropic and composite, rotating beams show the reliability of the proposed method reinforced by accurate results.
Stancari, Giulio
2014-09-11
Electron lenses are pulsed, magnetically confined electron beams whose current-density profile is shaped to obtain the desired effect on the circulating beam. Electron lenses were used in the Fermilab Tevatron collider for bunch-by-bunch compensation of long-range beam-beam tune shifts, for removal of uncaptured particles in the abort gap, for preliminary experiments on head-on beam-beam compensation, and for the demonstration of halo scraping with hollow electron beams. Electron lenses for beam-beam compensation are being commissioned in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Hollow electron beam collimation and halo control were studied as an option to complement the collimation system for the upgrades of the Large Hadron Collider (LHC) at CERN; a conceptual design was recently completed. Because of their electric charge and the absence of materials close to the proton beam, electron lenses may also provide an alternative to wires for long-range beam-beam compensation in LHC luminosity upgrade scenarios with small crossing angles. At Fermilab, we are planning to install an electron lens in the Integrable Optics Test Accelerator (IOTA, a 40-m ring for 150-MeV electrons) as one of the proof-of-principle implementations of nonlinear integrable optics to achieve large tune spreads and more stable beams without loss of dynamic aperture.
Nonlinear flap-lag-axial equations of a rotating beam with arbitrary precone angle
NASA Technical Reports Server (NTRS)
Kvaternik, R. G.; White, W. F., Jr.; Kaza, K. R. V.
1978-01-01
In an attempt both to unify and extend the analytical basis of several aspects of the dynamic behavior of flexible rotating beams, the second-degree nonlinear equations of motion for the coupled flapwise bending, lagwise bending, and axial extension of an untwisted, torsionally rigid, nonuniform, rotating beam having an arbitrary angle of precone with the plane perpendicular to the axis of rotation are derived using Hamilton's principle. The derivation of the equations is based on the geometric nonlinear theory of elasticity and the resulting equations are consistent with the assumption that the strains are negligible compared to unity. No restrictions are imposed on the relative displacements or angular rotations of the cross sections of the beam other than those implied by the assumption of small strains. Illustrative numerical results, obtained by using an integrating matrix as the basis for the method of solution, are presented both for the purpose of validating the present method of solution and indicating the range of applicability of the equations of motion and the method of solution.
NASA Astrophysics Data System (ADS)
Łuczko, J.
2002-08-01
A geometrically non-linear model of the rotating shaft is introduced, which includes Kárman non-linearity, non-linear curvature effects, large displacements and rotations as well as gyroscopic effects. Through applying Timoshenko-type assumptions, the shear effects are also included in the model. Convenient matrix descriptions are used in order to facilitate the analysis based on Galerkin and continuation methods. The model is used to analyze the phenomenon of internal resonance. The influence of some of the system's parameters on the amplitude and frequency of self-excited vibration is investigated.
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 π mm mrad for the targets of Cu, Y, and Ag, respectively.
A geometrical model for the Monte Carlo simulation of the TrueBeam linac.
Rodriguez, M; Sempau, J; Fogliata, A; Cozzi, L; Sauerwein, W; Brualla, L
2015-06-01
Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3 × 3 to 40 × 40 cm(2) at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for
A geometrical model for the Monte Carlo simulation of the TrueBeam linac
NASA Astrophysics Data System (ADS)
Rodriguez, M.; Sempau, J.; Fogliata, A.; Cozzi, L.; Sauerwein, W.; Brualla, L.
2015-06-01
Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3 × 3 to 40 × 40 cm2 at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for the
NASA Astrophysics Data System (ADS)
Konoshonkin, Alexander V.; Kustova, Natalia V.; Borovoi, Anatoli G.
2015-10-01
The open-source beam-splitting code is described which implements the geometric-optics approximation to light scattering by convex faceted particles. This code is written in C++ as a library which can be easy applied to a particular light scattering problem. The code uses only standard components, that makes it to be a cross-platform solution and provides its compatibility to popular Integrated Development Environments (IDE's). The included example of solving the light scattering by a randomly oriented ice crystal is written using Qt 5.1, consequently it is a cross-platform solution, too. Both physical and computational aspects of the beam-splitting algorithm are discussed. Computational speed of the beam-splitting code is obviously higher compared to the conventional ray-tracing codes. A comparison of the phase matrix as computed by our code with the ray-tracing code by A. Macke shows excellent agreement.
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1986-01-01
The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.
A Nonlinear Elastic Beam System with Inelastic Contact Constraints
Russell, D.L. White, L.W.
2002-12-19
In this paper we study freely propagating inertial, i.e., unforced, waves, in an elastic beam constrained so that all motion takes place above and on a flat, rigid support surface, subject to a gravitational force and a compressive longitudinal load. Contact between the beam and the support surface is assumed to be completely inelastic. A nonlinear beam model is used, incorporating a quartic extension of the familiar quadratic potential energy functional for the standard Euler-Bernoulli model. After briefly reviewing the rationale for the model and some of its properties, as developed in earlier articles, we present existence and uniqueness results for the constrained system obtained with the use of a 'penalty function' approach involving the addition of a 'uni-directional friction' dissipative term, active only when the constraint is violated, to the unconstrained system.
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.
Practical geometric calibration for helical cone-beam industrial computed tomography.
Zhang, Feng; Yan, Bin; Li, Lei; Xi, Xiaoqi; Jiang, Hua
2014-01-01
In helical cone-beam industrial computed tomography (ICT), the reconstructed images may be interfered by geometry artifacts due to the presence of mechanical misalignments. To obtain artifact-free reconstruction images, a practical geometric calibration method for helical scan is investigated based on Noo's analytic geometric calibration method for circular scan. The presented method is implemented by first dividing the whole ascending path of helical scan into several pieces, then acquiring the projections of a dedicated calibration phantom in circular scan at each section point, of which geometry parameters are calculated using Noo's analytic method. At last, the geometry parameters of each projection in a piece can be calculated by those of the two end points of the piece. We performed numerical simulations and real data experiments to study the performance of the presented method. The experimental results indicated that the method can obtain high-precision geometry parameters of helical scan and give satisfactory reconstruction images. PMID:24463383
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.
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.
High-efficiency beam manipulation combining geometric phase with anisotropic Huygens surface
NASA Astrophysics Data System (ADS)
Zhao, Wenyu; Jiang, Huan; Liu, Bingyi; Song, Jie; Jiang, Yongyuan
2016-05-01
Conventional geometric metasurfaces relying on space-variant metal antennas for beam manipulation suffer from strong Ohmic loss and incomplete polarization conversion. The efficiency is often limited to rather small values, especially when operating in transmission mode. Here, we tackle this challenge by deliberately constructing an equivalent sheet with anisotropic surface electric and magnetic polarizabilities using cross-shaped dielectric antennas. An incident circularly polarized light can be almost fully converted to a transmitted light of opposite helicity with an unprecedented efficiency up to 98%. Such a transmissive metasurface possessing the merits of high-efficiency, non-dispersion, and robust against variations can serve as an outstanding candidate for flat optics, such as anomalous refraction and beam focusing.
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)
Kharin, Nikolay A.
2001-05-01
The novel solution of the KZK equation for acoustic pressure of the second harmonic in slightly focused beam of a circular transducer was obtained in a closed form for moderately nonlinear absorbing media (Gol'dberg numbers ~ 1). The solution is based on the method of slowly changing wave profile in combination with the method of successive approximations. Two pairs of transducers (Valpey-Fisher Corp.) Were compared to investigate the influence of focusing on the applicability of the moderate nonlinearity approach. The first pair was of 0.25' diameter and the second was of 0.5' diameter. Both pairs has one transducer with flat surface and the other geometrically focused at 4'. The central frequency for all transducers was 5 MHz. Measurements were undertaken in the blood-mimicking solution of water and glycerine. The results demonstrated that for slightly focused transducers with circular apertures, the moderate nonlinearity approach is still valid, as it was proved for flat sources with the same source level, despite the higher pressures in the focal region. The peak pressure for the weakly focused system occurs at a shorter range than focal length.
Geometrical correction of the e-beam proximity effect for raster scan systems
NASA Astrophysics Data System (ADS)
Belic, Nikola; Eisenmann, Hans; Hartmann, Hans; Waas, Thomas
1999-06-01
Increasing demands on pattern fidelity and CD accuracy in e- beam lithography require a correction of the e-beam proximity effect. The new needs are mainly coming from OPC at mask level and x-ray lithography. The e-beam proximity limits the achievable resolution and affects neighboring structures causing under- or over-exposion depending on the local pattern densities and process settings. Methods to compensate for this unequilibrated does distribution usually use a dose modulation or multiple passes. In general raster scan systems are not able to apply variable doses in order to compensate for the proximity effect. For system of this kind a geometrical modulation of the original pattern offers a solution for compensation of line edge deviations due to the proximity effect. In this paper a new method for the fast correction of the e-beam proximity effect via geometrical pattern optimization is described. The method consists of two steps. In a first step the pattern dependent dose distribution caused by back scattering is calculated by convolution of the pattern with the long range part of the proximity function. The restriction to the long range part result in a quadratic sped gain in computing time for the transformation. The influence of the short range part coming from forward scattering is not pattern dependent and can therefore be determined separately in a second step. The second calculation yields the dose curve at the border of a written structure. The finite gradient of this curve leads to an edge displacement depending on the amount of underground dosage at the observed position which was previously determined in the pattern dependent step. This unintended edge displacement is corrected by splitting the line into segments and shifting them by multiples of the writers address grid to the opposite direction.
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.
Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics
Alex J. Dragt; Filippo Neri; Govindan Rangarajan; David Douglas; Liam M. Healy; Robert D. Ryne
1988-12-01
The purpose of this paper is to present a summary of new methods, employing Lie algebraic tools, for characterizing beam dynamics in charged-particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics, by a certain operator. The operators for the various elements can then be concatenated, following well-defined rules, to obtain a resultant operator that characterizes the entire system. This paper deals mostly with accelerator design and charged-particle beam transport. The application of Lie algebraic methods to light optics and electron microscopes is described elsewhere (1, see also 44). To keep its scope within reasonable bounds, they restrict their treatment of accelerator design and charged-particle beam transport primarily to the use of Lie algebraic methods for the description of particle orbits in terms of transfer maps. There are other Lie algebraic or related approaches to accelerator problems that the reader may find of interest (2). For a general discussion of linear and nonlinear problems in accelerator physics see (3).
A new pre-loaded beam geometric stiffness matrix with full rigid body capabilities
NASA Technical Reports Server (NTRS)
Bosela, P. A.; Fertis, D. G.; Shaker, F. J.
1992-01-01
Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis.
Direct determination of geometric alignment parameters for cone-beam scanners.
Mennessier, C; Clackdoyle, R; Noo, F
2009-03-21
This paper describes a comprehensive method for determining the geometric alignment parameters for cone-beam scanners (often called calibrating the scanners or performing geometric calibration). The method is applicable to x-ray scanners using area detectors, or to SPECT systems using pinholes or cone-beam converging collimators. Images of an alignment test object (calibration phantom) fixed in the field of view of the scanner are processed to determine the nine geometric parameters for each view. The parameter values are found directly using formulae applied to the projected positions of the test object marker points onto the detector. Each view is treated independently, and no restrictions are made on the position of the cone vertex, or on the position or orientation of the detector. The proposed test object consists of 14 small point-like objects arranged with four points on each of three orthogonal lines, and two points on a diagonal line. This test object is shown to provide unique solutions for all possible scanner geometries, even when partial measurement information is lost by points superimposing in the calibration scan. For the many situations where the cone vertex stays reasonably close to a central plane (for circular, planar, or near-planar trajectories), a simpler version of the test object is appropriate. The simpler object consists of six points, two per orthogonal line, but with some restrictions on the positioning of the test object. This paper focuses on the principles and mathematical justifications for the method. Numerical simulations of the calibration process and reconstructions using estimated parameters are also presented to validate the method and to provide evidence of the robustness of the technique. PMID:19242049
Direct determination of geometric alignment parameters for cone-beam scanners
Mennessier, C; Clackdoyle, R; Noo, F
2009-01-01
This paper describes a comprehensive method for determining the geometric alignment parameters for cone-beam scanners (often called calibrating the scanners or performing geometric calibration). The method is applicable to x-ray scanners using area detectors, or to SPECT systems using pinholes or cone-beam converging collimators. Images of an alignment test object (calibration phantom) fixed in the field of view of the scanner are processed to determine the nine geometric parameters for each view. The parameter values are found directly using formulae applied to the projected positions of the test object marker points onto the detector. Each view is treated independently, and no restrictions are made on the position of the cone vertex, or on the position or orientation of the detector. The proposed test object consists of 14 small point-like objects arranged with four points on each of three orthogonal lines, and two points on a diagonal line. This test object is shown to provide unique solutions for all possible scanner geometries, even when partial measurement information is lost by points superimposing in the calibration scan. For the many situations where the cone vertex stays reasonably close to a central plane (for circular, planar, or near-planar trajectories), a simpler version of the test object is appropriate. The simpler object consists of six points, two per orthogonal line, but with some restrictions on the positioning of the test object. This paper focuses on the principles and mathematical justifications for the method. Numerical simulations of the calibration process and reconstructions using estimated parameters are also presented to validate the method and to provide evidence of the robustness of the technique. PMID:19242049
Beam heat load due to geometrical and resistive wall impedance in COLDDIAG
NASA Astrophysics Data System (ADS)
Casalbuoni, S.; Migliorati, M.; Mostacci, A.; Palumbo, L.; Spataro, B.
2012-11-01
One of the still open issues for the development of superconductive insertion devices is the understanding of the heat intake from the electron beam. With the aim of measuring the beam heat load to a cold bore and the hope to gain a deeper understanding in the underlying mechanisms, a cold vacuum chamber for diagnostics (COLDDIAG) was built. It is equipped with the following instrumentation: retarding field analyzers to measure the electron flux, temperature sensors to measure the beam heat load, pressure gauges, and mass spectrometers to measure the gas content. Possible beam heat load sources are: synchrotron radiation, wakefield effects due to geometrical and resistive wall impedance and electron/ion bombardment. The flexibility of the engineering design will allow the installation of the cryostat in different synchrotron light sources. COLDDIAG was first installed in the Diamond Light Source (DLS) in 2011. Due to a mechanical failure of the thermal transition of the cold liner, the cryostat had to be removed after one week of operation. After having implemented design changes in the thermal liner transition, COLDDIAG has been reinstalled in the DLS at the end of August 2012. In order to understand the beam heat load mechanism it is important to compare the measured COLDDIAG parameters with theoretical expectations. In this paper we report on the analytical and numerical computation of the COLDDIAG beam heat load due to coupling impedances deriving from unavoidable step transitions, ports used for pumping and diagnostics, surface roughness, and resistive wall. The results might have an important impact on future technological solutions to be applied to cold bore devices.
NASA Astrophysics Data System (ADS)
Cesnik, C. E. S.; Opoku, D. G.; Nitzsche, F.; Cheng, T.
2004-06-01
An active aeroelastic and aeroacoustic analysis of helicopter rotor systems is presented in this paper. It is a tightly coupled computational aeroelastic code that interfaces a particle-wake panel method code with an active nonlinear mixed variational intrinsic beam element code. In addition, a Ffowcs-Williams-Hawkings equation-based acoustic component is incorporated to complete the numerical implementation. The theory behind each component is summarized here as well as the method for coupling the aerodynamic and structural components. Sample acoustic and aeroelastic results are given for different model-scale rotors. Comparisons with available (passive) results show very good agreement. Preliminary study with an active twist rotor is also shown.
Nonlinear Potential Model of Space-Charge Electron Beams
NASA Astrophysics Data System (ADS)
Litz, Marc Stuart
1995-01-01
This body of work is new and comprises theoretical analysis, numerical simulation and experimental investigations of the vircator, a tunable, compact, simply constructed, high power reflexing electron device that is used as a microwave source. A 1D theoretical model is formulated that is based on a time-varying, nonlinear potential to better understand the sensitivities of individual electron trajectories to macroscopic parameters of the system. Self -consistent 2D (space) and 3D(velocity) numerical PIC simulations are used to find common dynamical behavior that links the individual test-particle trajectories examined in the 1D nonlinear model with the experimental measurements of the final state of the electron trajectories. The experiment designed and built for these studies is unique and contrasts with other virtual cathode electron beam sources because it operates at lower voltage, and longer pulse width than previous forms of the device. The anode-cathode (AK) gap spacing is externally tunable expediting parametric studies. In addition, it is repetitively pulsed, which permits discrimination between single-shot anomalies and repeatable variation that often occurs in pulsed power experimental devices. These attributes distinguish this experimental apparatus from previous experimental platforms. This novel, repetitively pulsed device has particular relevance to the industrial and medical applications of rf. The approach followed in the present studies is (1) to investigate the dynamic behavior of individual test -particles in a simplified 1D, nonlinear, time-varying, potential; (2) utilize a 2D, self-consistent, electromagnetic PIC code to generate single particle trajectories subject to the collective effects of the electron beam; and (3) measure macroscopic quantities of voltage, current, electromagnetic fields, and electron flux in an experimental platform. Results of the 3D experiments are compared to predictions of the 1D and 2D models. Electron flux
Evaluation and Correction of the Non-linear Distortion of CEBAF Beam Position Monitors
M. Spata, T.L. Allison, K.E. Cole, J. Musson, J. Yan
2011-09-01
The beam position monitors at CEBAF have four antenna style pickups that are used to measure the location of the beam. There is a strong nonlinear response when the beam is far from the electrical center of the device. In order to conduct beam experiments at large orbit excitation we need to correct for this nonlinearity. The correction algorithm is presented and compared to measurements from our stretched wire BPM test stand.
NASA Astrophysics Data System (ADS)
Afanasyev, An. N.; Uralov, A. M.; Grechnev, V. V.
2011-12-01
Propagation of shock related Moreton and EUV waves in the solar atmosphere is simulated by the nonlinear geometrical acoustics method. This method is based on the ray approximation and takes account of nonlinear wave features: dependence of the wave velocity on its amplitude, nonlinear dissipation of wave energy in the shock front, and the increase in its duration with time. The paper describes ways of applying this method to solve the propagation problem of a blast magnetohydrodynamic shock wave. Results of analytical modeling of EUV and Moreton waves in the spherically symmetric and isothermal solar corona are also presented. The calculations demonstrate deceleration of these waves and an increase in their duration. The calculation results of the kinematics of the EUV wave observed on the Sun on January 17, 2010 are presented as an example.
Geometric Parameters Estimation and Calibration in Cone-Beam Micro-CT.
Zhao, Jintao; Hu, Xiaodong; Zou, Jing; Hu, Xiaotang
2015-01-01
The quality of Computed Tomography (CT) images crucially depends on the precise knowledge of the scanner geometry. Therefore, it is necessary to estimate and calibrate the misalignments before image acquisition. In this paper, a Two-Piece-Ball (TPB) phantom is used to estimate a set of parameters that describe the geometry of a cone-beam CT system. Only multiple projections of the TPB phantom at one position are required, which can avoid the rotation errors when acquiring multi-angle projections. Also, a corresponding algorithm is derived. The performance of the method is evaluated through simulation and experimental data. The results demonstrated that the proposed method is valid and easy to implement. Furthermore, the experimental results from the Micro-CT system demonstrate the ability to reduce artifacts and improve image quality through geometric parameter calibration. PMID:26371008
Geometric Parameters Estimation and Calibration in Cone-Beam Micro-CT
Zhao, Jintao; Hu, Xiaodong; Zou, Jing; Hu, Xiaotang
2015-01-01
The quality of Computed Tomography (CT) images crucially depends on the precise knowledge of the scanner geometry. Therefore, it is necessary to estimate and calibrate the misalignments before image acquisition. In this paper, a Two-Piece-Ball (TPB) phantom is used to estimate a set of parameters that describe the geometry of a cone-beam CT system. Only multiple projections of the TPB phantom at one position are required, which can avoid the rotation errors when acquiring multi-angle projections. Also, a corresponding algorithm is derived. The performance of the method is evaluated through simulation and experimental data. The results demonstrated that the proposed method is valid and easy to implement. Furthermore, the experimental results from the Micro-CT system demonstrate the ability to reduce artifacts and improve image quality through geometric parameter calibration. PMID:26371008
Paradox of a nonlinear beam splitter and its resolution
Belinsky, A. V. Volkov, D. V.; Dmitriev, A. V.; Shulman, M. Kh.
2013-11-15
A nonlinear beam splitter is shown to be an interesting object of investigation for the following reasons. First, the classical and quantum theories of its description give directly opposite behaviors of the phase fluctuations: according to the classical theory, the phase is unchanged; according to the quantum theory, the phase fluctuations increase or decrease, depending on the suppression or growth of amplitude fluctuations. The fundamental cause of these differences has been established. Second, the quantum fluctuations of the input mode can be separated into the amplitude and phase ones, so that the predominantly phase fluctuations are directed into one output mode, say, the reflected one, while the amplitude fluctuations are directed into the other (transmitted) mode.
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.
Nonlinear Interaction of Elliptical Laser Beam with Collisional Plasma: Effect of Linear Absorption
NASA Astrophysics Data System (ADS)
Keshav, Walia; Sarabjit, Kaur
2016-01-01
In the present work, nonlinear interaction of elliptical laser beam with collisional plasma is studied by using paraxial ray approximation. Nonlinear differential equations for the beam width parameters of semi-major axis and semi-minor axis of elliptical laser beam have been set up and solved numerically to study the variation of beam width parameters with normalized distance of propagation. Effects of variation in absorption coefficient and plasma density on the beam width parameters are also analyzed. It is observed from the analysis that extent of self-focusing of beam increases with increase/decrease in plasma density/absorption coefficient.
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 μm, 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.
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.
NASA Astrophysics Data System (ADS)
Rafiee, M.; Liu, X. F.; He, X. Q.; Kitipornchai, S.
2014-07-01
The nonlinear free vibration of carbon nanotubes/fiber/polymer composite (CNTFPC) multi-scale plates with surface-bonded piezoelectric actuators is studied in this paper. The governing equations of the piezoelectric nanotubes/fiber/polymer multiscale laminated composite plates are derived based on first-order shear deformation plate theory (FSDT) and von Kármán geometrical nonlinearity. Halpin-Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. A perturbation scheme of multiple time scales is employed to determine the nonlinear vibration response and the nonlinear natural frequencies of the plates with immovable simply supported boundary conditions. The effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) on the linear and nonlinear natural frequencies of the piezoelectric nanotubes/fiber/polymer multiscale composite plate are investigated through a detailed parametric study.
NASA Astrophysics Data System (ADS)
Gu, Bing; Liu, Dahui; Wu, Jia-Lu; He, Jun; Cui, Yiping
2014-12-01
We present the Z-scan technique using azimuthal-variant vector beams for characterizing the nonlinear refractive index of an isotropic nonlinear medium. Compared with the conventional Z-scan measurements, the reliability of the vector beam Z-scan is improved because the focused azimuthal-variant vector beam exhibits a uniform-intensity focal ring instead of a focal spot. Experimentally, our investigation demonstrates that the Z-scan using radially polarized beams is a preferable technique for characterizing the optical nonlinearity of an imperfect sample.
Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity.
Polesana, P; Dubietis, A; Porras, M A; Kucinskas, E; Faccio, D; Couairon, A; Di Trapani, P
2006-05-01
The near-field dynamics of a femtosecond Bessel beam propagating in a Kerr nonlinear medium (fused silica) is investigated both numerically and experimentally. We demonstrate that the input Bessel beam experiences strong nonlinear reshaping. Due to the combined action of self-focusing and nonlinear losses the reshaped beam exhibits a radial compression and reduced visibility of the Bessel oscillations. Moreover, we show that the reshaping process starts from the intense central core and gradually replaces the Bessel beam profile during propagation, highlighting the conical geometry of the energy flow. PMID:16803062
A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation
NASA Technical Reports Server (NTRS)
Crivelli, Luis A.; Felippa, Carlos A.
1992-01-01
A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.
NASA Astrophysics Data System (ADS)
Rauter, N.; Lammering, R.
2015-04-01
In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1-S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1-S2 and S2-S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo-Hooke and Mooney-Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.
Ronald C. Davidson; W. Wei-li Lee; Hong Qin; Edward Startsev
2001-11-08
This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.
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.
Suppression of space charge induced beam halo in nonlinear focusing channel
NASA Astrophysics Data System (ADS)
Batygin, Yuri K.; Scheinker, Alexander; Kurennoy, Sergey; Li, Chao
2016-04-01
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
An optimization-based method for geometrical calibration in cone-beam CT without dedicated phantoms
NASA Astrophysics Data System (ADS)
Panetta, D.; Belcari, N.; DelGuerra, A.; Moehrs, S.
2008-07-01
In this paper we present a new method for the determination of geometrical misalignments in cone-beam CT scanners, from the analysis of the projection data of a generic object. No a priori knowledge of the object shape and positioning is required. We show that a cost function, which depends on the misalignment parameters, can be defined using the projection data and that such a cost function has a local minimum in correspondence to the actual parameters of the system. Hence, the calibration of the scanner can be carried out by minimizing the cost function using standard optimization techniques. The method is developed for a particular class of 3D object functions, for which the redundancy of the fan beam sinogram in the transaxial midplane can be extended to cone-beam projection data, even at wide cone angles. The method has an approximated validity for objects which do not belong to that class; in that case, a suitable subset of the projection data can be selected in order to compute the cost function. We show by numerical simulations that our method is capable to determine with high accuracy the most critical misalignment parameters of the scanner, i.e., the transversal shift and the skew of the detector. Additionally, the detector slant can be determined. Other parameters such as the detector tilt, the longitudinal shift and the error in the source-detector distance cannot be determined with our method, as the proposed cost function has a very weak dependence on them. However, due to the negligible influence of these latter parameters in the reconstructed image quality, they can be kept fixed at estimated values in both calibration and reconstruction processes without compromising the final result. A trade-off between computational cost and calibration accuracy must be considered when choosing the data subset used for the computation of the cost function. Results on real data of a mouse femur as obtained with a small animal micro-CT are shown as well, proving
NASA Technical Reports Server (NTRS)
Prasad, C. B.; Mei, Chuh
1987-01-01
Multiple-mode nonlinear analysis is carried out for beams subjected to acoustic excitation. Effects of both nonlinear damping and large-deflection are included in the analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening of the strain response peaks and the increase of modal frequency. An amplitude dependent nonlinear damping model is used in the anlaysis to study the effects and interactions of multiple modes, nonlinear stiffness and nonlinear damping on the random response of beams. Mean square maximum deflection, mean square maximum strain, and spectral density function of maximum strain for simple supported and clamped beams are obtained. It is shown analytically that nonlinear damping contributes significantly to the broadening of the response peak and to the mean square deflection and strain.
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
Reciprocity breaking during nonlinear propagation of adapted beams through random media.
Palastro, J P; Peñano, J; Nelson, W; DiComo, G; Helle, M; Johnson, L A; Hafizi, B
2016-08-22
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate phase aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown, providing the first analysis of AO applied to high peak power laser beams. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere. PMID:27557166
NASA Astrophysics Data System (ADS)
Liu, Peipei; Sohn, Hoon; Park, Byeongjin
2015-06-01
Damage often causes a structural system to exhibit severe nonlinear behaviors, and the resulting nonlinear features are often much more sensitive to the damage than their linear counterparts. This study develops a laser nonlinear wave modulation spectroscopy (LNWMS) so that certain types of damage can be detected without any sensor placement. The proposed LNWMS utilizes a pulse laser to generate ultrasonic waves and a laser vibrometer for ultrasonic measurement. Under the broadband excitation of the pulse laser, a nonlinear source generates modulations at various frequency values due to interactions among various input frequency components. State space attractors are reconstructed from the ultrasonic responses measured by LNWMS, and a damage feature called Bhattacharyya distance (BD) is computed from the state space attractors to quantify the degree of damage-induced nonlinearity. By computing the BD values over the entire target surface using laser scanning, damage can be localized and visualized without relying on the baseline data obtained from the pristine condition of a target structure. The proposed technique has been successfully used for visualizing fatigue crack in an aluminum plate and delamination and debonding in a glass fiber reinforced polymer wind turbine blade.
A geometrical approach to control and controllability of nonlinear dynamical networks
Wang, Le-Zhi; Su, Ri-Qi; Huang, Zi-Gang; Wang, Xiao; Wang, Wen-Xu; Grebogi, Celso; Lai, Ying-Cheng
2016-01-01
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. 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 meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control. PMID:27076273
A geometrical approach to control and controllability of nonlinear dynamical networks.
Wang, Le-Zhi; Su, Ri-Qi; Huang, Zi-Gang; Wang, Xiao; Wang, Wen-Xu; Grebogi, Celso; Lai, Ying-Cheng
2016-01-01
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. 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 meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control. PMID:27076273
Studies of non-linear optical effects for agile beam steering
NASA Astrophysics Data System (ADS)
Vachss, F.; McMichael, I.; Yeh, P.
1993-11-01
The objective of this program is the demonstration of a new technique for massless beam steering of high energy laser radiation. Using the effect of nonlinear electrostriction in acousto-optic devices, we show large improvements in diffraction efficiency and resolution. These results are obtained through the development of a novel geometry for acousto-optic beam steering and of a prototype device designed to take advantage of this geometry. Theoretical and experimental results of this effort establish the validity of large aperture, high frequency nonlinear acousto-optic beam steering. The results are found to be applicable to steering of high power laser beams.
Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity
Sharma, Prerana
2015-07-31
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.
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
Effects of geometrical order on the linear and nonlinear optical properties of metal nanoparticles
NASA Astrophysics Data System (ADS)
McMahon, Matthew David
This dissertation describes experimental and computational studies of the effects of ordered arrangement on the linear and nonlinear optical properties of metal nanoparticles. The principal result is that second-harmonic light may be generated and observed from nanoparticle gratings having maximum in-plane symmetry, provided that one looks at non-normal observation angles. These measurements are made possible by a custom-built variable-angle microscope, and enable a variety of studies of the second-order nonlinear response of nanoparticles that were not previously feasible. In addition, the surface plasmon resonance of metal nanoparticles is studied by linear spectroscopy. A comparison of experimental data with computational modeling shows that under normal ambient conditions, Ag nanoparticles tarnish by a sulfidation reaction more readily than bulk silver, and that even a very thin surface layer of corroded material (Ag2S) considerably redshifts and weakens the localized surface plasmon resonance of a nanoparticle.
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.
Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.
2016-01-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs. PMID:27581625
Chaitanya, N Apurv; Jabir, M V; Banerji, J; Samanta, G K
2016-01-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs. PMID:27581625
Shaping of light beams by 3D direct laser writing on facets of nonlinear crystals.
Lightman, Shlomi; Gvishi, Raz; Hurvitz, Gilad; Arie, Ady
2015-10-01
We demonstrate experimentally spatial-mode conversions of light beams generated in a quadratic nonlinear process by micron-scale structures placed on the facets of nonlinear crystals. These structures were printed on the crystal facets using a three-dimensional (3D) direct laser writing system. The functional structures were designed to modify the phase of the beam at specific wavelengths, thereby enabling conversion of a fundamental Gaussian laser beam into different high-order Hermite-Gaussian modes, Laguerre-Gaussian modes, and zeroth-order Bessel beams of the second harmonic. This facet functionalization opens exciting new opportunities for robust and compact beam shaping in a nonlinear interaction without compromising the conversion efficiency. PMID:26421556
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.
2003-01-01
The use of stress predictions from equivalent linearization analyses in the computation of high-cycle fatigue life is examined. Stresses so obtained differ in behavior from the fully nonlinear analysis in both spectral shape and amplitude. Consequently, fatigue life predictions made using this data will be affected. Comparisons of fatigue life predictions based upon the stress response obtained from equivalent linear and numerical simulation analyses are made to determine the range over which the equivalent linear analysis is applicable.
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.
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.
Reciprocity breaking during nonlinear propagation of adapted beams through random media
NASA Astrophysics Data System (ADS)
Palastro, J. P.; Peñano, J.; Nelson, W.; DiComo, G.; Helle, M.; Johnson, L. A.; Hafizi, B.
2016-08-01
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate profile aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.
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 γ to be determined. In the paper, we obtain a general formula for computing the constant γ. 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
Effect of geometric elastic non-linearities on the impact response of flexible multi-body systems
NASA Astrophysics Data System (ADS)
Bakr, E. M.; Shabana, A. A.
1987-02-01
The intermittent motion behavior of large scale geometrically non-linear flexible multi-body systems due to impact loading is investigated. Impacts and the associated impulsive forces are incorporated into the dynamic formulation by using a generalized momentum balance. The solution of the momentum equation provides the jump discontinuities in the system velocities and reaction forces. Flexible components in the system are discretized by using the finite element method. Because of the large rotations of the system components, a set of reference co-ordinates are employed to describe the motion of a selected body reference. The rigid body modes of the finite element shape functions are eliminated by using a set of reference conditions and accordingly a unique displacement field is defined. In order to account for the inertia and elastic non-linearities which are, respectively, the results of the large rotations and finite deformations, the system inertia and stiffness characteristics have to be iteratively updated. Two numerical examples of different nature are presented. The first example is a high speed slider crank mechanism with a flexible connecting rod. In the second example, however, the dynamic response of a flexible multi-body aircraft during the touch down impact is predicted.
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
Comparison of Finite Element Non-Linear Beam Random Response with Experimental Results
NASA Astrophysics Data System (ADS)
Chen, R. R.; Mei, C.; Wolfe, HF
1996-09-01
A finite element formulation combined with the equivalent linearization technique and normal mode method is developed for the non-linear random response of beams subjected to acoustic and thermal loads applied simultaneously. To validate the present formulation and solution procedure, results are compared with the classical continuum solution and the Fokker-Planck-Kolmogorov equation solution. Comparison is also made with experimental data for a pre-stretched clamped beam. Random responses of thermally buckled simply supported beam, clamped beam and simply supported-clamped beam are presented. The comparison of the present simultaneously loaded response with the existing sequentially loaded results shows a significant difference between them.
Experimental Study on Nonlinear Vibrations of Fixed-Fixed Curved Beams
NASA Astrophysics Data System (ADS)
Kumar, Ajay; Patel, B. P.
2016-07-01
Nonlinear dynamic behavior of fixed-fixed shallow and deep curved beams is studied experimentally using non-contact type of electromagnetic shaker and acceleration measurements. The frequency response obtained from acceleration measurements is found to be in fairly good agreement with the computational response. The travellingwave phenomenon along with participation of higher harmonics and softening nonlinearity are observed. The experimental results on the internal resonance of curved beams due to direct excitation of anti-symmetric mode are reported for the first time. The deep curved beam depicts chaotic response at higher excitation amplitude.
Beam instabilities stabilization as a result of strong nonlinear interaction between waves
Soloshenko, I.A.; Taranov, V.B.; Tsyolko, V.V.; Shamrai, K.P.; Shulzhenko, P.M. )
1990-01-01
It is shown that the nonlinear interaction between unstable low-frequency ion waves and high-frequency electron waves growing in an ion beam plasma can result in stabilization of one of the modes if the level of the other is sufficiently high. A theoretical model of the phenomenon has been developed, and its predictions are in reasonable agreement with experimental results. The suppression mechanism is considered, and appears to be essentially nonlinear. The effect of this mutual suppression of ion beam instabilities may be important for improved ion beam transport.
NASA Astrophysics Data System (ADS)
Berczynski, P.; Kravtsov, Yu. A.
2004-10-01
A simple and effective method to describe Gaussian beams propagation and diffraction in arbitrary smoothly inhomogeneous 2D medium has been developed based on the eikonal form of complex geometrical optics. The method assumes the eikonal equation can be solved in paraxial approximation in curvilinear frame of references, connected with the central ray. The Riccati-type ordinary differential equation is derived for complex parameter characterizing the Gaussian beam width and phase front curvature. The same parameter was proved to define both the modulus and the argument of the complex amplitude. As a result, the problem of the Gaussian beam diffraction in inhomogeneous media has been reduced to the solution of the ordinary differential equation of the first order, which can be readily calculated numerically for arbitrary profile of dielectric permittivity.
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
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
NASA Astrophysics Data System (ADS)
Porras, Miguel A.; Ruiz-Jiménez, Carlos; Losada, Juan Carlos
2015-12-01
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 (NLUBB) whose inward Hänkel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines the NLUBB attractor is given. Steady or unsteady propagation depends on whether the attracting NLUBB has a small, exponentially growing, unstable mode. In the case of unsteady propagation, periodic, quasiperiodic, or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
Extension of non-linear beam models with deformable cross sections
NASA Astrophysics Data System (ADS)
Sokolov, I.; Krylov, S.; Harari, I.
2015-12-01
Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.
NASA Astrophysics Data System (ADS)
Nili Ahmadabadi, Z.; Khadem, S. E.
2014-09-01
This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free-free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.
BEAM-BASED NON-LINEAR OPTICS CORRECTIONS IN COLLIDERS.
PILAT, R.; LUO, Y.; MALITSKY, N.; PTITSYN, V.
2005-05-16
A method has been developed to measure and correct operationally the non-linear effects of the final focusing magnets in colliders, that gives access to the effects of multi-pole errors by applying closed orbit bumps, and analyzing the resulting tune and orbit shifts. This technique has been tested and used during 4 years of RHIC (the Relativistic Heavy Ion Collider at BNL) operations. I will discuss here the theoretical basis of the method, the experimental set-up, the correction results, the present understanding of the machine model, the potential and limitations of the method itself as compared with other non-linear correction techniques.
NASA Astrophysics Data System (ADS)
Chen, Ruixi; Mei, Chuh
1993-04-01
A finite element formulation combined with the equivalent linearization technique and the normal mode method is developed for the study of nonlinear random response of beams subjected to simultaneously applied acoustic and thermal loads. Examples include thermally buckled random response of simply supported beam, clamped-clamped beam and simply supported-clamped beam. To compare and validate the present formulation, results are compared with the solutions from existing sequential load method, and significant difference has been found. Results by classical continuum solution and the solution of Fokker-Planck-Kolmogorov equation are also derived and obtained for comparison.
Light steering of Air-Gaussian beam in Nonlocal Nonlinear Medium
NASA Astrophysics Data System (ADS)
Chen, Ran; Zhang, Xiaping
2016-07-01
With a nonlocal model, we investigate the propagation dynamics of a single Airy-Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results show that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Espesically, by tuning the phase difference between the two beams, we can steer the centre of the bound AiG beams in nonlocal nonlinear media.
Bound states of breathing Airy-Gaussian beams in nonlocal nonlinear medium
NASA Astrophysics Data System (ADS)
Zhang, Xiaping
2016-05-01
With a nonlocal model, we investigate the propagation dynamics of a single Airy-Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results shows that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Especially, by tuning the phase difference between the two beams, we can steer the center of the bound AiG beams in nonlocal nonlinear media.
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.
Effect of Geometric Azimuthal Asymmetries of PPM Stack on Electron Beam Characteristics
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Heinen, Vernon (Technical Monitor)
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.
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.
Nonlinear interaction of intense hypergeometric Gaussian subfamily laser beams in plasma
NASA Astrophysics Data System (ADS)
Sobhani, H.; Vaziri (Khamedi), M.; Rooholamininejad, H.; Bahrampour, A. R.
2016-07-01
Propagation of Hypergeometric-Gaussian laser beam in a nonlinear plasma medium is investigated by considering the Source Dependent Expansion method. A subfamily of Hypergeometric-Gaussian beams with a non-negative, even and integer radial index, can be expressed as the linear superposition of finite number of Laguerre-Gaussian functions. Propagation of Hypergeometric-Gaussian beams in a nonlinear plasma medium depends on the value of radial index. The bright rings' number of these beams is changed during the propagation in plasma medium. The effect of beam vortex charge number l and initial (input) beam intensity on the self-focusing of Hypergeometric-Gaussian beams is explored. Also, by choosing the suitable initial conditions, Hypergeometric-Gaussian subfamily beams can be converted to one or more mode components that a typical of mode conversion may be occurred. The self-focusing of these winding beams can be used to control the focusing force and improve the electron bunch quality in laser plasma accelerators.
Modelling Gaussian beam propagation through thick nonlinear refractive and absorptive media
NASA Astrophysics Data System (ADS)
Namarathne, D.; Walden, S.; Shortell, M.; Jaatinen, E.
2016-04-01
A novel numerical finite difference beam propagation method developed for quadratic refractive index media is presented and applied to TEM00 Gaussian beams propagating through nonlinear optical media. The beam's diffraction through the medium was calculated by using the nonlinear Schrodinger equation on small slices which proved to be effective for thick samples. The performance of the model was compared to experimental z-scan observations of colloidal ZnO particles at low cw and high pulsed peak powers at a wavelength of 532 nm. Different optical behaviours were observed in these two power regimes. Negligible nonlinear absorption and refraction were observed at low cw powers, with strong defocusing arising through thermal lensing in the colloidal solution. For the pulsed experiments with peak powers up to 43-kW and 7-ns pulses, values for the intensity-dependent absorption were determined to be β = 1.0 × 10^{ - 10} {text{m/W}} and n_{{2{text{R}}}} = 2.0 × 10^{ - 18} {text{m}}2 /{text{W}}. Despite the very different nonlinear and thermal-optical behaviours in two power regimes, there was good agreement between the model and observations. This demonstrates the effectiveness of the approach in extracting the nonlinear properties of a medium even if it is not optically thin and in the case when a sample displays both strong nonlinear refraction and absorption.
Edward A. Startsev; Ronald C. Davidson; Hong Qin
2002-05-07
In this paper, a 3-D nonlinear perturbative particle simulation code (BEST) [H. Qin, R.C. Davidson and W.W. Lee, Physical Review Special Topics on Accelerators and Beams 3 (2000) 084401] is used to systematically study the stability properties of intense nonneutral charged particle beams with large temperature anisotropy (T{sub {perpendicular}b} >> T{sub {parallel}b}). The most unstable modes are identified, and their eigen frequencies, radial mode structure, and nonlinear dynamics are determined for axisymmetric perturbations with {partial_derivative}/{partial_derivative}{theta} = 0.
Effects of Transverse Physics on Nonlinear Evolution of Longitudinal Space-Charge Waves in Beams
K. Tian, I. Haber, R.A. Kishek, P.G. O'Shea, M. Reiser, D. Stratakis
2009-05-01
Longitudinal space-charge waves can introduce energy perturbations into charge particle beams and degrade the beam quality, which is critical to many modern applications of particle accelerators. Although many longitudinal phenomena arising from small perturbations can be explained by a one-dimensional cold fluid theory, nonlinear behavior of space-charge waves observed in experiments has not been well understood. In this paper, we summarize our recent investigation by means of more detailed measurements and self-consistent simulations. Combining the numerical capability of a PIC code, WARP, with the detailed initial conditions measured by our newly developed time resolved 6-D phase space mapping technique, we are able to construct a self consistent model for studying the complex physics of longitudinal dynamics of space-charge dominated beams. Results from simulation studies suggest that the unexplained nonlinear behavior of space-charge waves may be due to transverse mismatch or misalignment of beams.
Numerical simulation of nonlinear processes in a beam-plasma system
Efimova, A. A. Berendeev, E. A.; Vshivkov, V. A.; Dudnikova, G. I.
2015-10-28
In the present paper we consider the efficiency of the electromagnetic radiation generation due to various nonlinear processes in the beam-plasma system. The beam and plasma parameters were chosen close to the parameters in the experiment on the GOL-3 facility (BINP SB RAS). The model of the collisionless plasma is described by system of the Vlasov-Maxwell equations with periodic boundary conditions. The parallel numerical algorithm is based on the particles-in-cell method (PIC) with mixed Euler-Lagrangian domain decomposition. Various scenarios of nonlinear evolution in the beam-plasma system under the influence of an external magnetic field in case of a low density beam were studied. The energy transfer from one unstable mode to the others modes was observed.
Effects of nonlinear damping on random response of beams to acoustic loading
NASA Technical Reports Server (NTRS)
Mei, C.; Prasad, C. B.
1986-01-01
Effects of both nonlinear damping and large-deflection are included in the theoretical analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening of the strain response peak and the increase of the modal frequency. Two nonlinear damping models are considered in the analysis using a single-mode approach. Mean square maximum deflection, mean square maximum strain, and spectral density function of maximum strain for simply supported and clamped beams are obtained. It is demonstrated that nonlinear damping contributes significantly to the broadening of the response peak and to the mean square maximum deflection and strain.
NASA Astrophysics Data System (ADS)
Kong, Yan; Quan, Wei; Wei, Qi; Qiu, Peng
2016-05-01
We theoretically design a device composed of four nanoslits to dynamically modulate the propagation direction of light beam by embedding non-linear material and air, respectively. Directions of radiation fields are determined by the phase difference of the surface waves at the exit interface and distance of each slit. Numerical simulations using finite element method verify that the unidirectional excitation and beam focusing can be achieved easily by changing the intensity of incident light.
Nonlinear delta(f) Simulations of Collective Effects in Intense Charged Particle Beams
Hong Qin
2003-01-21
A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, et al., in Proc. of the Particle Accelerator Conference, Chicago, 2001 (IEEE, Piscataway, NJ, 2001), Vol. 1, p. 688.] at the Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very-high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles.
Random vibration of nonlinear beams by the new stochastic linearization technique
NASA Technical Reports Server (NTRS)
Fang, J.
1994-01-01
In this paper, the beam under general time dependent stationary random excitation is investigated, when exact solution is unavailable. Numerical simulations are carried out to compare its results with those yielded by the conventional linearization techniques. It is found that the modified version of the stochastic linearization technique yields considerably more accurate results for the mean square displacement of the beam than the conventional equivalent linearization technique, especially in the case of large nonlinearity.
Lin, Tai-Chia; Belić, Milivoj R.; Petrović, Milan S.; Chen, Goong
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.
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
NASA Astrophysics Data System (ADS)
Müller, Kei W.; Meier, Christoph; Wall, Wolfgang A.
2015-12-01
Networks of crosslinked biopolymer filaments such as the cytoskeleton are the subject of intense research. Oftentimes, mechanics on the scale of single monomers (∼ 5 nm) govern the mechanics of the entire network (∼ 10 μm). Until now, one either resolved the small scales and lost the big (network) picture or focused on mechanics above the single-filament scale and neglected the molecular architecture. Therefore, the study of network mechanics influenced by the entire spectrum of relevant length scales has been infeasible so far. We propose a method that reconciles both small and large length scales without the otherwise inevitable loss in either numerical efficiency or geometrical (molecular) detail. Both explicitly modeled species, filaments and their crosslinkers, are discretized with geometrically exact beam finite elements of Simo-Reissner type. Through specific coupling conditions between the elements of the two species, mechanical joints can be established anywhere along a beam's centerline, enabling arbitrary densities of chemical binding sites. These binding sites can be oriented to model the monomeric architecture of polymers. First, we carefully discuss the method and then demonstrate its capabilities by means of a series of numerical examples.
Ella, Lior Yuvaraj, D.; Suchoi, Oren; Shtempluk, Oleg; Buks, Eyal
2015-01-07
We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.
NASA Astrophysics Data System (ADS)
Ella, Lior; Yuvaraj, D.; Suchoi, Oren; Shtempluk, Oleg; Buks, Eyal
2015-01-01
We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.
Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D
Shen, Wei; Sheng, Zheng-Mao; Fu, G. Y.; Tobias, Benjamin; Zeeland, Michael Van; Wang, Feng
2015-04-15
In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.
Wu, Y.; Xu, Z.; Li, Z. H.; Tang, C. X.
2012-07-15
In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.
NASA Astrophysics Data System (ADS)
Yildirim, Tanju; Ghayesh, Mergen H.; Li, Weihua; Alici, Gursel
2016-01-01
An experimental investigation has been carried out on the nonlinear dynamics of a clamped-clamped Magneto-Rheological Elastomer (MRE) sandwich beam with a point mass when subjected to a point excitation. Three sets of experiments have been conducted namely for (i) an aluminium beam, (ii) a MRE sandwich beam in the absence of a magnetic field and (iii) a MRE sandwich beam in the presence of a magnetic field. An electrodynamic shaker was used to excite each system and the corresponding displacement of the point mass was measured: for the third experiment (iii), an array of magnets has been placed at various distances away from the centre of the point mass to investigate the effect of changing stiffness and damping properties on the nonlinear dynamical behaviour. An interesting feature for the third group is the beam point mass displacement was no longer symmetric as the stiffness and damping of the system are increased when moving towards the magnets. Both the first and second groups exhibited distinct nonlinear behaviour; however, for the third group this work shows that for a low magnetic field the sandwich beam exhibits two distinct resonance peaks, one occurring above and the other below the fundamental natural frequency of the transverse motion, with the right one larger. For a larger magnetic field, these peaks even out until the magnetic force was large enough that the hardening-type nonlinear behaviour changes to a softening-type; a significant qualitative change in the nonlinear dynamical behaviour of the system, due to the presence of the magnetic field, was observed.
Beam-shape effects in nonlinear Compton and Thomson scattering
Heinzl, T.; Seipt, D.; Kaempfer, B.
2010-02-15
We discuss intensity effects in collisions between beams of optical photons from a high-power laser and relativistic electrons. Our main focus is on the modifications of the emission spectra due to realistic finite-beam geometries. By carefully analyzing the classical limit we precisely quantify the distinction between strong-field QED Compton scattering and classical Thomson scattering. A purely classical, but fully covariant, calculation of the bremsstrahlung emitted by an electron in a plane-wave laser field yields radiation into harmonics, as expected. This result is generalized to pulses of finite duration and explains the appearance of line broadening and harmonic substructure as an interference phenomenon. The ensuing numerical treatment confirms that strong focusing of the laser leads to a broad continuum while higher harmonics become visible only at moderate focusing, and hence lower intensity. We present a scaling law for the backscattered photon spectral density which facilitates averaging over electron beam phase space. Finally, we propose a set of realistic parameters such that the observation of intensity-induced spectral red shift, higher harmonics, and their substructure becomes feasible.
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.
Terahertz radiation generation by nonlinear mixing of two laser beams over a thin foil
NASA Astrophysics Data System (ADS)
Chauhan, Santosh; Parashar, J.
2015-07-01
Terahertz radiation generation via nonlinear mixing of two laser beams incident over a thin metal foil is explored. The lasers exert a ponderomotive force on the electrons of metal foil at beat frequency which lies in the terahertz range. The metal foil acts as antenna, producing terahertz radiations, highly directional in nature.
Spata, Michael
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.
Terahertz radiation generation by nonlinear mixing of two laser beams over a thin foil
Chauhan, Santosh; Parashar, J.
2015-07-31
Terahertz radiation generation via nonlinear mixing of two laser beams incident over a thin metal foil is explored. The lasers exert a ponderomotive force on the electrons of metal foil at beat frequency which lies in the terahertz range. The metal foil acts as antenna, producing terahertz radiations, highly directional in nature.
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.
Beam loading in the nonlinear regime of plasma-based acceleration.
Tzoufras, M; Lu, W; Tsung, F S; Huang, C; Mori, W B; Katsouleas, T; Vieira, J; Fonseca, R A; Silva, L O
2008-10-01
A theory that describes how to load negative charge into a nonlinear, three-dimensional plasma wakefield is presented. In this regime, a laser or an electron beam blows out the plasma electrons and creates a nearly spherical ion channel, which is modified by the presence of the beam load. Analytical solutions for the fields and the shape of the ion channel are derived. It is shown that very high beam-loading efficiency can be achieved, while the energy spread of the bunch is conserved. The theoretical results are verified with the particle-in-cell code OSIRIS. PMID:18851537
Beam Loading in the Nonlinear Regime of Plasma-Based Acceleration
Tzoufras, M.; Lu, W.; Tsung, F. S.; Huang, C.; Mori, W. B.; Katsouleas, T.; Vieira, J.; Fonseca, R. A.; Silva, L. O.
2008-10-03
A theory that describes how to load negative charge into a nonlinear, three-dimensional plasma wakefield is presented. In this regime, a laser or an electron beam blows out the plasma electrons and creates a nearly spherical ion channel, which is modified by the presence of the beam load. Analytical solutions for the fields and the shape of the ion channel are derived. It is shown that very high beam-loading efficiency can be achieved, while the energy spread of the bunch is conserved. The theoretical results are verified with the particle-in-cell code OSIRIS.
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.
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.
Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams
Nikolas C. Logan and Ronald C. Davidson
2012-07-18
This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (TllT⊥ < 1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in accelerated particle beams, including Harris-type electrostatic instabilities, known to limit the luminosity and minimum spot size attainable in experiments. The thermodynamic bound on the field perturbation energy of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an arbitrary initial distribution function, including the effects of intense self-fields, finite geometry and nonlinear processes. This paper also includes analytical estimates of the nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic bi-Maxwellian distributions.
NASA Astrophysics Data System (ADS)
Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline
2001-12-01
Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.
Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
Bliokh, Konstantin Yu.
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.
Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids
NASA Astrophysics Data System (ADS)
Aureli, M.; Basaran, M. E.; Porfiri, M.
2012-03-01
In this paper, we study flexural vibrations of a cantilever beam with thin rectangular cross section submerged in a quiescent viscous fluid and undergoing oscillations whose amplitude is comparable with its width. The structure is modeled using Euler-Bernoulli beam theory and the distributed hydrodynamic loading is described by a single complex-valued hydrodynamic function which accounts for added mass and fluid damping experienced by the structure. We perform a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, to understand the dependence of the hydrodynamic function on the governing flow parameters. We find that increasing the frequency and amplitude of the vibration elicits vortex shedding and convection phenomena which are, in turn, responsible for nonlinear hydrodynamic damping. We establish a manageable nonlinear correction to the classical hydrodynamic function developed for small amplitude vibration and we derive a computationally efficient reduced order modal model for the beam nonlinear oscillations. Numerical and theoretical results are validated by comparison with ad hoc designed experiments on tapered beams and multimodal vibrations and with data available in the literature. Findings from this work are expected to find applications in the design of slender structures of interest in marine applications, such as biomimetic propulsion systems and energy harvesting devices.
Nonlinear tracking control of vibration amplitude for a parametrically excited microcantilever beam
NASA Astrophysics Data System (ADS)
Nguyen, Quoc Chi; Krylov, Slava
2015-03-01
In this paper, a feedback control algorithm to regulate oscillation amplitude of a microelectromechanical (MEMS) cantilever beam operated at parametric resonances is developed. The control objective is to drive the oscillation amplitude of the micro-beam, which is amplified using parametric excitation, to the desired values. The principle of the control algorithm is to establish an output tracking control based on the nonlinear dynamic model of the micro-beam, where the supply voltage is considered as a control input. The tracking control algorithm is designed to solve the singularities resulting from the zero-deflection state of the micro-beam. The Galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the beam into a set of ordinary differential equations (ODEs). Uniformly ultimate boundedness stability of the control system is proved using Lyapunov method. The effectiveness of the proposed control algorithm is illustrated via numerical simulations.
NASA Astrophysics Data System (ADS)
Mattei, P.-O.; Ponçot, R.; Pachebat, M.; Côte, R.
2016-07-01
In order to control the sound radiation by a structure, one aims to control vibration of radiating modes of vibration using "Energy Pumping" also named "Targeted Energy Transfer". This principle is here applied to a simplified model of a double leaf panel. This model is made of two beams coupled by a spring. One of the beams is connected to a nonlinear absorber. This nonlinear absorber is made of a 3D-printed support on which is clamped a buckled thin small beam with a small mass fixed at its centre having two equilibrium positions. The experiments showed that, once attached onto a vibrating system to be controlled, under forced excitation of the primary system, the light bistable oscillator allows a reduction of structural vibration up to 10 dB for significant amplitude and frequency range around the first two vibration modes of the system.
Linear and nonlinear analysis of a gyrotron traveling wave amplifier with misaligned electron beam
Jiao Chongqing; Luo Jirun
2006-11-15
This paper presents linear and self-consistent nonlinear theories to describe the beam-wave interaction in a gyrotron traveling wave amplifier (gyro-TWA) with a misaligned electron beam. A linear theory based on the linearized Vlasov equations is developed by using Laplace transforms. By setting appropriate initial values of the electron guiding center, the nonlinear theory without misalignment can be used to study the misalignment effect. The two theories are in good agreement in the small-signal region for the gyro-TWA. The effects of beam misalignment on the TE{sub 01} mode gyro-TWA operating at the fundamental are discussed and the corresponding physical mechanism is analyzed.
Nonlinear modes of an intense laser beam interacting with a periodic lattice of nanoparticle
Sepehri Javan, N. Homami, S. H. H.
2015-08-15
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.
Laser beam propagation through bulk nonlinear media: Numerical simulation and experiment
NASA Astrophysics Data System (ADS)
Kovsh, Dmitriy I.
This dissertation describes our efforts in modeling the propagation of high intensity laser pulses through optical systems consisting of one or multiple nonlinear elements. These nonlinear elements can be up to 103 times thicker than the depth of focus of the laser beam, so that the beam size changes drastically within the medium. The set of computer codes developed are organized in a software package (NLO_BPM). The ultrafast nonlinearities of the bound-electronic n2 and two-photon absorption as well as time dependent excited-state, free-carrier and thermal nonlinearities are included in the codes for modeling propagation of picosecond to nanosecond pulses and pulse trains. Various cylindrically symmetric spatial distributions of the input beam are modeled. We use the cylindrical symmetry typical of laser outputs to reduce the CPU and memory requirements making modeling a real- time task on PC's. The hydrodynamic equations describing the rarefaction of the medium due to heating and electrostriction are solved in the transient regime to determine refractive index changes on a nanosecond time scale. This effect can be simplified in some cases by an approximation that assumes an instantaneous expansion. We also find that the index change obtained from the photo-acoustic equation overshoots its steady-state value once the ratio between the pulse width and the acoustic transit time is greater than unity. We numerically study the sensitivity of the closed- aperture Z-scan experiment to nonlinear refraction for various input beam profiles. If the beam has a ring structure with a minimum (or zero) on axis in the far field, the sensitivity of Z-scan measurements can be increased by up to one order of magnitude. The linear propagation module integrated with the nonlinear beam propagation codes allows the simulation of typical experiments such as Z-scan and optical limiting experiments. We have used these codes to model the performance of optical limiters. We study two of the
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 χ(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 χxxxx(3) component of the third-order susceptibility tensor and its anisotropy sign and amplitude value for BaF2 and YVO4 crystals are estimated and discussed.
Samim, Masood; Sandkuijl, Daaf; Tretyakov, Ian; Cisek, Richard; Barzda, Virginijus
2013-01-01
Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red), which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures. PMID:24022688
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.
NASA Astrophysics Data System (ADS)
Abd El Baky, Hussien
--slip relation is developed considering the interaction between the interfacial normal and shear stress components along the bonded length. A new approach is proposed to describe the entire tau-s relationship based on three separate models. The first model captures the shear response of an orthotropic FRP laminate. The second model simulates the shear characteristics of an adhesive layer, while the third model represents the shear nonlinearity of a thin layer inside the concrete, referred to as the interfacial layer. The proposed bond--slip model reflects the geometrical and material characteristics of the FRP, concrete, and adhesive layers. Two-dimensional and three-dimensional nonlinear displacement-controlled finite element (FE) models are then developed to investigate the flexural and FRP/concrete interfacial responses of FRP-strengthened reinforced concrete beams. The three-dimensional finite element model is created to accommodate cases of beams having FRP anchorage systems. Discrete interface elements are proposed and used to simulate the FRP/concrete interfacial behaviour before and after cracking. The FE models are capable of simulating the various failure modes, including debonding of the FRP either at the plate end or at intermediate cracks. Particular attention is focused on the effect of crack initiation and propagation on the interfacial behaviour. This study leads to an accurate and refined interpretation of the plate-end and intermediate crack debonding failure mechanisms for FRP-strengthened beams with and without FRP anchorage systems. Finally, the FE models are used to conduct a parametric study to generalize the findings of the FE analysis. The variables under investigation include two material characteristics; namely, the concrete compressive strength and axial stiffness of the FRP laminates as well as three geometric properties; namely, the steel reinforcement ratio, the beam span length and the beam depth. The parametric study is followed by a statistical
Improved calibration of the nonlinear regime of a single-beam gradient optical trap.
Wilcox, Jamianne C; Lopez, Benjamin J; Campàs, Otger; Valentine, Megan T
2016-05-15
We report an improved method for calibrating the nonlinear region of a single-beam gradient optical trap. Through analysis of the position fluctuations of a trapped object that is displaced from the trap center by controlled flow we measure the local trap stiffness in both the linear and nonlinear regimes without knowledge of the magnitude of the applied external forces. This approach requires only knowledge of the system temperature, and is especially useful for measurements involving trapped objects of unknown size, or objects in a fluid of unknown viscosity. PMID:27177009
Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma
Wang Yunliang; Shukla, P. K.; Eliasson, B.
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.
Numerical investigation of beam-driven PWFA in quasi-nonlinear regime
NASA Astrophysics Data System (ADS)
Londrillo, P.; Gatti, C.; Ferrario, M.
2014-03-01
In beam-driven Plasma Based Wakefield Acceleration (PWFA), the quasi-nonlinear model has been designed to combine high efficient 'blowout' regimes, where cold and overdense driving electron beams form a totally rarefied plasma channel, with low charge beam distribution assuring the excited wakefield preserves relevant linear properties. This scheme can have applications in experimental facilities, like SPARC 150 MeV linac at LNF-INFN laboratories, where low-emittance, low-charge narrow electron beams can be produced to be injected on a preformed plasma channel. Here we present a preliminary numerical investigation of this configuration, using the fully 3D ALaDyn PIC code, as a preparatory work to design optimal conditions for the COMB experimental set-up. Specific numerical tools, having computational and diagnostic advantages in PWFA conditions and checks of the numerical outcomes with analytical results, are also presented and discussed.
Nonlinear physics and energetic particle transport features of the beam-plasma instability
NASA Astrophysics Data System (ADS)
Carlevaro, Nakia; Falessi, Matteo V.; Montani, Giovanni; Zonca, Fulvio
2015-10-01
> 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 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 analysed.
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.
NASA Astrophysics Data System (ADS)
Invernizzi, Davide; Dozio, Lorenzo
2016-05-01
The equations of motions governing the free vibrations of prismatic slender beams rotating in a plane at constant angular velocity are derived according to a geometrically exact approach. Compared to other modeling methods, additional stiffening terms induced by pre-stress are found in the dynamic equations after fully consistent linearization about the deformed equilibrium configuration. These terms include axial, bending and torsional stiffening effects which arise when second-order generalized strains are retained. It is shown that their contribution becomes relevant at moderate to high angular speeds, where high means that the equilibrium state is subject to strains close to the limit where a physically linear constitutive law still applies. In particular, the importance of the axial stiffening is specifically investigated. The natural frequencies as a function of the angular velocity and other system parameters are computed and compared with benchmark cases available in the literature. Finally, the error on the modal characteristics of the rotating beam is evaluated when the linearization is carried out about the undeformed configuration.
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. Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E.
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.
Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam
NASA Astrophysics Data System (ADS)
Rizov, V.
2016-03-01
Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.
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.
Nonlinear control via approximate input-output linearization - The ball and beam example
NASA Technical Reports Server (NTRS)
Hauser, John; Sastry, Shankar; Kokotovic, Petar
1992-01-01
A study is made of approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree. For such systems, a method is provided for constructing approximate systems that are input-output linearizable. The analysis presented in this note is motivated through its application to a common undergraduate control laboratory experiment, the ball and beam system, where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization.
NASA Astrophysics Data System (ADS)
An, Weiming; Joshi, Chan; Mori, Warren; Lu, Wei
2014-10-01
We study the electron beam evolution in a nonlinear blowout PWFA when the accelerated beam has a very small matched spot size that can cause the plasma ions collapsing towards the beam. Contrary to the common belief, very small emittance growth of the accelerated electron beam is found when the plasma ion collapsing destroys the perfect linear focusing force in the plasma wake field. The improved quasi-static PIC code QuickPIC also allows us to use very high resolution and to model asymmetric spot sizes. Simulation results show that the accelerated beam will reach a steady state after several cm propagation in the plasma (which is why we can do simulations and not let the drive beam evolve). We find that for round beams the ion density (which is Li+) enhancement is indeed by factors of 100, but that the emittance only grows by around 20 percent. For asymmetric spot sizes, the ion collapse is less and emittance growth is zero in the plane with the largest emittance and about 20 percent in the other plane.
Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water.
Hafizi, B; Palastro, J P; Peñano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-04-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown, and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. The phenomenon of gain-focusing discussed here for propagation in water is expected to be of general occurrence applicable to any medium supporting nonlinear focusing and stimulated Raman scattering. PMID:25831383
Nonlinear beam dynamics studies at Indiana University. Final report, August 1, 1993--July 31, 1997
Lee, S.Y.
1998-03-31
During the three-year funding period the author`s achievements can be summarized as follows: (1) The author has systematically studied the effect of phase modulation on bunch distribution. (2) The author has found that a frequently observed proton beam instability when the velocity of cooling electrons differs from that of protons is due to Hopf bifurcation. The equilibrium proton beam distribution becomes a limiting cycle attractor. This technique can be used to measure the temperature of cooling electrons. (3) The author has studied mechanisms of controlled bunch dilution. Evolution of beam bunch profile is measured while the beam is perturbed by the modulation of a secondary rf system. The experimental data reveal that mean square bunch length {sigma}{sup 2}(t) exhibits two characteristic time scales. He finds that overlapping parametric resonances plays an important role in beam diffusion. (4) He has studied the effects of global chaos on the halo formation of space charge dominated beams. He has analyzed the halo produced by a modulating mismatched space charge dominated beam in a uniform focusing channel. He found that the halo formation is determined by a single scaling parameter, the space charge perveance parameter divided by the phase advance per unit length. The condition of global chaos can thus be predicted. In June 1994, Indiana University has served as the host of the USPAS (United States Particle Accelerator School). In July 1994, IUCF has also served as the host site of the workshop on the future direction of hadron facilities. In October 1994, the author organized a successful workshop on space charge dominated beams and application of high brightness beams. During this period of this funding, he has had many visitors from SSC, SLAC, Fermilab, and Brookhaven National Laboratory. He has carried out many nonlinear beam dynamics experiments at the IUCF Cooler Ring. He has published about 30 refereed journal papers related to this project. These
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.
Nonlinear theory of beam-wave interaction in the pasotron with a phase-mixed electron beam
Bliokh, Yu.P.; Nusinovich, G.S.
2006-02-15
The nonlinear theory describing the interaction processes in traveling-wave-amplifier (TWT) and backward-wave-oscillator (BWO) configurations of pasotrons is developed. It is shown that space charge forces in electron bunches formed in the process of beam-wave interaction in the pasotron play a role completely different from that in linear-beam devices with a strong magnetic focusing of electron beams. While in the latter devices the space charge forces limit the device efficiency due to saturation of the axial bunching, in the pasotron they do not destroy electron bunches but cause the radial expansion of them, which may increase device efficiency. The role of these forces is compared with the ion focusing and the radial electric field of the wave, and it is shown that, under certain conditions, it may dominate. The efficiency of the pasotron-TWT with a phase-mixed beam well focused at the entrance may exceed 50%. In the pasotron-BWO, the efficiency is lower (up to 26% in the case studied), but it can grow as the equivalent of the Pierce gain parameter increases.
NASA Astrophysics Data System (ADS)
Anandrao, K. Sanjay; Gupta, R. K.; Ramchandran, P.; Venkateswara Rao, G.
2014-03-01
The effect of temperature-dependent material properties on the geometric nonlinear flexural response and thermal postbuckling behavior of shear flexible Functionally Graded Material (FGM) beams is investigated under various thermal and thermo-mechanical environments. The important aspects of the thermal and thermo-mechanical bending and thermal post-buckling of FGM beams are studied. The temperature variation across the thickness is obtained analytically and the finite element method (FEM) is used to predict the transverse deflections and stresses in the flexural analysis and the load-deflection paths for the thermal postbuckling analysis. The through thickness continuous variation of the material properties of the FGM beams is considered using the standard power law distribution. The von-Karman-type strain-displacement relations are used to account for the moderately large deflections. The FGM beams, with the classical hinged and clamped boundary conditions, are analyzed considering the axially immovable ends. The numerical results are provided to clearly bring out the importance of including the temperature dependency of the material properties to evaluate the realistic flexural response and thermal postbuckling behavior of the FGM beams subjected to thermal and thermo-mechanical loadings.
NASA Astrophysics Data System (ADS)
Reaungamornrat, S.; Otake, Y.; Uneri, A.; Schafer, S.; Mirota, D. J.; Nithiananthan, S.; Stayman, J. W.; Khanna, A. J.; Reh, D. D.; Gallia, G. L.; Taylor, R. H.; Siewerdsen, J. H.
2012-02-01
Conventional surgical tracking configurations carry a variety of limitations in line-of-sight, geometric accuracy, and mismatch with the surgeon's perspective (for video augmentation). With increasing utilization of mobile C-arms, particularly those allowing cone-beam CT (CBCT), there is opportunity to better integrate surgical trackers at bedside to address such limitations. This paper describes a tracker configuration in which the tracker is mounted directly on the Carm. To maintain registration within a dynamic coordinate system, a reference marker visible across the full C-arm rotation is implemented, and the "Tracker-on-C" configuration is shown to provide improved target registration error (TRE) over a conventional in-room setup - (0.9+/-0.4) mm vs (1.9+/-0.7) mm, respectively. The system also can generate digitally reconstructed radiographs (DRRs) from the perspective of a tracked tool ("x-ray flashlight"), the tracker, or the C-arm ("virtual fluoroscopy"), with geometric accuracy in virtual fluoroscopy of (0.4+/-0.2) mm. Using a video-based tracker, planning data and DRRs can be superimposed on the video scene from a natural perspective over the surgical field, with geometric accuracy (0.8+/-0.3) pixels for planning data overlay and (0.6+/-0.4) pixels for DRR overlay across all C-arm angles. The field-of-view of fluoroscopy or CBCT can also be overlaid on real-time video ("Virtual Field Light") to assist C-arm positioning. The fixed transformation between the x-ray image and tracker facilitated quick, accurate intraoperative registration. The workflow and precision associated with a variety of realistic surgical tasks were significantly improved using the Tracker-on-C - for example, nearly a factor of 2 reduction in time required for C-arm positioning, reduction or elimination of dose in "hunting" for a specific fluoroscopic view, and confident placement of the x-ray FOV on the surgical target. The proposed configuration streamlines the integration of C
Nonlinear δF Simulation Studies of High-Intensity, Non-Axisymetric Beam Propagation
NASA Astrophysics Data System (ADS)
Kakaes, Konstantin; Stoltz, Peter; Davidson, Ronald
1998-11-01
The nonlinear δF formalism, previously developed and applied for axisymmetric beam propagation (P.H. Stoltz, W.W. Lee, and R-C. Davidson, this conference), has been extended to the case of general variation in the transverse phase space (X,Y,X^',Y^'). The analysis considers a high-intensity ion beam in the thin-beam approximation (rb << S) propagating through a periodic focusing solenoidal field κ_z(s+S)=κ_z(s). The distribution function Fb is divided into a zero-order part (F_b^0) plus a perturbation (δ F_b) which evolve nonlinearly in the zero-order and perturbed field configurations. The perturbed distribution function δ F_b(X,Y,X^',Y^',s) and potential δΨ(X,Y,s) are allowed to have general X-Y dependence, whereas the zero-order distribution F_b^0 is taken to be axisymmetric (fracpartialpartialθ=0). Simulation results are presented for two cases: (a) uniform focusing field with κ_z(s)=barκ_z=const, and (b) periodic focusing field with κ_z(s)=barκ_z+δκ_z(s). Beam propagation is investigated for both sudden and adiabatic turn-on of δκ_z(s).
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.
On the Nonlinear Effects in Focused Ultrasound Beams with Frequency Power Law Attenuation
NASA Astrophysics Data System (ADS)
Jiménez, N.; Redondo, J.; Sánchez-Morcillo, V.; Iglesias, P. C.; Camarena, F.
When finite amplitude ultrasound propagation is considered, changes in spatial features of focused ultrasound beams can be observed. These nonlinear effects typically appear in thermoviscous fluids as focal displacements, beam-width variations or gain changes. However, in soft-tissue media, the frequency dependence of the attenuation doesn't obey a squared law. In this way, these complex media response leads to weak dispersion that prevents the cumulative processes of energy transfer to higher harmonics. In this work we explore the influence of different frequency power law attenuation responses and its influence on the self-defocusing effects in focused ultrasound beams. Thus, we numerically explore the spatial field distributions produced by low-Fresnel number devices and High Intensity Focused Ultrasound (HIFU) radiating trough different soft-tissue media.
Ultrahigh Brilliance Multi-MeV γ-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 (θ_{γ}<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) γ-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 γ-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
A nonlinear OPC technique for laser beam control in turbulent atmosphere
NASA Astrophysics Data System (ADS)
Markov, V.; Khizhnyak, A.; Sprangle, P.; Ting, A.; DeSandre, L.; Hafizi, B.
2013-05-01
A viable beam control technique is critical for effective laser beam transmission through turbulent atmosphere. Most of the established approaches require information on the impact of perturbations on wavefront propagated waves. Such information can be acquired by measuring the characteristics of the target-scattered light arriving from a small, preferably diffraction-limited, beacon. This paper discusses an innovative beam control approach that can support formation of a tight laser beacon in deep turbulence conditions. The technique employs Brillouin enhanced fourwave mixing (BEFWM) to generate a localized beacon spot on a remote image-resolved target. Formation of the tight beacon doesn't require a wavefront sensor, AO system, or predictive feedback algorithm. Unlike conventional adaptive optics methods which allow wavefront conjugation, the proposed total field conjugation technique is critical for beam control in the presence of strong turbulence and can be achieved by using this non-linear BEFWM technique. The phase information retrieved from the established beacon beam can then be used in conjunction with an AO system to propagate laser beams in deep turbulence.
Nonlinear resonance and envelope instability of intense beam in axial symmetric periodic channel
NASA Astrophysics Data System (ADS)
Li, Chao; Liu, Zhicong; Zhao, Yaliang; Qin, Qing
2016-03-01
When an intense charged particle beam propagates through a given periodic focusing channel, it will experience the phenomena of nonlinear resonance, collective instability or chaotic motion with different conditions. In this paper, the collective envelope instability mechanisms are studied for symmetric beam propagation in an axially symmetric periodic channel. The beam is characterized as collectively stable if there exists a stable fixed point (SFP) located at the matched beam condition (rm , 0) in (r ,pr) phase space. It is found that the well-known collective envelope instability is dynamically related to the period-two orbits bifurcation of the matched SFP, meanwhile the unique stable SFP turns into an unstable saddle-node, surrounded by 1/2 resonance islands. However, higher orders of resonance (l / n, n > 2) coming from period-n bifurcation will not lead to collective beam instability because a new SFP emerges immediately upon the bifurcation process. The orders of SFP bifurcation is numerically depicted by the envelope tune ν=ϕ/360, where ϕ is the eigenphase of the Poincar e ´ tangent map T(s) in one focusing period at SFP, as functions of depressed phase advance. With strong space charge, due to these resonances from SFP bifurcation could be overlapped, mismatched beam would even show chaotic motion. For specific parameters, regular orbits, resonance islands, chaotic regions formed by resonance overlapping are clearly depicted with frequency analysis and Lyapunov spectral exponents, a method that may prove useful when extended to higher phase-space dimensions.
NASA Technical Reports Server (NTRS)
Ball, R. E.
1972-01-01
A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.
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)
Berczynski, Pawel; Bliokh, Konstantin Yu.; Kravtsov, Yuri A.; Stateczny, Andrzej
2006-06-01
We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.
NASA Astrophysics Data System (ADS)
Mottez, Fabrice; Chanteur, Gerard
1991-12-01
A 2D (in configuration space), 3D (in velocity space) electrostatic explicit particle code is used to investigate the interaction between an ion beam flowing along the magnetic field and a highly magnetized plasma. The beam drift velocity Vdi is larger than Vte, the electron thermal velocity, and much larger than the thermal velocities of the core and beam ions. Two instabilities are found to develop. First, the interaction between the ion beam and electrons leads to the rapid growth of parallel modes and to the fast diffusion of electrons along the magnetic field, predominantly in the ion beam direction. This ion-electron instability is rapidly quenched by electron heating. Second, and ion-ion instability develops, which involves oblique modes leading to a selective heating of ions in a direction oblique to B. It is shown that the heating via the electron-ion instability is a necessary step for the development of the ion-ion instability. Finally, it is shown that the nonlinear development of the ion-ion instability gives rise to purely perpendicular modes that are not linearly unstable.
NASA Astrophysics Data System (ADS)
Qin, Hong; Davidson, Ronald C.; Startsev, Edward A.
2004-11-01
A wide range of collective effects in high intensity charged particle beams have been numerically studied using the nonlinear delta-f particle simulation method implemented in the Beam Equilibrium Stability and Transport (BEST) code. For the electron-ion two-stream instability in high intensity accelerators and storage rings, the secondary electron yield effects are self-consistently studied by coupling the secondary electron yield library CMEE with the instability simulations. Progress has also been made in applying the delta-f particle simulation method to bunched beams, and a three-dimensional equilibrium solver has been implemented. With the help of recently developed parallel diagnostic techniques, we are able to characterize the chaotic particle dynamics under the influences of collective instabilities as well as three-dimensional equilibrium fields. To further extend the application areas of the delta-f particle simulation method, 2D domain decomposition is being developed using the Message Passing Interface, and three-dimensional equilibria with anisotropic temperature in the transverse and longitudinal directions are being investigated. References: [1] R. C. Davidson and H. Qin, An Introduction to the Physics of Intense Charged Particle Beams in High Energy Accelerators, World Scientific (2001). [2] H. Qin, Physics of Plasmas 10, 2078 (2003). [3] H. Qin, E. A. Startsev, and R. C. Davidson, Physical Review Special Topics on Accelerators and Beams 6, 014401 (2003).
The nonlinear interaction of two-crossed focussed ultrasonic beams in the presence of turbulence
NASA Astrophysics Data System (ADS)
Rife, Stephen C.
1988-06-01
This paper examines the scattering of a nonlinearly generated sum frequency acoustic wave component from a region of turbulence defined by the overlap volume of two mutually perpendicular crossed focussed ultrasonic beams. The scattered sum frequency pressure amplitude is measured at different radial scan positions across the jet flow stream providing conclusions that explain some qualitative results governing the sum frequency scattering mechanism. Information about the instantaneous velocity components of the turbulent field in the sound-sound interaction volume is measured with an electronic spectrum analyzer. Average spectral shapes of the spectrum near the sum frequency represent information about the probability distribution function of the turbulent velocities. Acoustic measurements are correlated with velocity measurements of circular jets. These correlations demonstrate that the focussed crossed beam apparatus is an effective diagnostic tool for the experimental study of turbulent fluid fields in water. The results of the nonlinear crossed beam experiments indicate the apparatus can be utilized as a diagnostic tool to measure some parameters of turbulent velocity. The measured pressure of the radiated sum frequency correlates with turbulent velocities in the interaction region. Measurements of the Doppler shift and sum-frequency broadening are used to determine mean velocity and turbulent rms velocities respectively.
NASA Astrophysics Data System (ADS)
Li, Y.
1996-08-01
The field, the propagation and the imaging characteristics of two Gaussian optical beams with orthogonal polarization passing through a family of Kerr-law nonlinear shifted parabolic graded-index rod lenses are investigated. The coupled differential equations of the dimensionless beam-width parameters of two Gaussian optical beams are derived by using a variational approach and then solved. It is concluded that there are two regimes of propagation and that the power, the incident waist radius and the position of one beam have large effects on the field, the propagation and the imaging characteristics of the other beam.
Strong quantum squeezing near the pull-in instability of a nonlinear beam
NASA Astrophysics Data System (ADS)
Passian, Ali; Siopsis, George
2016-08-01
Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. We predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. By taking into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator. We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.
Strong quantum squeezing near the pull-in instability of a nonlinear beam
Passian, Ali; Siopsis, George
2016-08-04
Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. Here, we predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. When we take into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator.more » We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.« less
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.
Sonnad, Kiran G.; Cary, John R.
2015-04-15
A procedure to obtain a near equilibrium phase space distribution function has been derived for beams with space charge effects in a generalized periodic focusing transport channel. The method utilizes the Lie transform perturbation theory to canonically transform to slowly oscillating phase space coordinates. The procedure results in transforming the periodic focusing system to a constant focusing one, where equilibrium distributions can be found. Transforming back to the original phase space coordinates yields an equilibrium distribution function corresponding to a constant focusing system along with perturbations resulting from the periodicity in the focusing. Examples used here include linear and nonlinear alternating gradient focusing systems. It is shown that the nonlinear focusing components can be chosen such that the system is close to integrability. The equilibrium distribution functions are numerically calculated, and their properties associated with the corresponding focusing system are discussed.
Nonlinear control via approximate input-output linearization - The ball and beam example
NASA Technical Reports Server (NTRS)
Hauser, John; Sastry, Shankar; Kokotovic, Petar
1989-01-01
This paper presents an approach for the approximate input-output linearization of nonlinear systems, particularly those for which relative degree is not well defined. It is shown that there is a great deal of freedom in the selection of an approximation and that, by designing a tracking controller based on the approximating system, tracking of reasonable trajectories can be achieved with small error. The approximating system is itself a nonlinear system, with the difference that it is input-output linearizable by state feedback. Some properties of the accuracy of the approximation are demonstrated and, in the context of the ball and beam example, it is shown to be far superior to the Jacobian approximation. The results are focused on finding regular SISO systems which are close to systems which are not regular and controlling these approximate regular systems.
Kong, Ling-Bao; Wang, Hong-Yu; Hou, Zhi-Ling; Jin, Hai-Bo; Du, Chao-Hai
2013-12-15
The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.
Gupta, Naveen Singh, Arvinder; Singh, Navpreet
2015-11-15
This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on a numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.
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.
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.
Nonlinear dual-spectral image fusion for improving cone-beam-CT-based breast cancer diagnosis
NASA Astrophysics Data System (ADS)
Chen, Zikuan; Ning, Ruola; Conover, David; Willison, Kathleen
2006-03-01
Cone-beam breast computed tomography (CB Breast CT) can easily detect micro-calcifications and distinguish fat and glandular tissues from normal breast tissue. However, it may be a challenging task for CB Breast CT to distinguish benign from malignant tumors because of the subtle difference in x-ray attenuation. Due to the use of polyenergetic x-ray source, the x-ray and tissue interaction exhibits energy-dependent attenuation behavior, a phenomenon that, to date, has not been used for breast tissue characterization. We will exploit this spectral nature by equipping our CB Breast CT with dual-spectral imaging. The dual-spectral cone-beam scanning produces two spectral image datasets, from which we propose a nonlinear dual-spectral image fusion scheme to combine them into a single dataset, thereby incorporating the spectral information. In implementation, we will perform dual-spectral image fusion through a bi-variable polynomial that can be established by applying dual-spectral imaging to a reference material (with eight different thicknesses). From the fused dataset, we can reconstruct a volume, called a reference-equivalent volume or a fusion volume. By selecting the benign tissue as a reference material, we obtain a benign-equivalent volume. Likewise, we obtain a malignant-equivalent volume as well. In the pursuit of the discrimination of benign versus malignant tissues in a breast image, we perform intra-image as well as inter-image processing. The intra-image processing is an intensity transformation imposed only to a tomographic breast image itself, while the inter-image processing is exerted on two tomographic images extracted from two volumes. The nonlinear fusion scheme possesses these properties: 1) no noise magnification; 2) no feature dimensionality problem, and 3) drastic enhancement among specific features offered by nonlinear mapping. Its disadvantage lies in the possible misinterpretation resulting from nonlinear mapping.
Sepehri Javan, N; Adli, F
2013-10-01
Nonlinear dynamics of an intense circularly polarized laser beam interacting with a hot magnetized plasma is investigated. Using a relativistic fluid model, a modified nonlinear Schrödinger equation is derived based on a quasineutral approximation, which is valid for hot plasma. Using a three-dimensional model, spatial-temporal development of the laser pulse is investigated. The occurrence of some nonlinear phenomena such as self-focusing, self-modulation, light trapping, and filamentation of the laser pulse is discussed. Also the effect of polarization and external magnetic field on the nonlinear evolution of these phenomena is studied. PMID:24229288
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.
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+μu+ɛg(ωt,x)u3=0,μ>0,x∈[0,π] with hinged boundary conditions is considered. Here ɛ is a small positive parameter, g( ωt, x) is real analytic in all variables and quasi-periodic in t with a frequency vector ω = ( ω1, ω2, … , ωm). It is proved that the above equation admits small-amplitude quasi-periodic solutions.
Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies
Chang, Jing; Gao, Yixian Li, Yong
2015-05-15
Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 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. .
Nonlinear propagation of a randomized laser beam through an expanding plasma.
Myatt, J; Pesme, D; Hüller, S; Maximov, A; Rozmus, W; Capjack, C E
2001-12-17
We present simulations of the interaction of a random phase plate laser beam with an underdense, expanding plasma for conditions typical of recent LULI experiments. We use a new code that describes the paraxial propagation of the laser, accounting for the nonlinear evolution of the plasma in an isothermal fluid description with weakly collisional electrons. The transmitted light, in excellent agreement with experiment, is shown to be strongly redshifted as a result of self-phase modulation due to self-focusing. PMID:11736585
Nonlinear ripple dynamics on amorphous surfaces patterned by ion beam sputtering.
Muñoz-García, Javier; Castro, Mario; Cuerno, Rodolfo
2006-03-01
Erosion by ion-beam sputtering (IBS) of amorphous targets at off-normal incidence frequently produces a (nanometric) rippled surface pattern, strongly resembling macroscopic ripples on aeolian sand dunes. A suitable generalization of continuum descriptions of the latter allows us to describe theoretically for the first time the main nonlinear features of ripple dynamics by IBS, namely, wavelength coarsening and nonuniform translation velocity, that agree with similar results in experiments and discrete models. These properties are seen to be the anisotropic counterparts of in-plane ordering and (interrupted) pattern coarsening in IBS experiments on rotating substrates and at normal incidence. PMID:16606197
Model for nonlinear evolution of localized ion ring beam in magnetoplasma
Scales, W. A.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.
2012-06-15
An electrostatic hybrid model, which investigates the nonlinear evolution of a localized ion ring beam in a magnetoplasma, is described and applied to the generation and evolution of turbulence in the very low frequency (VLF) ({Omega}{sub ci}<{omega}<{Omega}{sub ce}) range, where {Omega}{sub ci(e)} is the ion (electron) gyro frequency. Electrons are treated as a fluid and the ions with the particle-in-cell method. Although the model is electrostatic, it includes the effects of energy loss by convection of electromagnetic VLF waves out of the instability region by utilizing a phenomenological model for effective collisions with the fluid electrons. In comparison with a more conventional electrostatic hybrid model, the new model shows much more efficient extraction of energy from the ion ring beam and reduced background plasma heating over a range of parameters.
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.
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
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 TiO2, N- and C-doped TiO2, or TiO2/SiO2 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
Beam quality from self and ionization induced trapping in the nonlinear LWFA regime
NASA Astrophysics Data System (ADS)
Davidson, Asher; Lu, Wei; Joshi, Chan; Silva, Luis; Martins, Joana; Fonseca, Ricardo; Mori, Warren
2011-10-01
In plasma based accelerators (LWFA and PWFA), the methods of injecting high quality electron bunches into the accelerating wakefield is of utmost importance for various applications. Understanding how injection occurs in both self and controlled scenarios is therefore important. We present results from high fidelity OSIRIS simulations on the beam quality that can be obtained from self and ionized induced trapping in the nonlinear LWFA regime. We compare trapping thresholds from the simulations to analytical expressions. We also quantify how the beam quality of 1.5-5 GeV beams can be improved through angle and energy selection as well as quantify the slice energy spread and emittance. We also study the effect of ion motion and the axial density profile. Preliminary results on inputting beams from OSIRS into the FEL code GENESIS will be presented. This work was supported by UC Lab Fees Research Award No. 09-LR-05-118764-DOUW, DOE grants DOE DE-FC02-07ER41500 and DE-FG02-92ER40727 and by NSF grants NSF PHY-0904039 and NSF PHY-0936266. The simulations were performed on Jaguar under an INCITE award.
NASA Astrophysics Data System (ADS)
Saccomandi, Giuseppe; Vitolo, Raffaele
2014-08-01
Using the theory of 1 + 1 hyperbolic systems we put in perspective the mathematical and geometrical structure of the celebrated circularly polarized waves solutions for isotropic hyperelastic materials determined by Carroll [Acta Mechanica 3, 167-181 (1967)]. We show that a natural generalization of this class of solutions yields an infinite family of linear solutions for the equations of isotropic elastodynamics. Moreover, we determine a huge class of hyperbolic partial differential equations having the same property of the shear wave system. Restricting the attention to the usual first order asymptotic approximation of the equations determining transverse waves we provide the complete integration of this system using generalized symmetries.
Nonlinear Interaction of the Beat-Photon Beams with the Brain Neurocenters: Laser Neurophysics
NASA Astrophysics Data System (ADS)
Stefan, V. Alexander
2010-03-01
I propose a novel mechanism for laser-brain interaction: Nonlinear interaction of ultrashort pulses of beat-photon, (φ1-- φ2), or double-photon, (φ1+φ2), footnotetextMaria Goeppert-Mayer, "Uber Elementarakte mit zwei Quantenspr"ungen, Ann Phys 9, 273, 95. (1931). beams with the corrupted brain neurocenters, causing a particular neurological disease. The open-scull cerebral tissue can be irradiated with the beat-photon pulses in the range of several 100s fs, with the laser irradiances in the range of a few mW/cm^2, repetition rate of a few 100s Hz, and in the frequency range of 700-1300nm generated in the beat-wave driven free electron laser.footnotetextV. Alexander Stefan, The Interaction of Photon Beams with the DNA Molecules: Genomic Medical Physics. American Physical Society, 2009 APS March Meeting, March 16-20, 2009, abstract #K1.276; V. Stefan, B. I. Cohen, and C. Joshi, Nonlinear Mixing of Electromagnetic Waves in Plasmas Science 27 January 1989:Vol. 243. no. 4890, pp. 494 -- 500 (January 1989). This method may prove to be an effective mechanism in the treatment of neurological diseases: Parkinson's, Lou Gehrig's, and others.
Finite elements for a beam system with nonlinear contact under periodic excitation
NASA Astrophysics Data System (ADS)
Hazim, H.; Rousselet, B.
Solar arrays are structures which are connected to satellites; during launch, they are in a folded position and submitted to high vibrations. In order to save mass, the flexibility of the panels is not negligible and they may strike each other; this may damage the structure. To prevent this, rubber snubbers are mounted at well chosen points of the structure; a prestress is applied to the snubber; but it is quite difficult to check the amount of prestress and the snubber may act only on one side; they will be modeled as one sided springs (see figure 2). In this article, some analysis for responses (displacements) in both time and frequency domains for a clamped-clamped Euler-Bernoulli beam model with a spring are presented. This spring can be unilateral or bilateral fixed at a point. The mounting (beam +spring) is fixed on a rigid support which has a sinusoidal motion of constant frequency. The system is also studied in the frequency domain by sweeping frequencies between two fixed values, in order to save the maximum of displacements corresponding to each frequency. Numerical results are compared with exact solutions in particular cases which already exist in the literature. On the other hand, a numerical and theoretical investigation of nonlinear normal mode (NNM) can be a new method to describe nonlinear behaviors, this work is in progress.
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
NASA Astrophysics Data System (ADS)
Misra, Nilanjal; Rapolu, Mounika; Venugopal Rao, S.; Varshney, Lalit; Kumar, Virendra
2016-05-01
The optical nonlinearity of metal nanoparticles in dielectrics is of special interest because of their high polarizability and ultrafast response that can be utilized in potential device applications. In this study nanocomposite thin films containing in situ generated Ag nanoparticles dispersed in an aliphatic urethane acrylate (AUA) matrix were synthesized using electron beam curing technique, in presence of an optimized concentration of diluent Trimethylolpropanetriacrylate (TMPTA). The metal nanocomposite films were characterized using UV-visible spectrophotometry, transmission electron microscope (TEM) and field emission scanning electron microscope (FE-SEM) techniques. Ag nanoparticle impregnated films demonstrated an absorption peak at ∼420 nm whose intensity increased with increase in the Ag concentration. The optical limiting property of the coatings was tested using a nanosecond Nd-YAG laser operated at third harmonic wavelength of 355 nm. For a 25 ns pulse and 10 Hz cycle, Ag-polymer coatings showed good optical limiting property and the threshold fluence for optical limiting was found to be ∼3.8×10-2 J/cm2 while the transmission decreased to 82%. The nonlinear optical coefficients were also determined using the standard Z-scan technique with picosecond (∼2 ps, 1 kHz) and femtosecond (∼150 fs, 100 MHz) pulses. Open aperture Z-scan data clearly suggested two-photon absorption as the dominant nonlinear absorption mechanism. Our detailed studies suggest these composites are potential candidates for optical limiting applications.
NASA Astrophysics Data System (ADS)
Fisher, Robert A.; Wilson, Leroy E.
Various papers on nonlinear optical beam manipulation and high-energy beam propagation through the atmosphere are presented. Individual topics addressed include: suppression of Raman amplification using large Stokes seeds, review of multiple-short-pulse SBS experiments and theory, laser-induced gratings for beam manipulation in a gas, considerations for computing realistic atmospheric distortion parameter profiles, effect of turbulent diffusion on laser propagation, use of multiple photon processes in krypton for laser guiding of electron beams, effect of ionization on intense electron beam propagation in low-pressure media, lidar measurements of the troposphere and middle atmosphere, seasonal and diurnal changes in cloud obscuration to visible and IR energy transmission, new cloud composite climatologies using meteorological satellite imagery, effect of neutral atmospheric structure on beam propagation, small-scale electron density fluctuations in a disturbed ionospheric environment, and SDIO radio frequency communications in a structured environment.
NASA Technical Reports Server (NTRS)
Dowell, E. H.; Traybar, J.; Hodges, D. H.
1977-01-01
An experimental study of the large deformation of a cantilevered beam under a gravity tip load has been made. The beam root is rotated so that the tip load is oriented at various angles with respect to the beam principal axes. Static twist and bending deflections of the tip and bending natural frequencies have been measured as a function of tip load magnitude and orientation. The experimental data are compared with the results of a recently developed non-linear structural theory. Agreement is reasonably good when bending deflections are small compared to the beam span, but systematic differences occur for larger deflections.
Chen, Hao; Zhong, Shouming; Li, Min; Liu, Xingwen; Adu-Gyamfi, Fehrs
2016-07-01
In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T-S fuzzy systems with interval time-varying delays and nonlinear perturbations. Based on the common ratio α, the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov-Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach. PMID:27138648
NASA Astrophysics Data System (ADS)
Vicari, L.
2002-11-01
We present a new pump probe laser beams configuration for the nonlinear optical characterization of microemulsions. We detect the variation of the on-axis optical intensity of the probe beam as generated by the concentration profile induced in an optically thin film of microemulsion by the pump beam. A mathematical model has been introduced to describe the phenomenon. The technique allows the determination of both Kerr-like optical nonlinearity and time constants and, therefore, it gives information both on cluster dimension and their shape. We discuss its application to WAD (water/AOT/decane, where AOT denotes sodium-bis-di-ethyl-sulfosuccinate) with the application of a strong electric field of optical source. Comparison between theoretical predictions and experimental results confirms the presence of giant optical nonlinearity in the absence of turbidity divergence. Chainlike shape of clusters, of the kind already reported with the application of strong electric field, could justify this result.
Vicari, L
2002-11-01
We present a new pump probe laser beams configuration for the nonlinear optical characterization of microemulsions. We detect the variation of the on-axis optical intensity of the probe beam as generated by the concentration profile induced in an optically thin film of microemulsion by the pump beam. A mathematical model has been introduced to describe the phenomenon. The technique allows the determination of both Kerr-like optical nonlinearity and time constants and, therefore, it gives information both on cluster dimension and their shape. We discuss its application to WAD (water/AOT/decane, where AOT denotes sodium-bis-di-ethyl-sulfosuccinate) with the application of a strong electric field of optical source. Comparison between theoretical predictions and experimental results confirms the presence of giant optical nonlinearity in the absence of turbidity divergence. Chainlike shape of clusters, of the kind already reported with the application of strong electric field, could justify this result. PMID:15010903
Determination of turbulent vorticity by the nonlinear scattering of crossed ultrasonic beams
NASA Astrophysics Data System (ADS)
Korman, Murray S.
2000-07-01
The nonlinear interaction of two, mutually perpendicular crossed ultrasonic beams, overlapping in the presence of turbulence, generates a scattered sum frequency component that radiates outside the interaction region. In the absence of turbulence, virtually no scattered sum frequency component exists (outside the interaction region). A theoretical investigation is reported which relates the angular dependence of the time-dependent Doppler shift (of the scattered sum frequency) to the time-dependent velocity fluctuations of the turbulent eddies. When a second set of focused crossed beams is operated with an overlap region slightly displaced from the first set (by 1.27 mm), one can measure the vorticity using Doppler shift information from four distinct combination frequencies obtained at two different scattering angles. Experimental results are presented using continuous wave (CW) focused primary beams of frequencies f1=1.8, f2=2.0, f3=2.2 and f4=2.3 MHz (generated by concave transducer units with 15 cm focal lengths). The turbulence is generated by a submerged water jet with nozzle diameter D=0.635 cm and exit velocity ≈7 m/s. Here the interaction region is located 37D from the nozzle exit. A 4 MHz circular plane array receiving transducer detects four distinct scattered sum frequency components (at specific angles) using a spectrum analyzer to demonstrate the effect. The receiver is located 14D from the interaction region.
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
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.
NASA Astrophysics Data System (ADS)
Sasmal, Saptarshi; Kalidoss, S.
2015-05-01
In the present study, investigations on fiber-reinforced plastic (FRP) plated-reinforced concrete (RC) beam are carried out. Numerical investigations are performed by using a nonlinear finite element analysis by incorporating cracking and crushing of concrete. The numerical models developed in the present study are validated with the results obtained from the experiment under monotonic load using the servo-hydraulic actuator in displacement control mode. Further, the validated numerical models are used to evaluate the influence of different parameters. It is found from the investigations that increase in the elastic modulus of adhesive layer and CFRP laminate increases the interfacial stresses whereas increase in laminate modulus decreases the displacement and reinforcement strain of the beam. It is also observed that increase in the adhesive layer can largely reduce the interfacial stresses, whereas increase in laminate thickness increases it. However, increase in laminate thickness decreases the displacement and reinforcement strain of the beam significantly. It is mention worthy that increase in laminate length reduces the interfacial stresses, whereas CFRP width change does not affect the interfacial stresses. The study will be useful for the design and practicing engineers for arriving at the FRP-based strengthening schemes for RC structures judiciously.
Study on Nonlinear Theory and Code of Beam-Wave Interaction for Gyroklystron
NASA Astrophysics Data System (ADS)
Jianhua, Guo; Sheng, Yu; Xiang, Li; Hongfu, Li
2011-12-01
A nonlinear self-consistent theory of beam-wave interaction for gyroklystron with multiple cavities is analyzed in this paper. The electron motion equations and transient electromagnetic field equations in a complex form are deduced in detail. A calculation code including a time-dependent description of the electromagnetic fields and a self-consistent analysis of the electrons is designed and the corresponding software implementation is achieved using Fortran language. An example is presented for the operation of the code, namely a four-cavity, Ka-band gyroklystron operating in the TE011 mode at the fundamental of the cyclotron frequency. The numerical results show that a maximal saturated peak output power of 330 kW, corresponding to 39% efficiency and a saturated 3-dB bandwidth of 325 MHz is achieved with a 72.8 kv, 11.8 A electron beam at a focused magnetic field of 13 kG and a beam velocity ratio of 1.63 when the speed spread is 5%. By comparison, the numerical results agree with the experimental results.
He, Qingbo Xu, Yanyan; Lu, Siliang; Dai, Daoyi
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.
NASA Astrophysics Data System (ADS)
Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan
2012-12-01
Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.
NASA Astrophysics Data System (ADS)
Vasoya, Manish; Unni, Aparna Beena; Leblond, Jean-Baptiste; Lazarus, Veronique; Ponson, Laurent
2016-04-01
Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.
NASA Astrophysics Data System (ADS)
Papon, G.; Marquestaut, N.; Petit, Y.; Royon, A.; Dussauze, M.; Rodriguez, V.; Cardinal, T.; Canioni, L.
2014-03-01
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 χeff(2) ˜ 0.6 pm V-1) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired.
Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L.; Petit, Y.; Dussauze, M.; Rodriguez, V.; Cardinal, T.
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 χ{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.
NASA Astrophysics Data System (ADS)
Colaïtis, A.; Hüller, S.; Pesme, D.; Duchateau, G.; Tikhonchuk, V. T.
2016-03-01
The Crossed Beam Energy Transfer (CBET) of two large laser beams is modeled using two approaches: (i) the time-independent Paraxial Complex Geometrical Optics (PCGO) for stochastically distributed Gaussian-shaped beamlets and (ii) the time-dependent conventional paraxial propagation of smoothed laser beams. Each description of the laser propagation is coupled to a hydrodynamics code. Both approaches are compared in a well-defined plasma configuration with density- and velocity- profiles corresponding to an inhomogeneous plasma, including a resonance zone in which the matching conditions for a resonant coupling between the two laser beams are fulfilled. The comparison is made for laser beams smoothed by random phase plates and for "regular beams" without speckles. The role of the laser speckles is also investigated for each approach. In general, a good agreement is found between the PCGO simulations and the fully time-dependent paraxial-type simulations, carried out with the code Harmony, past a transient period on the picosecond time scale. The PCGO-based CBET model is applied to the hydrodynamics simulations of a CBET experiment, the results of which reproduce essential features of the experimental data. Based on these comparisons, performed for interaction parameters up to 2 × 10 14 W cm - 2 μ m 2 , the PCGO approach proves to be a reliable method to be implemented in the hydrodynamics codes to describe the CBET in mm-scale plasmas.
Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.
Akemann, Walther; Léger, Jean-François; Ventalon, Cathie; Mathieu, Benjamin; Dieudonné, Stéphane; Bourdieu, Laurent
2015-11-01
Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions. PMID:26561090
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.
Non-Linear Steady State Vibrations of Beams Excited by Vortex Shedding
NASA Astrophysics Data System (ADS)
LEWANDOWSKI, R.
2002-05-01
In this paper the non-linear vibrations of beams excited by vortex-shedding are considered. In particular, the steady state responses of beams near the synchronization region are taken into account. The main aerodynamic properties of wind are described by using the semi-empirical model proposed by Hartlen and Currie. The finite element method and the strip method are used to formulate the equation of motion of the system treated. The harmonic balance method is adopted to derive the amplitude equations. These equations are solved with the help of the continuation method which is very convenient to perform the parametric studies of the problem and to determine the response curve in the synchronization region. Moreover, the equations of motion are also integrated using the Newmark method. The results of calculations of several example problems are also shown to confirm the efficiency and accuracy of the presented method. The results obtained by the harmonic balance method and by the Newmark methods are in good agreement with each other.
High power microwave beam steering based on gyromagnetic nonlinear transmission lines
Romanchenko, I. V. Rostov, V. V.; Gunin, A. V.; Konev, V. Yu.
2015-06-07
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.
Karaton, Muhammet
2014-01-01
A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667
Cornacchia, M.; Evans, L.
1985-06-01
A nonlinear lens may be used to study the effect of high-order multipolar field imperfections on a stored proton beam. Such a nonlinear lens is particulary suitable to simulate field imperfections of the types encountered in coil dominated superconducting magnets. We have studied experimentally at the SPS the effect of high order (5th and 8th) single isolated resonances driven by the nonlinear lens. The width of these resonances is of the order one expects to be caused by field errors in superconducting magnets of the SSC type. The experiment shows that, in absence of tune modulation, these resonances are harmless. Slow crossings of the resonance, on the other hand, have destructive effects on the beam, much more so than fast crossings caused by synchrotron oscillations. In the design of future storage rings, sources of low-frequency tune modulation should be avoided as a way to reduce the harmful effects of high order multipolar field imperfection.
Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej
2006-06-01
We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law. PMID:16715163
Pili, Giorgio; Grimaldi, Luca; Fidanza, Christian; Florio, Elena T.; Petruzzelli, Maria F.; D'Errico, Maria P.; De Tommaso, Cristina; Tramacere, Francesco; Musaio, Francesca; Castagna, Roberta; Francavilla, Maria C.; Gianicolo, Emilio A.L.; Portaluri, Maurizio
2011-11-01
Purpose: To evaluate the probability of late cardiac mortality resulting from left breast irradiation planned with tangential fields and to compare this probability between the wedged beam and field-in-field (FIF) techniques and to investigate whether some geometric/dosimetric indicators can be determined to estimate the cardiac mortality probability before treatment begins. Methods and Materials: For 30 patients, differential dose-volume histograms were calculated for the wedged beam and FIF plans, and the corresponding cardiac mortality probabilities were determined using the relative seriality model. As a comparative index of the dose distribution uniformity, the planning target volume (PTV) percentages involved in 97-103% of prescribed dose were determined for the two techniques. Three geometric parameters were measured for each patient: the maximal length, indicates how much the heart contours were displaced toward the PTV, the angle subtended at the center of the computed tomography slice by the PTV contour, and the thorax width/thickness ratio. Results: Evaluating the differential dose-volume histograms showed that the gain in uniformity between the two techniques was about 1.5. With the FIF technique, the mean dose sparing for the heart, the left anterior descending coronary artery, and the lung was 15% (2.5 Gy vs. 2.2 Gy), 21% (11.3 Gy vs. 9.0 Gy), and 42% (8.0 Gy vs. 4.6 Gy) respectively, compared with the wedged beam technique. Also, the cardiac mortality probability decreased by 40% (from 0.9% to 0.5%). Three geometric parameters, the maximal length, angle subtended at the center of the computed tomography slice by the PTV contour, and thorax width/thickness ratio, were the determining factors (p = .06 for FIF, and p = .10 for wedged beam) for evaluating the cardiac mortality probability. Conclusion: The FIF technique seemed to yield a lower cardiac mortality probability than the conventional wedged beam technique. However, although our study
NASA Astrophysics Data System (ADS)
Inamura, T.; Nishiura, T.; Kawano, H.; Hosoda, H.; Nishida, M.
2012-06-01
Competition between the invariant plane (IP) condition at the habit plane, the twin orientation relation (OR) and the kinematic compatibility (KC) at the junction plane (JP) of self-accommodated B19‧ martensite in Ti-Ni was investigated via the geometrically nonlinear theory to understand the habit plane variant (HPV) clusters presented in Parts I and II of this work. As the IP condition cannot be satisfied simultaneously with KC, an additional rotation Q is necessary to form compatible JPs for all HPV pairs. The rotation J necessary to form the exact twin OR between the major correspondence variants (CVs) in each HPV was also examined. The observed HPV cluster was not the cluster with the smallest Q but the one satisfying Q = J with a { ? 1}B19‧ type I twin at JP. Both Q and J are crucial to understanding the various HPV clusters in realistic transformations. Finally, a scheme for the ideal HPV cluster composed of six HPVs is also proposed.
NASA Astrophysics Data System (ADS)
Kala, Zdeněk; Kala, Jiří
2012-09-01
The paper deals with the influence of correlation length, of Gauss random field, and of yield strength of a hotrolled I-beam under bending on the ultimate load carrying capacity limit state. Load carrying capacity is an output random quantity depending on input random imperfections. Latin Hypercube Sampling Method is used for sampling simulation. Load carrying capacity is computed by the programme ANSYS using shell finite elements and nonlinear computation methods. The nonlinear FEM computation model takes into consideration the effect of lateral-torsional buckling on the ultimate limit state.
Bayro-Corrochano, E J
2001-01-01
This paper shows the analysis and design of feedforward neural networks using the coordinate-free system of Clifford or geometric algebra. It is shown that real-, complex-, and quaternion-valued neural networks are simply particular cases of the geometric algebra multidimensional neural networks and that some of them can also be generated using support multivector machines (SMVMs). Particularly, the generation of radial basis function for neurocomputing in geometric algebra is easier using the SMVM, which allows one to find automatically the optimal parameters. The use of support vector machines in the geometric algebra framework expands its sphere of applicability for multidimensional learning. Interesting examples of nonlinear problems show the effect of the use of an adequate Clifford geometric algebra which alleviate the training of neural networks and that of SMVMs. PMID:18249926
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.
A nonlinear-optical method for combining high power laser beams
NASA Astrophysics Data System (ADS)
Chivian, Jay S.; Glosson, C. A.; Cotten, W. D.; Cantrell, C. D., III; Dimarco, S. F.
1989-04-01
The overall program goal was to investigate concepts for laser-controlled optics based on near-resonance non-linear dispersion in gases, and to demonstrate a laser-induced grating capable of high power laser beam combining. The theoretical work extended the previous year's effort in giving a more detailed view of those aspects which might prevent observation of a grating, and led to optimization of experimental parameters. Modifications and improvements were made to the experimental apparatus. No grating was observed over a wide range of experimental conditions, although the apparatus was capable of such demonstration had a grating existed. The most likely cause of trouble appears to be the complexity of the SF6 medium chosen for demonstration. As an apparatus check, a medium (e.g., vanadium dioxide) can be used in which it is known that a grating can be demonstrated. Measurements were extended on the effect of noble gas admixtures into SF6 on the absorption of 16.26 micrometers radiation; helium suppresses absorption, argon and xenon enhance absorption. It would be worthwhile to continue these studies in light of information to be gained regarding the effect of collisions on absorption spectra in molecular species.
NASA Astrophysics Data System (ADS)
Zambre, Yadunath Bhagvantrao
1988-03-01
A 2-1over2 dimensional analysis of klystrons, assuming cylindrical space symmetry but retaining all velocity effects, is presented. The model handles all relativistic, electromagnetic, and non-linear effects. The klystron geometry is viewed as a conducting cylinder (the tube) to which are attached a number of resonant cavities at various locations. Within this tube, particle in cell plasma simulation techniques are used to model the electron beam dynamics and electromagnetic fields. The effects of the cavities are then "patched in" by the use of eigenmode expansions over the cavity geometries. These expansions reduce the effects of the cavity fields into relatively simple time varying boundary conditions on the tube. The plasma simulation in the tube is carried out using a number of "macroparticles," each representing many electrons and each obeying the equations of motion for an electron. A time centered cycloid fitting algorithm is used to move the particles. A time centered spectral method using Fourier series in z and Chebyschev polynomials in r is used to advance the fields. A non-uniform grid permits the use of FFT's to carry out the Chebyschev expansions. A method for finding time periodic solutions is also presented. This method will compute a qualitatively correct transient solution and yield a quantitatively correct steady state solution.
Rykaczewski, K; Mieritz, D G; Liu, M; Ma, Y; Iezzi, E B; Sun, X; Wang, L P; Solanki, K N; Seo, D-K; Wang, R Y
2016-06-01
Focused ion beam and scanning electron microscope (FIB-SEM) instruments are extensively used to characterize nanoscale composition of composite materials, however, their application to analysis of organic corrosion barrier coatings has been limited. The primary concern that arises with use of FIB to mill organic materials is the possibility of severe thermal damage that occurs in close proximity to the ion beam impact. Recent research has shown that such localized artefacts can be mitigated for a number of polymers through cryogenic cooling of the sample as well as low current milling and intelligent ion beam control. Here we report unexpected nonlocalized artefacts that occur during FIB milling of composite organic coatings with pigment particles. Specifically, we show that FIB milling of pigmented polysiloxane coating can lead to formation of multiple microscopic voids within the substrate as far as 5 μm away from the ion beam impact. We use further experimentation and modelling to show that void formation occurs via ion beam heating of the pigment particles that leads to decomposition and vaporization of the surrounding polysiloxane. We also identify FIB milling conditions that mitigate this issue. PMID:26695001
Post-buckling behavior of a beam-column on a nonlinear elastic foundation with a gap
NASA Technical Reports Server (NTRS)
Kuznetsov, E. N.; Johns, T. G.
1980-01-01
The structural behavior of an elastic beam-column placed with a gap between two nonlinearity elastic layers each resting on a rigid foundation was examined. The beam-column was laterally supported at both ends and subjected to a uniform transverse load and axial compression. Its slenderness was such that the axial compressive force exceeds the amount that would be necessary to buckle it as a simple supported column. The elastic layers were represented by an elastic foundation with a strongly nonlinear specific reaction taken as a rapidly increasing function of the layer compression. The analytical model developed simulated the entire pattern of the deflection and stress state including layer and end support reactions, under gradually increasing axial force.
Umeda, Takayuki
2008-06-15
Nonlinear evolution of the electron two-stream instability in a current-carrying plasma is examined by using a two-dimensional electromagnetic particle-in-cell simulation. Formation of electron phase-space holes is observed as an early nonlinear consequence of electron-beam-plasma interactions. Lower-hybrid waves, electrostatic, and electromagnetic whistler mode waves are also excited by different mechanisms during the ensuing nonlinear wave-particle interactions. It is shown by the present computer simulation with a large simulation domain and a long simulation time that these low-frequency waves can disturb the electrostatic equilibrium of electron phase-space holes, suggesting that the lifetime of electron phase-space holes sometimes becomes shorter in a current-carrying plasma.
NASA Astrophysics Data System (ADS)
Derbov, V. L.; Mel'Nikov, L. A.; Novikov, A. D.
1989-08-01
A modification of the generalized method of moments is applied to off-axis Gaussian beams in nonlinear inhomogeneous media. Numerical estimates of the induced astigmatism, spot distortion, and beam curvature are obtained for the conventional saturation spectroscopy scheme with a probing counterpropagating beam slightly deflected from the axis of the saturating beam. It is shown that this deflection causes asymmetry in the radial dependence of the saturation resonance frequency shift.
NASA Astrophysics Data System (ADS)
Cervenka, Pierre; de Moustier, Christian; Lonsdale, Peter F.
1994-10-01
Acoustic backscatter images of the seafloor obtained with sidescan sonar systems are displayed most often using a flat bottom assumption. Whenever this assumption is not valid, pixels are mapped incorrectly in the image frame, yielding distorted representations of the seafloor. Here, such distortions are corrected by using an appropriate representation of the relief, as measured by the sonar that collected the acoustic backscatter information. In addition, all spatial filtering operations required in the pixel relocation process take the sonar geometry into account. Examples of the process are provided by data collected in the Northeastern Pacific over Fieberling Guyot with the SeaMARC II bathymetric sidescan sonar system and the Sea Beam multibeam echo-sounder. The nearly complete (90%) Sea Beam bathymetry coverage of the Guyot serves as a reference to quantify the distortions found in the backscatter images and to evaluate the accuracy of the corrections performed with SeaMARC II bathymetry. As a byproduct, the processed SeaMARC II bathymetry and the Sea Beam bathymetry adapted to the SeaMARC II sonar geometry exhibit a 35m mean-square difference over the entire area surveyed.
Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel
2014-12-10
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.
NASA Astrophysics Data System (ADS)
Brojan, Miha; Cebron, Matjaz; Kosel, Franc
2012-06-01
This work studies large deflections of slender, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed continuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be nonlinearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by comparing them with results from previous studies and with a laboratory experiment.
Edward A. Startsev; Ronald C. Davidson
2004-04-09
To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
Second- and third-harmonic generation with vector Gaussian beams
NASA Astrophysics Data System (ADS)
Carrasco, Silvia; Saleh, Bahaa E. A.; Teich, Malvin C.; Fourkas, John T.
2006-10-01
We consider second-harmonic generation (SHG) and third-harmonic generation (THG) in a nonlinear optical crystal illuminated by a vector Gaussian beam, i.e., a Gaussian beam in which the axial component of the excitation field is considered. This component exhibits twice the Gouy phase shift of the transverse component and vanishes at points on the beam axis. Harmonic generation stemming from this component exhibits a unique dependence on geometrical factors associated with the location and focusing of the beam relative to the location of the crystal. Using the first Born approximation (undepleted fundamental beam), we derive analytical formulas for the quantities that characterize these geometrical factors for a nonlinear optical crystal described by an arbitrary nonlinear susceptibility tensor, for both SHG and THG and for all polarization components. We also determine the efficiencies of these processes as functions of the geometry of the experimental arrangement for phase-matched crystals as well as for crystals of infinite length.
Zhang, Hong; Kong, Fengchong; Ren, Lei; Jin, Jian-Yue
2015-01-01
Cone beam computed tomography (CBCT) imaging is a key step in image guided radiation therapy (IGRT) to improve tumor targeting. The quality and imaging dose of CBCT are two important factors. However, X-ray scatter in the large cone beam field usually induces image artifacts and degrades the image quality for CBCT. A synchronized moving grid (SMOG) approach has recently been proposed to resolve this issue and shows great promise. However, the SMOG technique requires two projections in the same gantry angle to obtain full information due to signal blockage by the grid. This study aims to develop an inter-projection interpolation (IPI) method to estimate the blocked image information. This approach will require only one projection in each gantry angle, thus reducing the scan time and patient dose. IPI is also potentially suitable for sparse-view CBCT reconstruction to reduce the imaging dose. To be compared with other state-of-the-art spatial interpolation (called inpainting) methods in terms of signal-to-noise ratio (SNR) on a Catphan and head phantoms, IPI increases SNR from 15.3dB and 12.7dB to 29.0dB and 28.1dB, respectively. The SNR of IPI on sparse-view CBCT reconstruction can achieve from 28dB to 17dB for undersample projection sets with gantry angle interval varying from 1 to 3 degrees for both phantoms. PMID:26005721
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.
NASA Astrophysics Data System (ADS)
Dantu, Subbarao; Uma, R.
2000-10-01
The nonlinear Schrodinger equation in cylindrical geometry with saturating nonlinearity like the ponderomotive or relativistic nonlinearity in a plasma is analysed with the help of Symmetry Group Analysis. The symmetry group of the equation is deduced and a fiber-preserving subgroup of linear transformations are identified that leave such a nonlinear Schrodinger equation invariant. The MACSYMA-based Lie algebra of the symmetry group is realized to the extent possible. The theory results in an ordinary differential equation apart from a dictated beam profile. The resulting ordinary differential equation for self-focusing is compared with similar equations obtained from other existing theories of self-focusing in cylindrical geometry like the modified paraxial theory based on harmonic-oscillator basis, the moments theory and the variational theory . New types of solutions are identified and the limitations of the different methods are indicated.Acknowledgements: Financial assistance of CSIR(India)(Research Project,03(0815)/97/ EMR-II) for this work is acknowledged.
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}+μ u+\\varepsilonφ(t)h(u)=0} with hinged boundary conditions is considered, where μ > 0, {\\varepsilon} is a small positive parameter, {φ} is a real analytic quasi-periodic function in t with a frequency vector ω = ( ω 1, ω 2 . . . , ω m ), and the nonlinearity h is a real analytic odd function of the form {h(u)=η_1u+η_{2bar{r}+1}u^{2bar{r}+1}+sum_{k≥ bar{r}+1}η_{2k+1}u^{2k+1},η_1,η_{2bar{r}+1} neq0, bar{r} in {mathbb {N}}.} The above equation admits a quasi-periodic solution.
Gao, Q. D.; Budny, R. V.
2015-03-15
By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (T{sub i,e}) and toroidal velocity (V{sub ϕ}) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.
Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media
NASA Astrophysics Data System (ADS)
Chen, Chidao; Peng, Xi; Chen, Bo; Peng, Yulian; Zhou, Meiling; Yang, Xiangbo; Deng, Dongmei
2016-05-01
We investigate the propagation of an Airy-Gaussian vortex (AiGV) beam in free space and Kerr media. It is interesting to see that the beam will perform self-healing and main lobe focusing both in free space and Kerr media when the vortex locates at the center of the plane. By controlling the number of the topological charge, the beam distribution factor χ 0 and the position of the vortex, we can control the intensity distribution of the AiGV beam in the out plane both in free space and Kerr media. It is found that when the vortex is close to the center of the plane, it has a strong effect on the intensity distribution of the beam. When the beam propagates in the number of the topological charge, the partial collapse will take place even with low initial input power. We find that the main lobe focusing contributes to this partial collapse.
Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams
NASA Astrophysics Data System (ADS)
Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.
2015-04-01
In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized
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.
NASA Astrophysics Data System (ADS)
Tilley, Steven; Siewerdsen, Jeffrey H.; Zbijewski, Wojciech; Stayman, J. Webster
2016-03-01
Flat-panel cone-beam CT (FP-CBCT) is a promising imaging modality, partly due to its potential for high spatial resolution reconstructions in relatively compact scanners. Despite this potential, FP-CBCT can face difficulty resolving important fine scale structures (e.g, trabecular details in dedicated extremities scanners and microcalcifications in dedicated CBCT mammography). Model-based methods offer one opportunity to improve high-resolution performance without any hardware changes. Previous work, based on a linearized forward model, demonstrated improved performance when both system blur and spatial correlations characteristics of FP-CBCT systems are modeled. Unfortunately, the linearized model relies on a staged processing approach that complicates tuning parameter selection and can limit the finest achievable spatial resolution. In this work, we present an alternative scheme that leverages a full nonlinear forward model with both system blur and spatially correlated noise. A likelihood-based objective function is derived from this forward model and we derive an iterative optimization algorithm for its solution. The proposed approach is evaluated in simulation studies using a digital extremities phantom and resolution-noise trade-offs are quantitatively evaluated. The correlated nonlinear model outperformed both the uncorrelated nonlinear model and the staged linearized technique with up to a 86% reduction in variance at matched spatial resolution. Additionally, the nonlinear models could achieve finer spatial resolution (correlated: 0.10 mm, uncorrelated: 0.11 mm) than the linear correlated model (0.15 mm), and traditional FDK (0.40 mm). This suggests the proposed nonlinear approach may be an important tool in improving performance for high-resolution clinical applications.
Tilley, Steven; Siewerdsen, Jeffrey H.; Zbijewski, Wojciech; Stayman, J. Webster
2016-01-01
Flat-panel cone-beam CT (FP-CBCT) is a promising imaging modality, partly due to its potential for high spatial resolution reconstructions in relatively compact scanners. Despite this potential, FP-CBCT can face difficulty resolving important fine scale structures (e.g, trabecular details in dedicated extremities scanners and microcalcifications in dedicated CBCT mammography). Model-based methods offer one opportunity to improve high-resolution performance without any hardware changes. Previous work, based on a linearized forward model, demonstrated improved performance when both system blur and spatial correlations characteristics of FP-CBCT systems are modeled. Unfortunately, the linearized model relies on a staged processing approach that complicates tuning parameter selection and can limit the finest achievable spatial resolution. In this work, we present an alternative scheme that leverages a full nonlinear forward model with both system blur and spatially correlated noise. A likelihood-based objective function is derived from this forward model and we derive an iterative optimization algorithm for its solution. The proposed approach is evaluated in simulation studies using a digital extremities phantom and resolution-noise trade-offs are quantitatively evaluated. The correlated nonlinear model outperformed both the uncorrelated nonlinear model and the staged linearized technique with up to a 86% reduction in variance at matched spatial resolution. Additionally, the nonlinear models could achieve finer spatial resolution (correlated: 0.10 mm, uncorrelated: 0.11 mm) than the linear correlated model (0.15 mm), and traditional FDK (0.40 mm). This suggests the proposed nonlinear approach may be an important tool in improving performance for high-resolution clinical applications. PMID:27110051
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
NASA Astrophysics Data System (ADS)
Wang, Qian; Li, Bincheng
2015-12-01
In this paper, photocarrier radiometry (PCR) technique with multiple pump beam sizes is employed to determine simultaneously the electronic transport parameters (the carrier lifetime, the carrier diffusion coefficient, and the front surface recombination velocity) of silicon wafers. By employing the multiple pump beam sizes, the influence of instrumental frequency response on the multi-parameter estimation is totally eliminated. A nonlinear PCR model is developed to interpret the PCR signal. Theoretical simulations are performed to investigate the uncertainties of the estimated parameter values by investigating the dependence of a mean square variance on the corresponding transport parameters and compared to that obtained by the conventional frequency-scan method, in which only the frequency dependences of the PCR amplitude and phase are recorded at single pump beam size. Simulation results show that the proposed multiple-pump-beam-size method can improve significantly the accuracy of the determination of the electronic transport parameters. Comparative experiments with a p-type silicon wafer with resistivity 0.1-0.2 Ω.cm are performed, and the electronic transport properties are determined simultaneously. The estimated uncertainties of the carrier lifetime, diffusion coefficient, and front surface recombination velocity are approximately ±10.7%, ±8.6%, and ±35.4% by the proposed multiple-pump-beam-size method, which is much improved than ±15.9%, ±29.1%, and >±50% by the conventional frequency-scan method. The transport parameters determined by the proposed multiple-pump-beam-size PCR method are in good agreement with that obtained by a steady-state PCR imaging technique.
Wang, Qian; Li, Bincheng
2015-12-07
In this paper, photocarrier radiometry (PCR) technique with multiple pump beam sizes is employed to determine simultaneously the electronic transport parameters (the carrier lifetime, the carrier diffusion coefficient, and the front surface recombination velocity) of silicon wafers. By employing the multiple pump beam sizes, the influence of instrumental frequency response on the multi-parameter estimation is totally eliminated. A nonlinear PCR model is developed to interpret the PCR signal. Theoretical simulations are performed to investigate the uncertainties of the estimated parameter values by investigating the dependence of a mean square variance on the corresponding transport parameters and compared to that obtained by the conventional frequency-scan method, in which only the frequency dependences of the PCR amplitude and phase are recorded at single pump beam size. Simulation results show that the proposed multiple-pump-beam-size method can improve significantly the accuracy of the determination of the electronic transport parameters. Comparative experiments with a p-type silicon wafer with resistivity 0.1–0.2 Ω·cm are performed, and the electronic transport properties are determined simultaneously. The estimated uncertainties of the carrier lifetime, diffusion coefficient, and front surface recombination velocity are approximately ±10.7%, ±8.6%, and ±35.4% by the proposed multiple-pump-beam-size method, which is much improved than ±15.9%, ±29.1%, and >±50% by the conventional frequency-scan method. The transport parameters determined by the proposed multiple-pump-beam-size PCR method are in good agreement with that obtained by a steady-state PCR imaging technique.
Nonlinear modeling of MEMS piezoelectric energy harvesters
NASA Astrophysics Data System (ADS)
Wang, Y. C.; Huang, T. W.; Shu, Y. C.; Lin, S. C.; Wu, W. J.
2016-04-01
This article presents the modeling of nonlinear response of micro piezoelectric energy harvesters under amplified base excitation. The micro transducer is a composite cantilever beam made of the PZT thick film deposited on the stainless-steel substrate. The model is developed based on the Euler-Bernoulli beam theory considering geometric and inertia nonlinearities, and the reduced formulation is derived based on the Hamiltonian variational principle. The harmonic balance method is used to simulate the nonlinear frequency response under various magnitudes of excitation and electric loads. The hardening type of nonlinearity is predicted and is found to be in good agreement with experiment. However, the softening response is also observed in different samples fabricated under different conditions. Such disagreement is under investigation.
NASA Astrophysics Data System (ADS)
Zhu, Ronghua; Xie, Huimin; Dai, Xianglu; Zhu, Jianguo; Jin, Aizi
2014-09-01
Stress generated during thin film deposition is a critical issue for many applications. In general, the possible origins of the residual stress include intrinsic and extrinsic stresses. Since high residual stresses can cause detrimental effects on the film, such as delamination and wrinkle, it is of great importance to quantify the residual stress for the optimal design and the evaluation of its mechanical behavior. In this study, a method combining focused ion beam (FIB) milling and geometric phase analysis (GPA) is developed to assess the residual stress of thin films. The procedures of the residual stress measurement using this method include grating fabrication and slot milling by FIB, high-resolution scanning electron microscope (SEM) imaging of the grating before and after stress relaxation, and deformation analysis by GPA. The residual stress can be inferred from the released deformation using the reference displacements of the finite element model. As an application, this method was utilized to measure the residual stress in a TiAlSiN film, and the measured result is in good agreement with that obtained by the curvature method. In order to analyze the measurement error, the influence factors of Ga+ bombardment and the deposited platinum layer on the stress calculation are also discussed in detail.
El-Taibany, W.F.; Moslem, Waleed M.
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.
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: τ1 = 1.98 ± 0.40 ps and τ2 = 17.9 ± 6.8 ps.
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.
NASA Astrophysics Data System (ADS)
Lindlein, Norbert; Leuchs, Gerd
This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can perform several million floating-point operations in a second also revolutionized the methods of geometrical optics and so several analytical methods lost importance whereas numerical methods such as ray tracing became very important. Therefore, the emphasis in this chapter is also on modern numerical methods such as ray tracing and some other systematic methods such as the paraxial matrix theory.
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 | χxxxx(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.
Bindoni, Luca . E-mail: lucabindoni@inwind.it
2005-06-15
A technique for geometric and dosimetric pretreatment verification of step-and-shoot intensity modulated radiotherapy treatments (IMRT) using a beam imaging system (BIS) made up of a charge-coupled device (CCD) digital camera optically coupled with a metal-plate/phosphor screen is described. Some physical properties of BIS were investigated in order to demonstrate its capability to perform measurements with a high spatial resolution and a high sampling rate. High-speed imaging, with a minimum charge integration time on the CCD of 120 ms, can be performed. The study of the signal-to-noise ratio as a function of sampling time is presented. In-plane and cross-line pixel size was measured to be 0.368{+-}0.004 mm/pixel, which agrees within 0.5% of the manufacturer value of 0.366 mm. Spatial linearity results are very good and there are no detectable image distortions on whole 30x30 cm{sup 2} detector area. A software routine was written to automatically extract positions of the collimator leaves from the images of the field shaped by the multileaf collimator (MLC) and also to compare them with the coordinates from the treatment planning system (TPS), thus directly testing both the MLC positioning and the treatment parameters transfer from TPS to the linear accelerator in a fast and precise way. The dosimetric capabilities (characteristics) of the imaging device for photon beams with energies of 6 and 15 MV were studied. Additional plexiglass buildup layers, depending on x-ray energy, were needed to reach maximum efficiency. The energy dependence of the BIS response versus dose and dose rate was found to be linear over a wide range. Relative output factors of BIS as a function of field size, compared with values measured with an ionization chamber, were in good accord for smaller field sizes {<=}10x10 cm{sup 2} but showed differences up to 4% for all the energies at the respective buildup depth for bigger fields. Square field profiles at water-equivalent buildup depths
Focal-Plane Imaging of Crossed Beams in Nonlinear Optics Experiments
NASA Technical Reports Server (NTRS)
Bivolaru, Daniel; Herring, G. C.
2007-01-01
An application of focal-plane imaging that can be used as a real time diagnostic of beam crossing in various optical techniques is reported. We discuss two specific versions and demonstrate the capability of maximizing system performance with an example in a combined dual-pump coherent anti-Stokes Raman scattering interferometric Rayleigh scattering experiment (CARS-IRS). We find that this imaging diagnostic significantly reduces beam alignment time and loss of CARS-IRS signals due to inadvertent misalignments.
Proton Beam Fast Ignition Fusion: Nonlinear Generation of Bθ-Fields by Knock-on Electrons
NASA Astrophysics Data System (ADS)
Stefan, V. Alexander
2011-10-01
The knock-on electrons, generated by the fast proton beam in interaction with the free and bound electrons in a precompressed DT fusion pellet, outrun the proton beam, generating the Bθ-fields ahead of the beam, which may lead to the defocusing of the beam, if Bθ < 0. The Bθ-fields are generated due to the magnetic instability, ∂Bθ/ ∂t ~ (c/ σ) ∇ x jne, where jne is the knock-on electron current density, σ is the background plasma conductivity, and c the speed of light. The instability growth rate compensates for relatively low knock-on generation efficiency by a proton beam. The saturation level,(electron trapping mechanism), of the B-field ahead of the beam, is of the order of 10 MG and is reached on the time scale of 10 ps. M. Roth et al, Phys. Rev. Lett. 86, 436 (2001); M. Tabak et al, Phys. Plasmas 1 (5), 1626 (1994); H. L. Buchanan, F. W. Chambers, E. P. Lee, S. S. Yu, R. J. Briggs, and M. N. Rosenbluth, LLNL, UCRL Report 82586, 1979.
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.
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.
Ali Shan, S.; 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.
Progress on optimization of the nonlinear beam dynamics in the MEIC collider rings
None, None
2015-07-13
One of the key design features of the Medium-energy Electron-Ion Collider (MEIC) proposed by Jefferson Lab is a small beta function at the interaction point (IP) allowing one to achieve a high luminosity of up to 10^{34} cm^{-2}s^{-1}. The required strong beam focusing unavoidably causes large chromatic effects such as chromatic tune spread and beam smear at the IP, which need to be compensated. This paper reports recent progress in our development of a chromaticity correction scheme for the ion ring including optimization of dynamic aperture and momentum acceptance.
Progress on Optimization of the Nonlinear Beam Dynamics in the MEIC Collider Rings
Morozov, Vasiliy S.; Derbenev, Yaroslav S.; Lin, Fanglei; Pilat, Fulvia; Zhang, Yuhong; Cai, Y.; Nosochkov, Y. M.; Sullivan, Michael; Wang, M.-H.; Wienands, Uli
2015-09-01
One of the key design features of the Medium-energy Electron-Ion Collider (MEIC) proposed by Jefferson Lab is a small beta function at the interaction point (IP) allowing one to achieve a high luminosity of up to 10^{34} cm^{-2}s^{-1}. The required strong beam focusing unavoidably causes large chromatic effects such as chromatic tune spread and beam smear at the IP, which need to be compensated. This paper reports recent progress in our development of a chromaticity correction scheme for the ion ring including optimization of dynamic aperture and momentum acceptance.
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.
Piezomagnetoelastic broadband energy harvester: Nonlinear modeling and characterization
NASA Astrophysics Data System (ADS)
Aravind Kumar, K.; Ali, S. F.; Arockiarajan, A.
2015-11-01
Piezomagnetoelastic energy harvesters are one among the widely explored configurations to improve the broadband characteristics of vibration energy harvesters. Such nonlinear harvesters follow a Moon beam model with two magnets at the base and one at the tip of the beam. The present article develops a geometric nonlinear mathematical model for the broadband piezomagnetoelastic energy harvester. The electromechanical coupling and the nonlinear magnetic potential equations are developed from the dimensional system parameters to describe the nonlinear dynamics exhibited by the system. The developed model is capable of characterizing the monostable, bistable and tristable operating regimes of the piezomagnetoelastic energy harvester, which are not explicit in the Duffing representation of the system. Bifurcations and attractor motions are analyzed as nonlinear functions of the distance between base magnets and the field strength of the tip magnet. The model is further used to characterize the potential wells and stable states, with due focus on the performance of the system in broadband energy harvesting.
NASA Astrophysics Data System (ADS)
Shafiei, Navvab; Kazemi, Mohammad; Ghadiri, Majid
2016-08-01
This study is concerned with the small-scale effect on the nonlinear flapwise bending vibration of rotating cantilever and propped cantilever nanobeams. Euler-Bernoulli beam theory is used to model the nanobeam with nonlinearity. Nonlinear strain-displacement relations are employed to account for geometric nonlinearity of the system. The axial forces are modeled as the true spatial and thermal variations due to the rotation. Hamilton's principle is used to derive the nonlinear governing equation and nonlocal nonlinear boundary conditions based on Eringen's nonlocal elasticity theory. Finally, the differential quadrature method is used in conjunction with the direct iterative method to derive the nonlinear vibration frequencies of the nanobeam. The effects of the angular velocity, nonlocal small-scale parameter, temperature change and nonlinear amplitude on nonlinear vibration of the rotary nanobeam are discussed. The results of this work can be used in nanosensors, nanomotors, nanoturbines and NEMS applications.
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines
NASA Astrophysics Data System (ADS)
Franchetti, G.; Schmidt, F.
2015-06-01
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom).
Nonlinear optical properties of bulk cuprous oxide using single beam Z-scan at 790 nm
Serna, J.; Rueda, E.; García, H.
2014-11-10
The two-photon absorption (TPA) coefficient β and the nonlinear index of refraction n{sub 2} for bulk cuprous oxide (Cu{sub 2}O) direct gap semiconductor single crystal have been measured by using a balance-detection Z-scan single beam technique, with an excellent signal to noise ratio. Both coefficients were measured at 790 nm using a 65 fs laser pulse at a repetition rate of 90.9 MHz, generated by a Ti:Sapphire laser oscillator. The experimental values for β were explained by using a model that includes allowed-allowed, forbidden-allowed, and forbidden-forbidden transitions. It was found that the forbidden-forbidden transition is the dominant mechanism, which is consistent with the band structure of Cu{sub 2}O. The low value for β found in bulk, as compared with respect to thin film, is explained in terms of the structural change in thin films that result in opposite parities of the conduction and valence band. The n{sub 2} is also theoretically calculated by using the TPA dispersion curve and the Kramers-Kronig relations for nonlinear optics.
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
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.
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.
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.
Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals
NASA Astrophysics Data System (ADS)
Assanto, Gaetano; Minzoni, Antonmaria A.; Smyth, Noel F.; Worthy, Annette L.
2010-11-01
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.
Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation
Mi, Lufang; Cong, Hongzi
2015-07-15
In this paper, we consider the d-dimensional beam equation with convolution potential under periodic boundary conditions. We will apply the Kolmogorov-Arnold-Moser theorem in Eliasson and Kuksin [Ann. Math. 172, 371-435 (2010)] into this system and obtain that for sufficiently small ε, there is a large subset S′ of S such that for all s ∈ S′, the solution u of the unperturbed system persists as a time-quasi-periodic solution which has all Lyapunov exponents equal to zero and whose linearized equation is reducible to constant coefficients.
NASA Astrophysics Data System (ADS)
Tsysar, S. A.; Nikolaeva, A. V.; Svet, V. D.; Khokhlova, V. A.; Yuldashev, P. V.; Sapozhnikov, O. A.
2015-10-01
In the paper the use of receiving and radiating system, which allows to determine the parameters of bone by nonlinear pulse-echo technique and to image of brain structures through the skull bones, was proposed. Accuracy of the skull bone characterization is due to higher measured harmonic and is significantly better than in linear case. In the experimental part focused piezoelectric transducer with diameter 100 mm, focal distance 100 mm, the frequency of 1.092 MHz was used. It was shown that skull bone profiling can be performed with the use of 3rd harmonic since 1st harmonic can be used for visualization of the underlying objects. The use of wideband systems for both skull profiling and brain visualization is restricted by skull attenuation and resulting low effective sensitivity.
Tsysar, S. A. Nikolaeva, A. V.; Khokhlova, V. A.; Yuldashev, P. V.; Svet, V. D.; Sapozhnikov, O. A.
2015-10-28
In the paper the use of receiving and radiating system, which allows to determine the parameters of bone by nonlinear pulse-echo technique and to image of brain structures through the skull bones, was proposed. Accuracy of the skull bone characterization is due to higher measured harmonic and is significantly better than in linear case. In the experimental part focused piezoelectric transducer with diameter 100 mm, focal distance 100 mm, the frequency of 1.092 MHz was used. It was shown that skull bone profiling can be performed with the use of 3rd harmonic since 1st harmonic can be used for visualization of the underlying objects. The use of wideband systems for both skull profiling and brain visualization is restricted by skull attenuation and resulting low effective sensitivity.
Lan Pengfei; Lu Peixiang; Cao Wei
2006-01-15
The relativistic nonlinear Thomson scattering of a tightly focused intense laser pulse by an electron is investigated, and the temporal and spectral characters of the radiation are discussed. In a tightly focused laser pulse with an intensity of approximately 10{sup 20} W/cm{sup 2} and a pulse duration of 20 fs, the electron is scattered away from the focus quickly by the ponderomotive force and therefore the radiation emitted at the focus is much higher than that at other regions. As a result, a single ultrashort pulse of 3.8 as is generated and its corresponding spectrum is broadened to 200 orders of the frequency of the driving laser. With increasing the laser intensity, the signal-to-noise of the radiated pulse increases, and the pulse duration decreases. Moreover, the phase behavior of the spectral components and the dependence of the radiated power on the laser intensity are discussed.
Selvaraj, J
2014-06-15
Purpose: To determine required PTV margins for ≤1% loss in mean population TCP using systematic (Σ) and random (σ) errors calculated from daily cone-beam CT (CBCT) images of head and neck patients. Methods: Daily CBCT images were acquired for 50 head and neck patients. The CBCT image sets acquired at each fraction were registered with planning CT to obtain positional errors for each patient for each fraction. Systematic and random errors were calculated from data collected for 50 patients as described in IPEM On Target report. CTV delineation uncertainty of 2mm is added quadratically to systematic error. Assuming a spherical target volume, the dose in each voxel of target volume is summed for each fraction in the treatment by shifting the dose grid to calculate mean population TCP inclusive of geometric uncertainties using a Monte Carlo method. These simulations were repeated for the set of Σ and σ in each axis for different PTV margins and drop in TCP for each margin are obtained. In order to study the effect of dose-response curve on PTV margins, two different σα of 0.048 Gy-1 and 0.218 Gy-1 representing steep and shallow dose-response curves are studied. Σ were 2.5, 2.5, 2.1 mm and σ were 0.3, 0.3 0.2 mm respectively in x, y and z axis respectively. Results: PTV margins based on tumor radiobiological characteristics are 4.8, 4.8 and 4 mm in x, y and z axis assuming 25 treatment fractions for σα 0.048 Gy-1 (steep) and 4.2,4.2 and 2.2 for σα of 0.218 Gy-1 (shallow). While the TCP-based margins did not differ much in x and y axis, it is considerably smaller in z axis for shallow DRC. Conclusion: TCP based margins are substantially smaller than physical dose-based margin recipes. This study also demonstrates the importance of considering tumor radiobiological characteristics while deriving margins.
ACTIVE MEDIA: Nonlinear thermally induced distortions of a laser beam in a cryogenic disk amplifier
NASA Astrophysics Data System (ADS)
Vyatkin, A. G.; Khazanov, Efim A.
2009-09-01
Taking into account the temperature dependences of the heat conductivity, the refractive index, and the thermal expansion coefficient, we calculated the temperature, elastic stresses, a thermally induced lens and depolarisation of a beam in a cryogenic disk amplifier (an Yb:YAG disk placed between a copper cylinder and a sapphire disk cooled by liquid nitrogen). When the active element (the thickness is 0.6 mm, the orientation is [001], the atomic concentration of Yb is 10%) is pumped by radiation from a diode laser (the beam diameter is 6 mm), the temperature does not exceed 140 K for the heat release power of 100 W. In this case, elastic stresses in the active element are six times lower than the maximum permissible value. The focal distance of the thermally induced lens is 5.5 m and the depolarisation rate is 0.038% per two passes through the active element. Although the heat conductivity of the active element rapidly decreases with temperature, the thermal load can be increased by 1.5-2 times when the dimensions of the active element remain constant.
Nonlinear thermally induced distortions of a laser beam in a cryogenic disk amplifier
Vyatkin, A G; Khazanov, Efim A
2009-09-30
Taking into account the temperature dependences of the heat conductivity, the refractive index, and the thermal expansion coefficient, we calculated the temperature, elastic stresses, a thermally induced lens and depolarisation of a beam in a cryogenic disk amplifier (an Yb:YAG disk placed between a copper cylinder and a sapphire disk cooled by liquid nitrogen). When the active element (the thickness is 0.6 mm, the orientation is [001], the atomic concentration of Yb is 10%) is pumped by radiation from a diode laser (the beam diameter is 6 mm), the temperature does not exceed 140 K for the heat release power of 100 W. In this case, elastic stresses in the active element are six times lower than the maximum permissible value. The focal distance of the thermally induced lens is 5.5 m and the depolarisation rate is 0.038% per two passes through the active element. Although the heat conductivity of the active element rapidly decreases with temperature, the thermal load can be increased by 1.5-2 times when the dimensions of the active element remain constant. (active media)
Davidson, R.C.; Chen, C.
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
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
Davidson, R.C.; Lee, W.W.; Stoltz, P.
1997-08-01
This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.
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 Technical Reports Server (NTRS)
Grebowsky, G. J.
1982-01-01
Present LANDSAT data formats are reviewed to clarify how the geodetic location and registration capabilities were defined for P-tape products and RBV data. Since there is only one geometric model used in the master data processor, geometric location accuracy of P-tape products depends on the absolute accuracy of the model and registration accuracy is determined by the stability of the model. Due primarily to inaccuracies in data provided by the LANDSAT attitude management system, desired accuracies are obtained only by using ground control points and a correlation process. The verification of system performance with regards to geodetic location requires the capability to determine pixel positions of map points in a P-tape array. Verification of registration performance requires the capability to determine pixel positions of common points (not necessarily map points) in 2 or more P-tape arrays for a given world reference system scene. Techniques for registration verification can be more varied and automated since map data are not required. The verification of LACIE extractions is used as an example.
Dynamic analysis of very flexible beams
NASA Astrophysics Data System (ADS)
Fotouhi, R.
2007-08-01
The dynamic analysis of flexible beams with large deformations is difficult and few studies have been performed. In this paper, the vibration analysis of several very flexible beams with large deflections using the finite element approach is studied. The examples were a cantilever beam and rotating flexible robot arms. The results were compared with the results available in the published literature. Several successful checks on the finite element results were performed to ensure the accuracy of the solutions. Due to the geometrical nonlinearity, several static equilibrium shapes can exist for large deflections of a cantilever beam for a given load. Nonlinear dynamic finite element analysis was implemented to investigate the stability of these shapes.
Hinker, P.; Hansen, C.
1993-09-01
An algorithm is presented which describes an application independent method for reducing the number of polygonal primitives required to faithfully represent an object. Reducing polygon count without a corresponding reduction in object detail is important for: achieving interactive frame rates in scientific visualization, reducing mass storage requirements, and facilitating the transmission of large, multi-timestep geometric data sets. This paper shows how coplanar and nearly coplanar polygons can be merged into larger complex polygons and re-triangulated into fewer simple polygons than originally required. The notable contributions of this paper are: (1) a method for quickly grouping polygons into nearly coplanar sets, (2) a fast approach for merging coplanar polygon sets and, (3) a simple, robust triangulation method for polygons created by 1 and 2. The central idea of the algorithm is the notion of treating polygonal data as a collection of segments and removing redundant segments to quickly form polygon hulls which represent the merged coplanar sets.
Rasouli, Saifollah; Ghasemi, H; Tavassoly, M T; Khalesifard, H R
2011-06-01
In this paper, the application of "parallel" moiré deflectometry in measuring the nonlinear refractive index of materials is reported. In "parallel" moiré deflectometry the grating vectors are parallel, and the resulting moiré fringes are also parallel to the grating lines. Compared to "rotational" moiré deflectometry and the Z-scan technique, which cannot easily determine the moiré fringe's angle of rotation and is sensitive to power fluctuations, respectively, "parallel" moiré deflectometry is more reliable, which allows one to measure the radius of curvature of the light beam by measuring the moiré fringe spacing. The nonlinear refractive index of the sample, including the sense of the change, is obtained from the moiré fringe spacing curve. The method is applied for measuring the nonlinear refractive index of ferrofluids. PMID:21629313
Valeš, Jan
2015-03-10
The paper deals with statistical analysis of the resistance of simply supported I-beams subjected to bending. The resistance was solved by applying the geometrically nonlinear solution. The influence of lateral-beam buckling on resistance is studied. Initial geometrical imperfections originating from the first eigenmode of lateral-beam buckling and from the cross section rotation at the stability lost were ascribed to the beams. These imperfections consist of initial axial lateral buckling and rotation of cross sections along the beam axis length. The correlation between the amplitudes of these imperfections is considered to be the parameter of solutions within the interval from -1 to 1. The influence of this correlation on the change of mean values and standard deviations of random resistance of beams with nondimensional slenderness close to 1 is studied. The imperfections mentioned were considered, together with geometrical and material characteristics of cross section and material characteristics of steel, to be random quantities.
NASA Astrophysics Data System (ADS)
Wang, Yi-Ren; Liang, Tzu-Wen
2015-08-01
The objective of this study was to optimize the damping effects of a lumped-mass vibration absorber (LMVA) attached to a hinged-hinged nonlinear beam held on a nonlinear elastic foundation. The LMVA was located at various points along the beam and supported by a spring from beneath. Analysis was performed on the internal resonance conditions with the aim of eliminating internal resonance and reducing the amplitude of vibrations in the beam by altering the location and mass of the LMVA as well as the spring constant. We employed the method of multiple scales (MOMS) for the analysis of frequency response in various modes. Fixed points plots were constructed and 3D maximum amplitude contour plots (3D MACPs) were compiled to identify the LMVA combinations with the optimal damping effects. The best damping results in the 3rd mode were achieved when the LMVA was placed between 1/4l and 1/2l in combinations of M^ (mass of LMVA/mass of beam) and K˜ (LMVA spring constant/elastic foundation spring constant) followed a linear relationship of K˜=10M^.
Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak
2015-10-15
The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show that the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.
Three-Dimensional Postbuckling Analysis of Curved Beams
NASA Technical Reports Server (NTRS)
Pai, P. Frank; Lee, Seung-Yoon
2002-01-01
Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.
NASA Astrophysics Data System (ADS)
Kurkin, S. A.; Koronovski, A. A.; Hramov, A. E.
2009-08-01
Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.
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.
A case study of analysis methods for large deflections of a cantilever beam
NASA Astrophysics Data System (ADS)
Craig, L. D.
1994-05-01
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.
Influence of axial loads on the nonplanar vibrations of cantilever beams
NASA Astrophysics Data System (ADS)
Carvalho, Eulher C.; Gonçalves, Paulo B.; Del Prado, Zenón; Rega, Giuseppe
2012-11-01
The three-dimensional motions of cantilever beams have been extensively studied in the past. This structural element can be found in several applications, including MEMS and NEMS. In many applications the beam is subjected to axial loads which can play an important role in the dynamics of very slender beams. In this paper a cantilever inextensible beam subject to a concentrated axial load and a lateral harmonic excitation is investigated. Special attention is given to the effect of axial load on the frequency-amplitude relation, bifurcations and instabilities of the beam, a problem not tackled in the previous literature on this subject. To this aim, the nonlinear integro-differential equations describing the flexural-flexural-torsional couplings of the beam are used, together with the Galerkin method, to obtain a set of discretized equations of motion, which are in turn solved by numerical integration using the Runge-Kutta method. Both inertial and geometric nonlinearities are considered in the present analysis. Due to symmetries of the beam cross section, the beam exhibits a 1:1 internal resonance which has an important role on the nonlinear oscillations and bifurcation scenario. The results show that the axial load influences the stiffness of the beam changing its nonlinear behavior from hardening to softening. A detailed parametric analysis using several tools of nonlinear dynamics, unveils the complex dynamics of the beam in the parametric or external resonance regions. Bifurcations leading to multiple coexisting solutions are observed.
Deflection of a flexural cantilever beam
NASA Astrophysics Data System (ADS)
Sherbourne, A. N.; Lu, F.
The behavior of a flexural elastoplastic cantilever beam is investigated in which geometric nonlinearities are considered. The result of an elastica analysis by Frisch-Fay (1962) is extended to include postyield behavior. Although a closed-form solution is not possible, as in the elastic case, simple algebraic equations are derived involving only one unknown variable, which can also be expressed in the standard form of elliptic integrals if so desired. The results, in comparison with those of the small deflection analyses, indicate that large deflection analyses are necessary when the relative depth of the beam is very small over the length. The present exact solution can be used as a reference by those who resort to a finite element method for more complicated problems. It can also serve as a building block to other beam problems such as a simply supported beam or a beam with multiple loads.
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.
Geometric Phase for Adiabatic Evolutions of General Quantum States
Wu, Biao; Liu, Jie; Niu, Qian; Singh, David J
2005-01-01
The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.
NASA Astrophysics Data System (ADS)
Jafari Bahman, F.; Maraghechi, B.
2013-02-01
Efficiency enhancement in free-electron laser is studied by three-dimensional and nonlinear simulation using tapered helical wiggler magnetic field or tapered ion-channel density. In order to reduce the saturation length, prebunched electron beam is used. A set of nonlinear and coupled differential equations are derived that provides the self-consistent description of the evolution of both an ensemble of electrons and the electromagnetic radiation. These equations are solved numerically to show that the combined effect of tapering and prebunching results in significant enhancement of power and considerable reduction of the saturation length. To have a deeper insight into the problem, an analytical treatment is also presented that uses the small signal theory to derive a modified pendulum equation.
Jafari Bahman, F.; Maraghechi, B.
2013-02-15
Efficiency enhancement in free-electron laser is studied by three-dimensional and nonlinear simulation using tapered helical wiggler magnetic field or tapered ion-channel density. In order to reduce the saturation length, prebunched electron beam is used. A set of nonlinear and coupled differential equations are derived that provides the self-consistent description of the evolution of both an ensemble of electrons and the electromagnetic radiation. These equations are solved numerically to show that the combined effect of tapering and prebunching results in significant enhancement of power and considerable reduction of the saturation length. To have a deeper insight into the problem, an analytical treatment is also presented that uses the small signal theory to derive a modified pendulum equation.
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.
Nonlinear ordinary difference equations
NASA Technical Reports Server (NTRS)
Caughey, T. K.
1979-01-01
Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.
Hramov, A. E.; Koronovskii, A. A.; Kurkin, S. A.; Filatova, A. E.
2012-11-15
The report is devoted to the results of the numerical study of the virtual cathode (VC) formation conditions in the relativistic electron beam (REB) under the influence of the self-magnetic and external axial magnetic fields. The azimuthal instability of the relativistic electron beam leading to the formation of the vortex electron structure in the system was found out. This instability is determined by the influence of the self-magnetic fields of the relativistic electron beam, and it leads to the decrease of the critical value of the electron beam current (current when the non-stationary virtual cathode is formed in the drift space). The typical dependencies of the critical current on the external uniform magnetic field value were discovered. The effect of the beam thickness on the virtual cathode formation conditions was also analyzed.
Moderately nonlinear ultrasound propagation in blood-mimicking fluid.
Kharin, Nikolay A; Vince, D Geoffrey
2004-04-01
In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma < 1) or strong waves (Gamma > 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading. PMID:15121252
NASA Astrophysics Data System (ADS)
Larré, Pierre-Élie; Carusotto, Iacopo
2016-03-01
We study the coherence properties of a laser beam after propagation along a one-dimensional lossless nonlinear optical waveguide. Within the paraxial, slowly-varying-envelope, and single-transverse-mode approximations, the quantum propagation of the light field in the nonlinear medium is mapped onto a quantum Gross-Pitaevskii-type evolution of a closed one-dimensional system of many interacting photons. Upon crossing the entrance and the back faces of the waveguide, the photon-photon interaction parameter undergoes two sudden jumps, resulting in a pair of quantum quenches of the system's Hamiltonian. In the weak-interaction regime, we use the modulus-phase Bogoliubov theory of dilute Bose gases to describe the quantum fluctuations of the fluid of light and predict that correlations typical of a prethermalized state emerge locally in their final form and propagate in a light-cone way at the Bogoliubov speed of sound in the photon fluid. This peculiar relaxation dynamics, visible in the light exiting the waveguide, results in a loss of long-lived coherence in the beam of light.
Spin Hall effect of light in inhomogeneous nonlinear medium
NASA Astrophysics Data System (ADS)
Li, Hehe; Li, Xinzhong
2016-01-01
In this paper, we investigate the spin Hall effect of a polarized Gaussian beam (GB) in a smoothly inhomogeneous isotropic and nonlinear medium using the method of the eikonal-based complex geometrical optics which describes the phase front and cross-section of a light beam using the quadratic expansion of a complex-valued eikonal. The linear complex-valued eikonal terms are introduced to describe the polarization-dependent transverse shifts of the beam in inhomogeneous nonlinear medium which is called the spin Hall effect of beam. We know that the spin Hall effect of beam is affected by the nonlinearity of medium and include two parts, one originates from the coupling between the spin angular momentum and the extrinsic orbital angular momentum due to the curve trajectory of the center of gravity of the polarized GB and the other from the coupling between the spin angular momentum and the intrinsic orbital angular momentum due to the rotation of the beam with respect to the central ray.
Experimental verification of a bridge-shaped, nonlinear vibration energy harvester
Gafforelli, Giacomo Corigliano, Alberto; Xu, Ruize; Kim, Sang-Gook
2014-11-17
This paper reports a comprehensive modeling and experimental characterization of a bridge shaped nonlinear energy harvester. A doubly clamped beam at large deflection requires stretching strain in addition to the bending strain to be geometrically compatible, which stiffens the beam as the beam deflects and transforms the dynamics to a nonlinear regime. The Duffing mode non-linear resonance widens the frequency bandwidth significantly at higher frequencies than the linear resonant frequency. The modeling includes a nonlinear measure of strain coupled with piezoelectric constitutive equations which end up in nonlinear coupling terms in the equations of motion. The main result supports that the power generation is bounded by the mechanical damping for both linear and nonlinear harvesters. Modeling also shows the power generation is over a wider bandwidth in the nonlinear case. A prototype is manufactured and tested to measure the power generation at different load resistances and acceleration amplitudes. The prototype shows a nonlinear behavior with well-matched experimental data to the modeling.
Design of geometric phase measurement in EAST Tokamak
NASA Astrophysics Data System (ADS)
Lan, T.; Liu, H. Q.; Liu, J.; Jie, Y. X.; Wang, Y. L.; Gao, X.; Qin, H.
2016-07-01
The optimum scheme for geometric phase measurement in EAST Tokamak is proposed in this paper. The theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Meanwhile, the influences of some controllable parameters on geometric phase are evaluated. The feasibility and challenge of distinguishing geometric effect in the POINT signal are also assessed in detail.
NASA Astrophysics Data System (ADS)
Wilcox, Jamianne C.; Lopez, Benjamin J.; Campas, Otger; Valentine, Megan T.
2015-08-01
Optical traps allow for the precise application and measurement of pico-Newton forces in a wide variety of situations, and are particularly well suited for biophysical measurements of motor proteins and cells. Nearly all experiments exploit the linear regime of the optical trap, where force and displacement are related by a simple spring constant that does not depend on the trapped object's position. This typically limits the useful force range to < 100 pN for high-NA objective lenses and reasonable laser powers. Several biological studies require larger forces, which are not accessible in the linear regime of the trap. The best means to extend the maximum force is to make use of the entire nonlinear range; however, current techniques for calibrating the full nonlinear regime are limited. Here we report a new method for calibrating the nonlinear trap region that uses the fluctuations in the position of a trapped object when it is displaced from the center of a single gradient optical trap by controlled flow. From the position fluctuations, we measure the local trap stiffness, in both the linear and non-linear regimes. This approach requires only knowledge of the system temperature, and is especially useful for measurements involving trapped objects of unknown size, or objects in a fluid of unknown viscosity.
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.
Dibaji, Seyed Ahmad Reza; Banerjee, Rupak K; Liu, Yunbo; Soneson, Joshua E; Myers, Matthew R
2016-05-01
A technique useful for performing derating at acoustic powers where significant harmonic generation occurs is illustrated and validated with experimental measurements. The technique was previously presented using data from simulations. The method is based upon a Gaussian representation of the propagation modes, resulting in simple expressions for the modal quantities, but a Gaussian source is not required. The nonlinear interaction of modes within tissue is estimated from the nonlinear interaction in water, using appropriate amounts of source reduction and focal-point reduction derived from numerical simulations. An important feature of this nonlinear derating method is that focal temperatures can be estimated with little additional effort beyond that required to determine the focal pressure waveforms. Hydrophone measurements made in water were used to inform the derating algorithm, and the resulting pressure waveforms and increases in temperature were compared with values directly measured in tissue phantoms. For a 1.05 MHz focused transducer operated at 80 W and 128 W, the derated pressures (peak positive, peak negative) agreed with the directly measured values to within 11%. Focal temperature rises determined by the derating method agreed with values measured using a remote thermocouple technique with a difference of 17%. PMID:27250156
Sarkisov, S.S.; Williams, E.K.; Curley, M.; Smith, C.C.; Ila, D.; Venkateswarlu, P.; Poker, D.B.; Hensley, D.K.
1997-11-01
Ion implantation has been shown to produce a high density of metal colloids in glasses and crystalline materials. The high-precipitate volume fraction and small size of metal nanoclusters formed leads to values for the third-order susceptibility much greater than those for metal doped solids. This has stimulated interest in use of ion implantation to make nonlinear optical materials. On the other side, LiNbO{sub 3} has proved to be a good material for optical waveguides produced by MeV ion implantation. Light confinement in these waveguides is produced by refractive index step difference between the implanted region and the bulk material. Implantation of LiNbO{sub 3} with MeV metal ions can therefore result into nonlinear optical waveguide structures with great potential in a variety of device applications. The authors describe linear and nonlinear optical properties of a waveguide structure in LiNbO{sub 3}-based composite material produced by silver ion implantation in connection with mechanisms of its formation.
Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Muravyov, Alexander A.
2000-01-01
A recently developed finite-element-based equivalent linearization approach for the analysis of random vibrations of geometrically nonlinear multiple degree-of-freedom structures is validated. The validation is based on comparisons with results from a finite element based numerical simulation analysis using a numerical integration technique in physical coordinates. In particular, results for the case of a clamped-clamped beam are considered for an extensive load range to establish the limits of validity of the equivalent linearization approach.
Akimoto, Tetsuo . E-mail: takimoto@showa.gunma-u.ac.jp; Katoh, Hiroyuki; Kitamoto, Yoshizumi; Shirai, Katsuyuki; Shioya, Mariko; Nakano, Takashi
2006-04-01
Purpose: To evaluate the advantages of anatomy-based inverse optimization (IO) in planning high-dose-rate (HDR) brachytherapy. Methods and Materials: A total of 114 patients who received HDR brachytherapy (9 Gy in two fractions) combined with hypofractionated external beam radiotherapy (EBRT) were analyzed. The dose distributions of HDR brachytherapy were optimized using geometric optimization (GO) in 70 patients and by anatomy-based IO in the remaining 44 patients. The correlation between the dose-volume histogram parameters, including the urethral dose and the incidence of acute genitourinary (GU) toxicity, was evaluated. Results: The averaged values of the percentage of volume receiving 80-150% of the prescribed minimal peripheral dose (V{sub 8}-V{sub 15}) of the urethra generated by anatomy-based IO were significantly lower than the corresponding values generated by GO. Similarly, the averaged values of the minimal dose received by 5-50% of the target volume (D{sub 5}-D{sub 5}) obtained using anatomy-based IO were significantly lower than those obtained using GO. Regarding acute toxicity, Grade 2 or worse acute GU toxicity developed in 23% of all patients, but was significantly lower in patients for whom anatomy-based IO (16%) was used than in those for whom GO was used (37%), consistent with the reduced urethral dose (p <0.01). Conclusion: The results of this study suggest that anatomy-based IO is superior to GO for dose optimization in HDR brachytherapy for prostate cancer.
Geometrical approach to tumor growth.
Escudero, Carlos
2006-08-01
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells and particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former paper [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyze the unexplored three-dimensional case, for which interesting conclusions on tumor growth are derived. PMID:17025466
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 μm 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.
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.
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.
Nonlinear tuning of microresonators for dynamic range enhancement
Saghafi, M.; Dankowicz, H.; Lacarbonara, W.
2015-01-01
This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators. PMID:26345078
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.
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.
Batra, Karuna; Mitra, Sugata; Subbarao, D.; Sharma, R.P.; Uma, R.
2005-01-01
The task for the present study is to make an investigation of self-similarity in a self-focusing laser beam both theoretically and numerically using graphical user interface based interactive computer simulation model in MATLAB (matrix laboratory) software in the presence of saturating ponderomotive force based and relativistic electron quiver based plasma nonlinearities. The corresponding eigenvalue problem is solved analytically using the standard eikonal formalism and the underlying dynamics of self-focusing is dictated by the corrected paraxial theory for slow self-focusing. The results are also compared with computer simulation of self-focusing by the direct fast Fourier transform based spectral methods. It is found that the self-similar solution obtained analytically oscillates around the true numerical solution equating it at regular intervals. The simulation results are the main ones although a feasible semianalytical theory under many assumptions is given to understand the process. The self-similar profiles are called as self-organized profiles (not in a strict sense), which are found to be close to Laguerre-Gaussian curves for all the modes, the shape being conserved. This terminology is chosen because it has already been shown from a phase space analysis that the width of an initially Gaussian beam undergoes periodic oscillations that are damped when any absorption is added in the model, i.e., the beam width converges to a constant value. The research paper also tabulates the specific values of the normalized phase shift for solutions decaying to zero at large transverse distances for first three modes which can, however, be extended to higher order modes.
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Christian, Joy Julius
truly quantum regime, and allows, for the first time, the measurements of such phases associated with arbitrary non-cyclic evolutions of entangled linear-momentum photon -states. This non-classical manifestation of the geometrical phases is due to the entangled character of linear-momentum photon-states of two correlated photons produced by parametric down-conversion in non-linear crystals. Finally, the non-local aspect of the geometrical phase is contrasted with the fundamental non-locality of quantum mechanics due to the entangled character of quantum states.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
NASA Astrophysics Data System (ADS)
Andreone, A.; Di Gennaro, E.; Lamura, G.; Salluzzo, M.; Purnell, A.; Cohen, L. F.; Hao, L.; Gallop, J.; Cantoni, C.; Paranthaman, M.
2003-02-01
We present a study on the temperature and field dependence of the microwave surface impedance Zs in thin films of the superconducting MgB2 compound. Samples were prepared by e-beam evaporation of boron on r-plane sapphire followed by an ex situ annealing in Mg vapour. Critical temperature values range between 26 and 38 K. Surface impedance measurements (Zs = Rs + iXs) were performed from 2 K close to Tc in the microwave region up to 20 GHz via parallel plate or dielectrically loaded resonators in 'symmetric' (two MgB2 films) and asymmetric (an MgB2 film and a commercial YBCO control film) configurations. At high microwave power, frequency domain measurements show a characteristic signature associated with weak links and this appears to be the limiting factor governing the performance of these films.
Geometric Gyrokinetic Theory for Edge Plasma
Qin, H; Cohen, R H; Nevins, W M; Xu, X Q
2007-01-18
It turns out that gyrokinetic theory can be geometrically formulated as special cases of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the spacetime is a 7-dimensional fiber bundle P over the 4-dimensional spacetime M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the 7-dimensional phase space determines particles worldlines in the phase space. Through Liouville 6-form {Omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyro-symmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyro-symmetry. The objective is to decouple the gyro-phase dynamics from the rest of particle dynamics by finding the gyro-symmetry in {gamma}. Compared with other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the spacetime coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here can not be achieved using classical methods. What the
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.
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…
Berry phase in nonlinear systems
Liu, J.; Fu, L. B.
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.
New developments on the geometric nonholonomic integrator
NASA Astrophysics Data System (ADS)
Ferraro, Sebastián; Jiménez, Fernando; Martín de Diego, David
2015-04-01
In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28 Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220-9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behaviour. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behaviour of the proposed method with the example of the inhomogeneous sphere rolling without slipping on a table.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Transition from linear- to nonlinear-focusing regime in filamentation
Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin
2014-01-01
Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature. PMID:25434678
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.
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.
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics. PMID:25401574
Introduction to Dynamical Systems and Geometric Mechanics
NASA Astrophysics Data System (ADS)
Maruskin, Jared M.
2012-01-01
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explores similar systems that instead evolve on differentiable manifolds. In the study of geometric mechanics, however, additional geometric structures are often present, since such systems arise from the laws of nature that govern the motions of particles, bodies, and even galaxies. In the first part of the text, we discuss linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, PoincarÃ© maps, Floquet theory, the PoincarÃ©-Bendixson theorem, bifurcations, and chaos. The second part of the text begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms. The final chapters cover Lagrangian and Hamiltonian mechanics from a modern geometric perspective, mechanics on Lie groups, and nonholonomic mechanics via both moving frames and fiber bundle decompositions. The text can be reasonably digested in a single-semester introductory graduate-level course. Each chapter concludes with an application that can serve as a springboard project for further investigation or in-class discussion.
Descriptive Geometry and Geometric Modeling.
ERIC Educational Resources Information Center
Adams, J. Alan
1988-01-01
Describes experiences for engineering students to develop spatial awareness and reasoning capability. Describes geometric modeling, basic geometric concepts, operations, surface modeling, and conclusions. (YP)
Geometrical deployment for braided stent.
Bouillot, Pierre; Brina, Olivier; Ouared, Rafik; Yilmaz, Hasan; Farhat, Mohamed; Erceg, Gorislav; Lovblad, Karl-Olof; Vargas, Maria Isabel; Kulcsar, Zsolt; Pereira, Vitor Mendes
2016-05-01
The prediction of flow diverter stent (FDS) implantation for the treatment of intracranial aneurysms (IAs) is being increasingly required for hemodynamic simulations and procedural planning. In this paper, a deployment model was developed based on geometrical properties of braided stents. The proposed mathematical description is first applied on idealized toroidal vessels demonstrating the stent shortening in curved vessels. It is subsequently generalized to patient specific vasculature predicting the position of the filaments along with the length and local porosity of the stent. In parallel, in-vitro and in-vivo FDS deployments were measured by contrast-enhanced cone beam CT (CBCT) in idealized and patient-specific geometries. These measurements showed a very good qualitative and quantitative agreement with the virtual deployments and provided experimental validations of the underlying geometrical assumptions. In particular, they highlighted the importance of the stent radius assessment in the accuracy of the deployment prediction. Thanks to its low computational cost, the proposed model is potentially implementable in clinical practice providing critical information for patient safety and treatment outcome assessment. PMID:26891065
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes
NASA Astrophysics Data System (ADS)
Kirkendall, Christopher R.; Kwon, Jae W.
2016-03-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion.
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes
Kirkendall, Christopher R.; Kwon, Jae W.
2016-01-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion. PMID:26961749
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.
Inflation from geometrical tachyons
Thomas, Steven; Ward, John
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.
Geometrical pre-planning for conformal radiotherapy.
Tsougos, Ioannis; Schreibmann, Eduard; Lahanas, Michael; Theodorou, Kiki; Kappas, Constantin; Baltas, Dimos
2007-01-01
The optimum selection of beams and arcs in conformal techniques is of the outmost importance in modern radiotherapy. In this work we give a description of an analytic method to aid optimum selection, which is based on minimizing the intersection between beams and organs at risk (OAR) and on minimizing the intersection between the beam and the planning target volume (PTV). An arc-selection function that permits selection of irradiation arcs based on individual beam feasibility is introduce. The method simulates the treatment process by defining a computed beam feasibility, for every possible set of gantry-table angles, by taking into account accurately computer intersection volumes between the OAR and beams. The beams are shaped to conform the target using realistic parameters for the treatment process. The results are displayed on a virtual sphere centred at the isocenter with color-coded regions indicating beam feasibility. Arcs selections are performed by searching the map for successive gantry positions at a certain table angle, with feasibility values greater than a user-specified threshold. The accuracy of the method was confirmed by using geometrical regular shapes, as well as real clinical cases. PMID:17851850
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.
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-08-01
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
Nonlinear analysis and redesign of the mixed-mode bending delamination test
NASA Technical Reports Server (NTRS)
Reeder, J. R.; Crews, J. H., Jr.
1991-01-01
The Mixed Mode Bending (MMB) test uses a lever to simultaneously apply mode I and mode II loading to a split beam specimen. An iterative analysis that accounts for the geometric nonlinearity of the MMB test was developed. The analysis accurately predicted the measured load displacement response and the strain energy release rate, G, of an MMB test specimen made of APC2 (AS4/PEEK). The errors in G when calculated using linear theory were found to be as large as thirty percent in some cases. Because it would be inconvenient to use a nonlinear analysis to analyze MMB data, the MMB apparatus was redesigned to minimize the nonlinearity. The nonlinear analysis was used as a guide in redesigning the MMB apparatus. With the redesigned apparatus, loads were applied through a roller attached to the level and loaded just above the midplane of the test specimen. The redesigned apparatuus has geometric nonlinearity errors of less than three percent, even for materials substantially tougher than APC2. This apparatus was demonstrated by measuring the mixed mode delamination fracture toughness of APC2.
Columnar deformation of human red blood cell by highly localized fiber optic Bessel beam stretcher
Lee, Sungrae; Joo, Boram; Jeon, Pyo Jin; Im, Seongil; Oh, Kyunghwan
2015-01-01
A single human red blood cell was optically stretched along two counter-propagating fiber-optic Bessel-like beams in an integrated lab-on-a-chip structure. The beam enabled highly localized stretching of RBC, and it induced a nonlinear mechanical deformation to finally reach an irreversible columnar shape that has not been reported. We characterized and systematically quantified this optically induced mechanical deformation by the geometrical aspect ratio of stretched RBC and the irreversible stretching time. The proposed RBC mechanism can realize a versatile and compact opto-mechanical platform for optical diagnosis of biological substances in the single cell level. PMID:26601005
Columnar deformation of human red blood cell by highly localized fiber optic Bessel beam stretcher.
Lee, Sungrae; Joo, Boram; Jeon, Pyo Jin; Im, Seongil; Oh, Kyunghwan
2015-11-01
A single human red blood cell was optically stretched along two counter-propagating fiber-optic Bessel-like beams in an integrated lab-on-a-chip structure. The beam enabled highly localized stretching of RBC, and it induced a nonlinear mechanical deformation to finally reach an irreversible columnar shape that has not been reported. We characterized and systematically quantified this optically induced mechanical deformation by the geometrical aspect ratio of stretched RBC and the irreversible stretching time. The proposed RBC mechanism can realize a versatile and compact opto-mechanical platform for optical diagnosis of biological substances in the single cell level. PMID:26601005
Analysis of transverse shear strains in pre-twisted thick beams using variational asymptotic method
Ameen, Maqsood M.; Harursampath, Dineshkumar E-mail: dinesh@aero.iisc.ernet.in
2015-03-10
The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam ref-erence curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.
Tuning piezoresistive transduction in nanomechanical resonators by geometrical asymmetries
Llobet, J.; Sansa, M.; Lorenzoni, M.; Pérez-Murano, F.; Borrisé, X.; San Paulo, A.
2015-08-17
The effect of geometrical asymmetries on the piezoresistive transduction in suspended double clamped beam nanomechanical resonators is investigated. Tapered silicon nano-beams, fabricated using a fast and flexible prototyping method, are employed to determine how the asymmetry affects the transduced piezoresistive signal for different mechanical resonant modes. This effect is attributed to the modulation of the strain in pre-strained double clamped beams, and it is confirmed by means of finite element simulations.
Tuning piezoresistive transduction in nanomechanical resonators by geometrical asymmetries
NASA Astrophysics Data System (ADS)
Llobet, J.; Sansa, M.; Lorenzoni, M.; Borrisé, X.; San Paulo, A.; Pérez-Murano, F.
2015-08-01
The effect of geometrical asymmetries on the piezoresistive transduction in suspended double clamped beam nanomechanical resonators is investigated. Tapered silicon nano-beams, fabricated using a fast and flexible prototyping method, are employed to determine how the asymmetry affects the transduced piezoresistive signal for different mechanical resonant modes. This effect is attributed to the modulation of the strain in pre-strained double clamped beams, and it is confirmed by means of finite element simulations.
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: μSR measurements on single crystals
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.
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…
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
Levels of Geometric Understanding.
ERIC Educational Resources Information Center
Pegg, John; Davey, Geoff
1991-01-01
Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…
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
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2004-01-01
The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Nonlinear metamaterials for holography.
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency-the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Galushkin, M G; Mitin, Konstantin V; Ionin, Andrei A; Kotkov, A A
1998-10-31
Numerical simulation is used as the basis of an analysis of nonlinear optical properties of the active medium in intracavity four-wave mixing of the radiation of a pulsed electron-beam-controlled discharge CO{sub 2} laser on saturated-gain and refractive-index diffraction gratings. The reflection coefficient of the phase-conjugated signal is determined for various cavity Q-factors, specific input energies, and pressures of the laser-active mixture. A comparison is made of the theoretical and experimental results. It is found that the rate of formation of amplitude gratings is governed primarily by the initial population inversion and by the intensities of the interacting waves. It is shown that transient phase gratings make the dominant contribution to the phase-conjugate reflection coefficient at high pressures of the mixture. (nonlinear optical phenomena)
A geometric description of human intestine.
Coşkun, Ihsaniye; Yildiz, Hüseyin; Arslan, Kadri; Yildiz, Bahri
2007-01-01
Mathematical models of natural phenomena play a central role in the physical sciences. Moreover, modeling of the organs draws from some beautiful areas of mathematics, such as nonlinear dynamics, multiscale transforms and stability analysis. In this study, a geometric recognition of the separate intestine sections (duodenum, jejunum, ileum, cecum and colon) of the human is presented. The human intestine was considered a tubular shape along a special curve and two male Turkish men were used for the modeling study. The length (cm) and diameter (mm) of the intestines were measured with a digital compass and formulated. These models were compared with their original photographs. It has been concluded that the geometric modeling and experimental work were consistent. These kinds of organ modeling techniques will also profit to medical lecturers to show 3-D figures to their students. PMID:17580658
Geometrical aspects of quantum spaces
Ho, P.M.
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.
Beam-beam interaction in P-P colliding accelerators
Parzen, G.
1982-08-01
One model for beam growth due to the beam-beam interaction in P-P colliding accelerators is that it is due to the presence of non-linear forces generated by the fields produced by the beam plus some radomizing effect like noise, or a tune modulation. According to this model, to limit beam-beam effects, one should try to limit the size of the non-linear forces and the sources of noise or tune modulation. This model can also be used to compare the severity of beam-beam effects in two situations by comparing the size of the non-linear forces. In this paper, this approach will be used to study three problems: to compare the effects of beam-beam non-linear resonances in the ISR with those in ISABELLE; to estimate the strength of a spectrometer magnet that may be placed at one of the beam crossing points, without appreciably increasing the beam-beam effects; and to compare the beam-beam interaction for colliding beam accelerators with different crossing-angles and different ..beta../sub x/ and ..beta../sub y/ at the crossing points.
Geometrical deuteron stripping revisited
Neoh, Y. S.; Yap, S. L.
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.
Geometric measures of entanglement
Uyanik, K.; Turgut, S.
2010-03-15
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
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.
Spatial Non-Cyclic Geometric Phase in Neutron Interferometry
Filipp, Stefan; Hasegawa, Yuji; Loidl, Rudolf; Rauch, Helmut
2005-01-01
We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by some of the authors to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism. The extension to non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere. The theoretical treatment comprises the cyclic geometric phase as a special case, which is confirmed by experiment. PMID:27308131
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.
Nonlinear competition in nematicon propagation.
Laudyn, Urszula A; Kwasny, Michał; Piccardi, Armando; Karpierz, Mirosław A; Dabrowski, Roman; Chojnowska, Olga; Alberucci, Alessandro; Assanto, Gaetano
2015-11-15
We investigate the role of competing nonlinear responses in the formation and propagation of bright spatial solitons. We use nematic liquid crystals (NLCs) exhibiting both thermo-optic and reorientational nonlinearities with continuous-wave beams. In a suitably prepared dye-doped sample and dual beam collinear geometry, thermal heating in the visible affects reorientational self-focusing in the near infrared, altering light propagation and self-trapping. PMID:26565843
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
Geometric diffusion of quantum trajectories.
Yang, Fan; Liu, Ren-Bao
2015-01-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Nonlinear resonances of a single-wall carbon nanotube cantilever
NASA Astrophysics Data System (ADS)
Kim, I. K.; Lee, S. I.
2015-03-01
The dynamics of an electrostatically actuated carbon nanotube (CNT) cantilever are discussed by theoretical and numerical approaches. Electrostatic and intermolecular forces between the single-walled CNT and a graphene electrode are considered. The CNT cantilever is analyzed by the Euler-Bernoulli beam theory, including its geometric and inertial nonlinearities, and a one-mode projection based on the Galerkin approximation and numerical integration. Static pull-in and pull-out behaviors are adequately represented by an asymmetric two-well potential with the total potential energy consisting of the CNT elastic energy, electrostatic energy, and the Lennard-Jones potential energy. Nonlinear dynamics of the cantilever are simulated under DC and AC voltage excitations and examined in the frequency and time domains. Under AC-only excitation, a superharmonic resonance of order 2 occurs near half of the primary frequency. Under both DC and AC loads, the cantilever exhibits linear and nonlinear primary and secondary resonances depending on the strength of the excitation voltages. In addition, the cantilever has dynamic instabilities such as periodic or chaotic tapping motions, with a variation of excitation frequency at the resonance branches. High electrostatic excitation leads to complex nonlinear responses such as softening, multiple stability changes at saddle nodes, or period-doubling bifurcation points in the primary and secondary resonance branches.
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.
NASA Astrophysics Data System (ADS)
Gunda, Jagadish Babu; Venkateswara Rao, Gundabathula
2016-04-01
Post-buckling and large amplitude free vibration analysis of composite beams with axially immovable ends is investigated in the present study using a simple intuitive formulation. Geometric nonlinearity of Von-Karman type is considered in the analysis which accounts for mid-plane stretching action of the beam. Intuitive formulation uses only two parameters: the critical bifurcation point and the axial stretching force developed due to membrane stretching action of the beam. Hinged-hinged, clamped-clamped and clamped-hinged boundary conditions are considered. Numerical accuracy of the proposed analytical closed-form solutions obtained from the intuitive formulation are compared to available finite element solutions for symmetric and asymmetric layup schemes of laminated composite beam which indicates the confidence gained on the present formulation.
NASA Technical Reports Server (NTRS)
Gray, Carl E., Jr.
1988-01-01
Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.
Galushkin, M G; Mitin, Konstantin V; Ionin, Andrei A; Kotkov, A A; Seleznev, L V
1998-08-31
An experimental investigation was made of phase conjugation in the course of intracavity degenerate four-wave mixing of radiation in the active medium of a pulsed electron-beam-controlled discharge CO{sub 2} laser generating long pulses. An analysis was carried out of the dependences of the energy and temporal characteristics of a phase-conjugated signal on the specific input energy deposited in the electron-beam-controlled discharge, on the Q-factor of the laser cavity, on the composition and pressure of the laser-active mixture, on the angle of interaction and optical delay between the probe and reference waves, on the ratio of the intensities of these two waves, and on the polarisation and spectral composition of laser radiation. The energy reflection coefficient of the phase-conjugated signal increased with increase in the input energy and with reduction in the probe wave intensity. An increase in the proportion of nitrogen and a reduction in the proportion of helium in the laser-active mixture increased the reflection coefficient and gave rise to a specific profile of the phase-conjugated signal with two maxima, attributed to amplitude and phase nonlinearities of the active medium. An increase in the specific input energy and of the cavity Q-factor reduced the response time of the phase-conjugate signal. (nonlinear optical phenomena and devices)
Beam halo in high-intensity beams
Wangler, T.P. )
1993-12-25
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. We describe 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. We present initial results 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.
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.
Characteristics of steady vibration in a rotating hub-beam system
NASA Astrophysics Data System (ADS)
Zhao, Zhen; Liu, Caishan; Ma, Wei
2016-02-01
A rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub's inertia and its rotating speed. To highlight the essential nature behind the vibration phenomena, we analyze the steady vibration of a rotating Euler-Bernoulli beam with a quasi-steady-state stretch. Newton's law is used to derive the equations governing the beam's elastic motion and the hub's rotation. A combination of these equations results in a nonlinear partial differential equation (PDE) that fully reflects the mutual interaction between the two kinds of motion. Via the Fourier series expansion within a finite interval of time, we reduce the PDE into an infinite system of a nonlinear ordinary differential equation (ODE) in spatial domain. We further nondimensionalize the ODE and discretize it via a difference method. The frequencies and modal shapes of a general rotating beam are then determined numerically. For a low-speed beam where the ignorance of geometric stiffening is feasible, the beam's vibration characteristics are solved analytically. We validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature. Finally, systematic simulations are performed to demonstrate how the beam's eigenfrequencies vary with the hub's inertia and rotating speed.